{"version":1,"snapshot":"2026-10-15","documents":{"archive/01881573f5be-RRLS_INVARIANT_DISCOVERY.md":{"url":"archive/01881573f5be-RRLS_INVARIANT_DISCOVERY.md","title":"RRLS Invariant Discovery Engine","kind":"Research note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/RRLS_INVARIANT_DISCOVERY.md","bytes":20370,"sha256":"01881573f5be63c09474c010406d511da3341a1d672e87ac743d2e722ea8a51c","savedDate":"2026-09-05","date":"2026-09-05","dateKind":"Saved source date","declaredDates":[],"projectId":"rrls","projectIds":["rrls"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"RRLS Invariant Discovery Engine","line":1,"id":"source-h-1"},{"level":2,"title":"Scope and result","line":3,"id":"source-h-2"},{"level":2,"title":"What the proposed target means","line":20,"id":"source-h-3"},{"level":2,"title":"The invariant catalogue","line":46,"id":"source-h-4"},{"level":2,"title":"Why the matrix features survive coordinate changes","line":68,"id":"source-h-5"},{"level":2,"title":"A global parity distinction that local structure misses","line":96,"id":"source-h-6"},{"level":2,"title":"The first complete-catalogue collision","line":122,"id":"source-h-7"},{"level":2,"title":"The finite refinement experiment","line":157,"id":"source-h-8"},{"level":2,"title":"The remaining exact counterexample","line":178,"id":"source-h-9"},{"level":2,"title":"Composition: what is preserved and what is missing","line":199,"id":"source-h-10"},{"level":2,"title":"Verification, cost, and preserved failures","line":234,"id":"source-h-11"},{"level":2,"title":"Run it on a PC","line":255,"id":"source-h-12"}],"journey":{"question":{"text":"What does “RRLS Invariant Discovery Engine” establish within its declared scope?","label":"The reading question","source":"archive/01881573f5be-RRLS_INVARIANT_DISCOVERY.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The engine was built, run, extended in response to counterexamples, and tested on a fresh cohort. 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Protocol: AT-FR-ALIGNMENT-03."],"projectId":"matter","projectIds":["matter"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"At / Fr harmonic follow-up","line":1,"id":"source-h-1"},{"level":2,"title":"Frozen question and calculation","line":9,"id":"source-h-2"},{"level":2,"title":"Additional source data","line":25,"id":"source-h-3"},{"level":2,"title":"Results","line":33,"id":"source-h-4"},{"level":2,"title":"Source audit and preserved corrections","line":55,"id":"source-h-5"},{"level":2,"title":"Interpretation and next test","line":62,"id":"source-h-6"},{"level":2,"title":"Reproduction","line":68,"id":"source-h-7"},{"level":2,"title":"All calculated entries","line":74,"id":"source-h-8"}],"journey":{"question":{"text":"What does “At / Fr harmonic follow-up” establish within its declared scope?","label":"The reading question","source":"archive/03af7a213e27-At_Fr_Followup_Report.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The original narrow alignment does not generalize as a common offset across the additional transitions examined. One additional At entry has a nominal offset of +22.118469 cents, but its sensitivity envelope crosses the fixed target boundary. The four new Fr transitions have offsets −1.813563, +14.005259, +18.245693 and +26.252356 cents. A shared correction that brings one of these values to zero cannot bring all four to zero.","label":"The source’s opening statement","source":"archive/03af7a213e27-At_Fr_Followup_Report.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"Run python3 calculate.py, then python3 audit.py. Only Python 3.11+ standard-library features are needed for the calculation and arithmetic audit. python3 build_report.py additionally needs matplotlib. Source URLs and hashes are recorded; full third-party papers are not redistributed. If sources/Teigelhoefer2012.txt is available from pdftotext -layout on the linked thesis, audit.py also repeats the 45-branch PDF text check; otherwise it explicitly reports that check as unavailable. 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We therefore do not manufacture a binomial significance by calling them independent random draws.","label":"Interpretation and next test","source":"archive/03af7a213e27-At_Fr_Followup_Report.md","sectionId":"source-h-6","provenance":"Source excerpt"}},"figures":[{"url":"archive/866b49c70a06-At_Fr_Followup.png","caption":"Additional At and Fr offsets","originalPath":"/At_Fr_Followup.png","reference":"At_Fr_Followup.png","provenance":"Markdown image","basis":"Original source figure referenced by this document","sha256":"866b49c70a06ceec392866270821cadb7c854cfc107b31e2c6a541ad9d81aa0d"}],"illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The original narrow alignment does not generalize as a common offset across the additional transitions examined. One additional At entry has a nominal offset of +22.118469 cents, but its sensitivity envelope crosses the fixed target boundary. The four new Fr transitions have offsets −1.813563, +14.005259, +18.245693 and +26.252356 cents. A shared correction that brings one of these values to zero cannot bring all four to zero.","words":2558},"archive/03e1b6b1c0c4-FOUNDATION_CONTRACT.md":{"url":"archive/03e1b6b1c0c4-FOUNDATION_CONTRACT.md","title":"Foundation contract — Fixed Grid String Lab 0.2.0","kind":"Research note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Fixed Grid String Lab/FOUNDATION_CONTRACT.md","bytes":8657,"sha256":"03e1b6b1c0c40cabf06bafbffac506f51ebe87bc2afa19a31f8fd28a7e3b10e2","savedDate":"2026-09-21","date":"2026-09-21","dateKind":"Saved source date","declaredDates":[],"projectId":"gauge","projectIds":["gauge"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Foundation contract — Fixed Grid String Lab 0.2.0","line":1,"id":"source-h-1"},{"level":2,"title":"1. 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Four resolved visible H I Balmer features from the NIST strong-line table are compared with the exact frequency capacity of the revision-1.53 observer.","words":163},"archive/04183c7d3acc-RRLS_v29_SEMANTIC_CANONICALIZATION_REPORT.md":{"url":"archive/04183c7d3acc-RRLS_v29_SEMANTIC_CANONICALIZATION_REPORT.md","title":"RRLS v0.29 — Semantic Canonicalization Probe","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/RRLS_v29_SEMANTIC_CANONICALIZATION_REPORT.md","bytes":4740,"sha256":"04183c7d3accda7ee3a33bc1a18bb1690278df3499a4545b7023eadfd7a1d1a3","savedDate":"2026-09-06","date":"2026-09-06","dateKind":"Saved source date","declaredDates":[],"projectId":"rrls","projectIds":["rrls"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"RRLS v0.29 — Semantic Canonicalization Probe","line":1,"id":"source-h-1"},{"level":2,"title":"Status","line":3,"id":"source-h-2"},{"level":2,"title":"Main result","line":9,"id":"source-h-3"},{"level":2,"title":"Semantic collapse appears early","line":20,"id":"source-h-4"},{"level":2,"title":"Fresh peak controls","line":30,"id":"source-h-5"},{"level":2,"title":"Actual early jump","line":43,"id":"source-h-6"},{"level":2,"title":"The new wall","line":55,"id":"source-h-7"},{"level":2,"title":"Variable order is a real coordinate problem","line":65,"id":"source-h-8"},{"level":2,"title":"Proof-safe semantic witnesses","line":75,"id":"source-h-9"},{"level":2,"title":"What v0.29 establishes","line":81,"id":"source-h-10"},{"level":2,"title":"Next theorem target","line":87,"id":"source-h-11"}],"journey":{"question":{"text":"What does “RRLS v0.29 — Semantic Canonicalization Probe” establish within its declared scope?","label":"The reading question","source":"archive/04183c7d3acc-RRLS_v29_SEMANTIC_CANONICALIZATION_REPORT.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"A new direct CNF→ROBDD compiler canonicalizes residual functions symbolically, without first enumerating complete truth tables. For one fixed variable order and one shared ROBDD manager, equal roots mean equal Boolean functions.","label":"Main result","source":"archive/04183c7d3acc-RRLS_v29_SEMANTIC_CANONICALIZATION_REPORT.md","sectionId":"source-h-3","provenance":"Source excerpt"},"checks":{"text":"v0.29 adds conservative polynomial semantic witnesses for recognized languages. Any polynomially certified UNSAT residual has semantic key FALSE. Recognized GF(2) systems can be normalized to exact RREF witnesses; 2-SAT has an implication-closure witness.","label":"Proof-safe semantic witnesses","source":"archive/04183c7d3acc-RRLS_v29_SEMANTIC_CANONICALIZATION_REPORT.md","sectionId":"source-h-9","provenance":"Source excerpt"},"nextQuestion":{"text":"where Q_t is the canonical quotient of all live futures.","label":"Next theorem target","source":"archive/04183c7d3acc-RRLS_v29_SEMANTIC_CANONICALIZATION_REPORT.md","sectionId":"source-h-11","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"v0.29 attacks the wall exposed by v0.28: many syntactically different residual CNFs can represent only a handful of Boolean futures.","words":687},"archive/068ce17145c0-Reality_Revision_1.14.md":{"url":"archive/068ce17145c0-Reality_Revision_1.14.md","title":"Theory of Reality — revision 1.14","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Reality_Revision_1.14.md","bytes":11301,"sha256":"068ce17145c0a0cfeb91b6e72700326a34aeaa5712ea990125571cd591bf99e9","savedDate":"2026-09-05","date":"2026-09-05","dateKind":"Saved source date","declaredDates":[],"projectId":"rope","projectIds":["rope"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Theory of Reality — revision 1.14","line":1,"id":"source-h-1"},{"level":2,"title":"1. 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Every wavelength, including an arbitrary synthetic one, lies on the same predetermined branches. No atomic model is needed to predict these branches.","label":"The source’s opening statement","source":"archive/07cef9ed332f-Parallel_Lines_Check.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"All 59 original At/Fr entries were checked against the equation without fitting any parameters. A second formula, computed directly from photon frequency, checks 1,000 arbitrary synthetic wavelengths. Both checks agree within 10⁻⁸ cents; the exact floating-point residuals are in CHECK_RESULTS.json. The zoomed figure shows every At entry from 690 to 940 nm and an equal number of synthetic points. 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Claim discipline","line":197,"id":"source-h-4"},{"level":3,"title":"1.1 Meaning of “prove”","line":221,"id":"source-h-5"},{"level":3,"title":"1.2 Foundation contract — revision 1.77, extended in 1.78","line":233,"id":"source-h-6"},{"level":2,"title":"2. Primitive structure","line":243,"id":"source-h-7"},{"level":3,"title":"Axiom A1: projection coherence","line":266,"id":"source-h-8"},{"level":3,"title":"Axiom A2: coordinate covariance","line":275,"id":"source-h-9"},{"level":3,"title":"Axiom A3: measured probabilities require a measure","line":285,"id":"source-h-10"},{"level":3,"title":"Definition 2.1: fiber","line":297,"id":"source-h-11"},{"level":3,"title":"Definition 2.2: complete compatible state","line":307,"id":"source-h-12"},{"level":2,"title":"3. The seven typed layers","line":326,"id":"source-h-13"},{"level":3,"title":"3.1 Canonical serialization","line":347,"id":"source-h-14"},{"level":3,"title":"Theorem 3.1: canonical projection coherence [M]","line":377,"id":"source-h-15"},{"level":3,"title":"3.2 Is \\(D_7\\) a wall?","line":387,"id":"source-h-16"},{"level":3,"title":"Theorem 3.2: completeness of the finite compatible diagram [M]","line":401,"id":"source-h-17"},{"level":2,"title":"4. Law descent: how an upper layer confines a lower law","line":413,"id":"source-h-18"},{"level":3,"title":"Theorem 4.1: factorization or law-descent theorem [M]","line":417,"id":"source-h-19"},{"level":3,"title":"4.1 Stochastic lower behavior","line":457,"id":"source-h-20"},{"level":3,"title":"4.2 The hidden-mechanism theorem","line":472,"id":"source-h-21"},{"level":3,"title":"Theorem 4.2: coarsest deterministic repair [M]","line":492,"id":"source-h-22"},{"level":3,"title":"Corollary 4.3: operational proof of hidden state [M/E boundary]","line":515,"id":"source-h-23"},{"level":3,"title":"4.3 Conservation-law descent","line":521,"id":"source-h-24"},{"level":2,"title":"5. Effects, causes, and the limit of inverse inference","line":539,"id":"source-h-25"},{"level":3,"title":"5.1 Linear effect model","line":541,"id":"source-h-26"},{"level":3,"title":"5.2 Exact Boolean inverse","line":573,"id":"source-h-27"},{"level":3,"title":"Theorem 5.1: latent relabeling non-identifiability [M]","line":592,"id":"source-h-28"},{"level":3,"title":"5.3 Why an unconstrained \\(G\\) destroys science","line":618,"id":"source-h-29"},{"level":2,"title":"6. Reversible hidden-coordinate transport","line":636,"id":"source-h-30"},{"level":3,"title":"Theorem 6.1: visible-to-hidden ripple [M]","line":654,"id":"source-h-31"},{"level":3,"title":"Theorem 6.2: generic collision-capacity bound [M]","line":672,"id":"source-h-32"},{"level":2,"title":"7. Time, process, loop, and helix","line":692,"id":"source-h-33"},{"level":3,"title":"7.1 A state is not a process","line":694,"id":"source-h-34"},{"level":3,"title":"7.2 Linear and cyclic time","line":724,"id":"source-h-35"},{"level":3,"title":"7.3 Infinite cyclic dimension addressing","line":747,"id":"source-h-36"},{"level":3,"title":"7.4 Cycle twist or monodromy","line":767,"id":"source-h-37"},{"level":3,"title":"7.5 Polarity","line":787,"id":"source-h-38"},{"level":2,"title":"8. Exact increments, ULPs, and computation in bits","line":812,"id":"source-h-39"},{"level":3,"title":"8.1 Typed dyadic scalar","line":814,"id":"source-h-40"},{"level":3,"title":"8.2 Default increments","line":838,"id":"source-h-41"},{"level":3,"title":"8.3 Observer-relative reality ULP","line":854,"id":"source-h-42"},{"level":3,"title":"8.4 Precision towers","line":879,"id":"source-h-43"},{"level":2,"title":"9. Schrödinger's cat in the language","line":903,"id":"source-h-44"},{"level":3,"title":"9.1 Decoherence","line":959,"id":"source-h-45"},{"level":2,"title":"10. Two-slit observation","line":974,"id":"source-h-46"},{"level":2,"title":"11. Quantum computing","line":1041,"id":"source-h-47"},{"level":3,"title":"11.1 Layer interpretation for a circuit","line":1076,"id":"source-h-48"},{"level":2,"title":"12. Temperature, quanta, and selective entropy removal","line":1092,"id":"source-h-49"},{"level":3,"title":"12.1 Concrete 5 GHz scale","line":1132,"id":"source-h-50"},{"level":3,"title":"12.2 “Inverse microwave” as anti-Stokes conversion","line":1152,"id":"source-h-51"},{"level":3,"title":"12.3 Active reset","line":1180,"id":"source-h-52"},{"level":3,"title":"12.4 Optimization target","line":1202,"id":"source-h-53"},{"level":2,"title":"13. Typed higher-layer frequencies, magnets, and energy","line":1227,"id":"source-h-54"},{"level":2,"title":"14. Exact mathematical discovery","line":1289,"id":"source-h-55"},{"level":3,"title":"Theorem 14.1: invariant-language completeness [M]","line":1306,"id":"source-h-56"},{"level":2,"title":"15. Real measured prediction","line":1330,"id":"source-h-57"},{"level":3,"title":"15.1 Holdout results [E/C]","line":1358,"id":"source-h-58"},{"level":2,"title":"16. What would constitute evidence for a hidden mechanism?","line":1371,"id":"source-h-59"},{"level":3,"title":"16.1 The target signature","line":1373,"id":"source-h-60"},{"level":3,"title":"16.2 Intervention requirement","line":1389,"id":"source-h-61"},{"level":3,"title":"16.3 Tomography requirement","line":1405,"id":"source-h-62"},{"level":3,"title":"16.4 Model contest","line":1417,"id":"source-h-63"},{"level":2,"title":"17. Can seven-dimensional physics be proved?","line":1444,"id":"source-h-64"},{"level":3,"title":"Theorem 17.1 (replacement): deterministic closure is idempotent [M]","line":1448,"id":"source-h-65"},{"level":3,"title":"17.1 A decisive physical success criterion","line":1464,"id":"source-h-66"},{"level":2,"title":"18. Optional Christian metaphysical interpretation","line":1481,"id":"source-h-67"},{"level":3,"title":"18.1 God as ground, not coordinate","line":1485,"id":"source-h-68"},{"level":3,"title":"18.2 Trinity guardrail","line":1497,"id":"source-h-69"},{"level":3,"title":"18.3 Free choice and authorization","line":1525,"id":"source-h-70"},{"level":3,"title":"18.4 Miracles","line":1554,"id":"source-h-71"},{"level":3,"title":"18.5 Biblical time","line":1564,"id":"source-h-72"},{"level":2,"title":"19. Adversarial tests and resolutions","line":1608,"id":"source-h-73"},{"level":2,"title":"20. Computational verification record","line":1632,"id":"source-h-74"},{"level":2,"title":"21. Compact formal statement","line":1666,"id":"source-h-75"},{"level":2,"title":"22. Conclusions","line":1700,"id":"source-h-76"},{"level":2,"title":"References","line":1714,"id":"source-h-77"},{"level":2,"title":"Reproducibility companion","line":1733,"id":"source-h-78"},{"level":2,"title":"Appendix A: Relativity integration","line":1739,"id":"source-h-79"},{"level":2,"title":"Appendix B: Three Millennium laboratories","line":1770,"id":"source-h-80"},{"level":2,"title":"Appendix C: D0 polarity and frozen errors","line":1809,"id":"source-h-81"},{"level":2,"title":"Appendix D: Independent falsification and the limits of D0","line":1881,"id":"source-h-82"},{"level":3,"title":"D.1 Exact finite RH certificate","line":1898,"id":"source-h-83"},{"level":3,"title":"D.2 Independent SAT check","line":1914,"id":"source-h-84"},{"level":3,"title":"D.3 Fault recovery with a frozen bias","line":1922,"id":"source-h-85"},{"level":3,"title":"D.4 Residual is not distance to solution","line":1952,"id":"source-h-86"},{"level":2,"title":"Appendix E. Restricted proofs and rejected universal estimates","line":1974,"id":"source-h-87"},{"level":3,"title":"E.1 A restricted Lagarias theorem","line":1982,"id":"source-h-88"},{"level":3,"title":"E.2 All-size pigeonhole error formulas","line":2009,"id":"source-h-89"},{"level":3,"title":"E.3 Exact fluid counterexamples to proposed estimates","line":2036,"id":"source-h-90"},{"level":3,"title":"E.4 The meaning of a frozen failure","line":2080,"id":"source-h-91"},{"level":2,"title":"Appendix F. Independent certificates and exact counting projections","line":2095,"id":"source-h-92"},{"level":3,"title":"F.1 Rational lower witnesses","line":2102,"id":"source-h-93"},{"level":3,"title":"F.2 A counting law that survives projection","line":2122,"id":"source-h-94"},{"level":3,"title":"F.3 Independent fluid algebra","line":2163,"id":"source-h-95"},{"level":3,"title":"F.4 Rejection tests and remaining trust","line":2173,"id":"source-h-96"},{"level":2,"title":"Appendix G. Arguments at the remaining proof gaps","line":2195,"id":"source-h-97"},{"level":3,"title":"G.1 Removing the prime-count restriction from a bounded RH verification","line":2202,"id":"source-h-98"},{"level":3,"title":"G.2 A lower-bound extension that cannot work","line":2256,"id":"source-h-99"},{"level":3,"title":"G.3 An exact continuation-summary bound","line":2279,"id":"source-h-100"},{"level":3,"title":"G.4 Why the quadratic fluid strategy fails more generally","line":2299,"id":"source-h-101"},{"level":3,"title":"G.5 Evidence boundary","line":2330,"id":"source-h-102"},{"level":2,"title":"Appendix H. A computable sufficient condition for all-time fluid smoothness","line":2339,"id":"source-h-103"},{"level":3,"title":"H.1 The conditional all-time statement","line":2350,"id":"source-h-104"},{"level":3,"title":"H.2 The estimate and its continuation argument","line":2375,"id":"source-h-105"},{"level":3,"title":"H.3 What the computer verifies","line":2414,"id":"source-h-106"},{"level":3,"title":"H.4 The boundary that remains","line":2435,"id":"source-h-107"},{"level":2,"title":"Appendix I. Relative error control beyond the total-smallness condition","line":2455,"id":"source-h-108"},{"level":3,"title":"I.1 A reference trajectory and its full error","line":2464,"id":"source-h-109"},{"level":3,"title":"I.2 An all-time specialization the engine computes","line":2490,"id":"source-h-110"},{"level":3,"title":"I.3 The next engineering prerequisite","line":2530,"id":"source-h-111"},{"level":2,"title":"Appendix J. Computed references with continuous-time and full-mode certificates","line":2552,"id":"source-h-112"},{"level":3,"title":"J.1 Continuous-time polynomial bounds","line":2561,"id":"source-h-113"},{"level":3,"title":"J.2 Every omitted output mode of the reference residual","line":2582,"id":"source-h-114"},{"level":3,"title":"J.3 An affine supersolution checked by algebra","line":2600,"id":"source-h-115"},{"level":3,"title":"J.4 Executed evidence and its limits","line":2632,"id":"source-h-116"},{"level":2,"title":"Appendix K. A sharper error estimate that certifies a previously unresolved input","line":2667,"id":"source-h-117"},{"level":3,"title":"K.1 The same input before and after the changes","line":2674,"id":"source-h-118"},{"level":3,"title":"K.2 Exact constrained quadratic optimization","line":2700,"id":"source-h-119"},{"level":3,"title":"K.3 Nonlinear references with accounted-for rounding","line":2750,"id":"source-h-120"},{"level":3,"title":"K.4 Checked outcome and the next failure","line":2770,"id":"source-h-121"},{"level":2,"title":"Appendix L. Directing the engine toward valid extension arguments","line":2806,"id":"source-h-122"},{"level":3,"title":"L.1 The shared objective","line":2811,"id":"source-h-123"},{"level":3,"title":"L.2 A finite certificate with unbounded path-length coverage","line":2826,"id":"source-h-124"},{"level":3,"title":"L.3 Refine the distinctions responsible for the fluid residual","line":2863,"id":"source-h-125"},{"level":3,"title":"L.4 Local error budgets","line":2885,"id":"source-h-126"},{"level":3,"title":"L.5 The new accepted input and the common audit","line":2919,"id":"source-h-127"},{"level":2,"title":"Appendix M. Hypothetical universes and checked proof transfer","line":2971,"id":"source-h-128"},{"level":3,"title":"M.1. A contracting comparison can close an error loop","line":2991,"id":"source-h-129"},{"level":3,"title":"M.2. A finite dynamics-to-SAT bridge with complete coverage","line":3025,"id":"source-h-130"},{"level":3,"title":"M.3. Transfer through a verified state map","line":3054,"id":"source-h-131"},{"level":2,"title":"Appendix N. Null-axis probes, observability, and a fluid projection obstruction","line":3086,"id":"source-h-132"},{"level":3,"title":"N.1. Linear hidden directions and allowed transformations","line":3094,"id":"source-h-133"},{"level":3,"title":"N.2. Signed recovery from paired squared-distance readings","line":3125,"id":"source-h-134"},{"level":3,"title":"N.3. No autonomous law for any fixed energy-derivative jet of all shears","line":3154,"id":"source-h-135"},{"level":3,"title":"N.4. Two further shortcut failures and validation","line":3199,"id":"source-h-136"},{"level":2,"title":"Appendix O. Active experiments, model rejection, and correction of the hierarchy","line":3229,"id":"source-h-137"},{"level":3,"title":"O.1. Intervention-relative cause classes","line":3233,"id":"source-h-138"},{"level":3,"title":"O.2. Choose a discriminating experiment before seeing its outcome","line":3248,"id":"source-h-139"},{"level":3,"title":"O.3. A concrete intervention that breaks an exact delay ambiguity","line":3261,"id":"source-h-140"},{"level":3,"title":"O.4. Evidence and limits of this release","line":3278,"id":"source-h-141"},{"level":3,"title":"O.5. A revisable theory","line":3288,"id":"source-h-142"},{"level":2,"title":"Appendix P. Capture, generator discovery, and the limits of an observed cycle","line":3294,"id":"source-h-143"},{"level":3,"title":"P.1. Keep the event model's semantics explicit","line":3298,"id":"source-h-144"},{"level":3,"title":"P.2. Finite observations do not select a universal generator language","line":3312,"id":"source-h-145"},{"level":3,"title":"P.3. Positive theorem: continuation in a bounded recurrence class","line":3324,"id":"source-h-146"},{"level":3,"title":"P.4. New computation and repaired failures","line":3336,"id":"source-h-147"},{"level":2,"title":"Appendix Q. Repeated model checks with a bounded false-rejection budget","line":3350,"id":"source-h-148"},{"level":3,"title":"Q.1. A single-observation cutoff is not an investigation-wide guarantee","line":3354,"id":"source-h-149"},{"level":3,"title":"Q.2. Written guarantee and its exact assumptions","line":3364,"id":"source-h-150"},{"level":3,"title":"Q.3. Fresh synthetic evidence and an independent check","line":3385,"id":"source-h-151"},{"level":3,"title":"Q.4. Research context, model revision, and next test","line":3399,"id":"source-h-152"},{"level":2,"title":"Appendix R. Accumulating weak residual evidence without optional-stopping inflation","line":3405,"id":"source-h-153"},{"level":3,"title":"R.1. Bounded target and assumptions","line":3409,"id":"source-h-154"},{"level":3,"title":"R.2. Written anytime-valid guarantee","line":3436,"id":"source-h-155"},{"level":3,"title":"R.3. Frozen synthetic validation","line":3454,"id":"source-h-156"},{"level":3,"title":"R.4. Relation to current primary research","line":3471,"id":"source-h-157"},{"level":3,"title":"R.5. What changed and what remains open","line":3475,"id":"source-h-158"},{"level":2,"title":"Appendix S. Unknown fixed scale without pretending to know the variance","line":3481,"id":"source-h-159"},{"level":3,"title":"S.1. Bounded question and exact model class","line":3485,"id":"source-h-160"},{"level":3,"title":"S.2. Established theorem and a crucial filtration boundary","line":3509,"id":"source-h-161"},{"level":3,"title":"S.3. Frozen finite computation and synthetic tests","line":3521,"id":"source-h-162"},{"level":3,"title":"S.4. Result, limits, and next test","line":3540,"id":"source-h-163"},{"level":2,"title":"Appendix T. One shared error budget for complementary model checks","line":3546,"id":"source-h-164"},{"level":3,"title":"T.1. The composition problem","line":3550,"id":"source-h-165"},{"level":3,"title":"T.2. Written joint guarantee","line":3556,"id":"source-h-166"},{"level":3,"title":"T.3. Frozen synthetic validation","line":3576,"id":"source-h-167"},{"level":3,"title":"T.4. Supported change and next test","line":3598,"id":"source-h-168"},{"level":2,"title":"Appendix U. Accumulating moderate Gaussian scale evidence","line":3604,"id":"source-h-169"},{"level":3,"title":"U.1. Bounded question and fixed alternatives","line":3608,"id":"source-h-170"},{"level":3,"title":"U.2. Written anytime guarantee and interpretation boundary","line":3637,"id":"source-h-171"},{"level":3,"title":"U.3. Frozen synthetic test and independent replay","line":3651,"id":"source-h-172"},{"level":3,"title":"U.4. Supported change, limitations, and next test","line":3671,"id":"source-h-173"},{"level":2,"title":"Appendix V. A common-filtration mean-plus-variance process","line":3677,"id":"source-h-174"},{"level":3,"title":"V.1. Why this is not a detector substitution","line":3681,"id":"source-h-175"},{"level":3,"title":"V.2. Written fixed-mixture guarantee","line":3687,"id":"source-h-176"},{"level":3,"title":"V.3. Frozen paired comparison","line":3712,"id":"source-h-177"},{"level":3,"title":"V.4. Supported change and unresolved design choice","line":3735,"id":"source-h-178"},{"level":2,"title":"Appendix W. A trained, frozen mean/variance/point allocation","line":3744,"id":"source-h-179"},{"level":3,"title":"W.1. Bounded question and predeclared separation","line":3748,"id":"source-h-180"},{"level":3,"title":"W.2. Written anytime bound","line":3758,"id":"source-h-181"},{"level":3,"title":"W.3. One held-out synthetic validation","line":3789,"id":"source-h-182"},{"level":3,"title":"W.4. Supported change, limits, and next test","line":3811,"id":"source-h-183"},{"level":2,"title":"Appendix X. Allocation-selection stability and a boundary warning","line":3821,"id":"source-h-184"},{"level":3,"title":"X.1. Bounded question and sealed-data rule","line":3825,"id":"source-h-185"},{"level":3,"title":"X.2. Finite stability results","line":3833,"id":"source-h-186"},{"level":3,"title":"X.3. Separate synthetic reference and counterexample to optimality","line":3850,"id":"source-h-187"},{"level":3,"title":"X.4. Supported correction, evidence classes, and next test","line":3867,"id":"source-h-188"},{"level":2,"title":"Appendix Y. Expanded allocation boundaries refute the released grid optimum","line":3877,"id":"source-h-189"},{"level":3,"title":"Y.1. Assumptions and frozen training-only protocol","line":3881,"id":"source-h-190"},{"level":3,"title":"Y.2. Finite results and counterexamples","line":3901,"id":"source-h-191"},{"level":3,"title":"Y.3. Supported correction, limits, and next test","line":3921,"id":"source-h-192"},{"level":2,"title":"Appendix Z. Fresh paired validation rejects a universal allocation replacement","line":3933,"id":"source-h-193"},{"level":3,"title":"Z.1. Frozen question, assumptions, and decision rule","line":3937,"id":"source-h-194"},{"level":3,"title":"Z.2. Fresh synthetic results and counterexample","line":3952,"id":"source-h-195"},{"level":3,"title":"Z.3. Supported correction, evidence classes, and next test","line":3974,"id":"source-h-196"},{"level":2,"title":"Appendix AA. An anytime-valid sign process for a declared heavy-tail class","line":3984,"id":"source-h-197"},{"level":3,"title":"AA.1. The bounded question and null class","line":3988,"id":"source-h-198"},{"level":3,"title":"AA.2. Written probability proof","line":4002,"id":"source-h-199"},{"level":3,"title":"AA.3. Frozen finite synthetic validation","line":4033,"id":"source-h-200"},{"level":3,"title":"AA.4. Counterexamples and interpretation","line":4055,"id":"source-h-201"},{"level":3,"title":"AA.5. Supported change, evidence classes, and next test","line":4063,"id":"source-h-202"},{"level":2,"title":"Appendix AB. Composite Born prediction, coded lift search, and projection collisions","line":4071,"id":"source-h-203"},{"level":3,"title":"AB.1. One theory, three different uses of seven and eight","line":4075,"id":"source-h-204"},{"level":3,"title":"AB.2. Exact and composite Born walls","line":4089,"id":"source-h-205"},{"level":3,"title":"AB.3. Prefix-coded dimensional lifts","line":4127,"id":"source-h-206"},{"level":3,"title":"AB.4. Projection collisions are universal decoder failures","line":4164,"id":"source-h-207"},{"level":3,"title":"AB.5. Foundational assumption map","line":4200,"id":"source-h-208"},{"level":3,"title":"AB.6. Executed evidence, preserved failures, and next test","line":4224,"id":"source-h-209"},{"level":2,"title":"Appendix AC. Information rate, adversarial tripwires, and the wall ledger","line":4249,"id":"source-h-210"},{"level":3,"title":"AC.1. General Born-evidence decomposition","line":4253,"id":"source-h-211"},{"level":3,"title":"AC.2. No finite data determine an unrestricted continuation","line":4323,"id":"source-h-212"},{"level":3,"title":"AC.3. Three-channel tripwire","line":4331,"id":"source-h-213"},{"level":3,"title":"AC.4. Bell, contextuality, and measurement-independence routes","line":4365,"id":"source-h-214"},{"level":3,"title":"AC.5. The thirteen walls and the next physical test","line":4383,"id":"source-h-215"},{"level":2,"title":"Appendix AD. P3-R1: an executable single-device hardware frontier","line":4405,"id":"source-h-216"},{"level":3,"title":"AD.1. Bounded physical question and claim ceiling","line":4407,"id":"source-h-217"},{"level":3,"title":"AD.2. An exactly marginal-preserving eight-cycle grammar","line":4421,"id":"source-h-218"},{"level":3,"title":"AD.3. Composite-null score and delayed-setting tripwire","line":4457,"id":"source-h-219"},{"level":3,"title":"AD.4. Executed adversarial software evidence","line":4477,"id":"source-h-220"},{"level":3,"title":"AD.5. Activation boundary and next honest wall","line":4489,"id":"source-h-221"},{"level":2,"title":"Appendix AE. Dimensional Chess C1: exact solution of a closed game universe","line":4497,"id":"source-h-222"},{"level":3,"title":"AE.1. Finite does not mean computationally feasible","line":4499,"id":"source-h-223"},{"level":3,"title":"AE.2. A collision-free symmetry lift","line":4511,"id":"source-h-224"},{"level":3,"title":"AE.3. Time cycles become a least fixed point","line":4531,"id":"source-h-225"},{"level":3,"title":"AE.4. Exact result and proof certificate","line":4547,"id":"source-h-226"},{"level":3,"title":"AE.5. The wall exposed by chess","line":4561,"id":"source-h-227"},{"level":2,"title":"Appendix AF. Dimensional Chess C2: interval bounds, certified pruning, and the full-chess gate","line":4577,"id":"source-h-228"},{"level":3,"title":"AF.1. Freeze the target before optimizing it","line":4579,"id":"source-h-229"},{"level":3,"title":"AF.2. D-/D+ becomes interval minimax","line":4610,"id":"source-h-230"},{"level":3,"title":"AF.3. Exact Disadvantage Pruning Theorem","line":4635,"id":"source-h-231"},{"level":3,"title":"AF.4. Exact KQK extension","line":4662,"id":"source-h-232"},{"level":3,"title":"AF.5. Strong future-law identity fails as the large quotient","line":4687,"id":"source-h-233"},{"level":3,"title":"AF.6. Measured ceiling of disadvantage pruning","line":4707,"id":"source-h-234"},{"level":3,"title":"AF.7. Counterexample-guided dimensional refinement","line":4723,"id":"source-h-235"},{"level":3,"title":"AF.8. Chess, quantum algorithms, and physical dimensions are separate gates","line":4742,"id":"source-h-236"},{"level":3,"title":"AF.9. Claim gate and next rung","line":4762,"id":"source-h-237"},{"level":2,"title":"Appendix AG. Dimensional Chess C3: the complete state reaches the initial position","line":4779,"id":"source-h-238"},{"level":3,"title":"AG.1. The legal-transition wall is crossed, not the solution wall","line":4781,"id":"source-h-239"},{"level":3,"title":"AG.2. Move-generation audit","line":4810,"id":"source-h-240"},{"level":3,"title":"AG.3. First exact interval probe of the normal start","line":4833,"id":"source-h-241"},{"level":3,"title":"AG.4. Forcing dominance formalizes ignored legal moves","line":4873,"id":"source-h-242"},{"level":3,"title":"AG.5. Updated wall and claim gate","line":4928,"id":"source-h-243"},{"level":2,"title":"Appendix AH. Dimensional Chess C4: constraint waves and relational phase","line":4951,"id":"source-h-244"},{"level":3,"title":"AH.1. Human search is selective constraint propagation","line":4953,"id":"source-h-245"},{"level":3,"title":"AH.2. Table-hidden geometric language","line":4993,"id":"source-h-246"},{"level":3,"title":"AH.3. Exact table-hidden results","line":5014,"id":"source-h-247"},{"level":3,"title":"AH.4. Predictive success does not equal scaling","line":5041,"id":"source-h-248"},{"level":3,"title":"AH.5. Constraint-delta lift","line":5054,"id":"source-h-249"},{"level":2,"title":"Appendix AI. Dimensional Chess C5: local tension and tactical entry","line":5097,"id":"source-h-250"},{"level":3,"title":"AI.1. Attack multiplicity is a field, not a verdict","line":5099,"id":"source-h-251"},{"level":3,"title":"AI.2. Tension-breaking entry","line":5138,"id":"source-h-252"},{"level":3,"title":"AI.3. Adversarial ordering","line":5162,"id":"source-h-253"},{"level":3,"title":"AI.4. Executable fixture and independent audit","line":5178,"id":"source-h-254"},{"level":3,"title":"AI.5. Counterexample and boundary","line":5207,"id":"source-h-255"},{"level":2,"title":"Appendix AJ. Dimensional Chess C6: legal exchange dependencies","line":5227,"id":"source-h-256"},{"level":3,"title":"AJ.1. From simultaneous counts to ordered interactions","line":5229,"id":"source-h-257"},{"level":3,"title":"AJ.2. Exact bounded proof layer","line":5268,"id":"source-h-258"},{"level":3,"title":"AJ.3. Deterministic recapture corpus","line":5289,"id":"source-h-259"},{"level":3,"title":"AJ.4. Independent audit","line":5311,"id":"source-h-260"},{"level":3,"title":"AJ.5. Consequence for the full-chess program","line":5321,"id":"source-h-261"},{"level":2,"title":"Appendix AK. Initial-position mate frontier R1","line":5336,"id":"source-h-262"},{"level":3,"title":"AK.1. Direct run on the orthodox root","line":5338,"id":"source-h-263"},{"level":3,"title":"AK.2. Measured frontier","line":5360,"id":"source-h-264"},{"level":3,"title":"AK.3. Independent result and ordering falsification","line":5371,"id":"source-h-265"},{"level":3,"title":"AK.4. Dual proof direction","line":5388,"id":"source-h-266"},{"level":2,"title":"Appendix AL. Dimensional Chess C7: horizon-safe projection","line":5411,"id":"source-h-267"},{"level":3,"title":"AL.1. Repetition coordinates have a finite activation horizon","line":5413,"id":"source-h-268"},{"level":3,"title":"AL.2. Polarity-aware ordering test","line":5445,"id":"source-h-269"},{"level":3,"title":"AL.3. Seven-ply quotient check","line":5460,"id":"source-h-270"},{"level":3,"title":"AL.4. Independently verified nine-ply frontier","line":5474,"id":"source-h-271"},{"level":3,"title":"AL.5. Boundary of the result","line":5496,"id":"source-h-272"},{"level":2,"title":"Appendix AM. Dimensional Chess C8: movement-frequency relations","line":5516,"id":"source-h-273"},{"level":3,"title":"AM.1. Relational move phase","line":5518,"id":"source-h-274"},{"level":3,"title":"AM.2. Learned pattern","line":5546,"id":"source-h-275"},{"level":3,"title":"AM.3. Transfer to seven and nine plies","line":5559,"id":"source-h-276"},{"level":3,"title":"AM.4. Counterexamples to stronger frequency claims","line":5584,"id":"source-h-277"},{"level":3,"title":"AM.5. Audit and boundary","line":5599,"id":"source-h-278"},{"level":2,"title":"Appendix AN. Dependent-sign evidence under a declared Markov null","line":5620,"id":"source-h-279"},{"level":3,"title":"AN.1. The bounded question","line":5622,"id":"source-h-280"},{"level":3,"title":"AN.2. Predictive likelihood-ratio martingale","line":5646,"id":"source-h-281"},{"level":3,"title":"AN.3. Fresh finite synthetic validation","line":5691,"id":"source-h-282"},{"level":3,"title":"AN.4. Counterexamples and boundary","line":5717,"id":"source-h-283"},{"level":2,"title":"Appendix AO. Hydrogen spectroscopy clock and tangent-rotor holdout","line":5736,"id":"source-h-284"},{"level":3,"title":"AO.1. What real data can calibrate","line":5738,"id":"source-h-285"},{"level":3,"title":"AO.2. Frozen spatial discrimination protocol","line":5773,"id":"source-h-286"},{"level":3,"title":"AO.3. Held-out result and counterexample","line":5788,"id":"source-h-287"},{"level":3,"title":"AO.4. Verification and evidence boundary","line":5810,"id":"source-h-288"},{"level":2,"title":"Appendix AP. Temperature, phase direction, and bounded missing components","line":5837,"id":"source-h-289"},{"level":3,"title":"AP.1. Why a failed model does not select one cause","line":5839,"id":"source-h-290"},{"level":3,"title":"AP.2. Frozen latent-component rescue","line":5856,"id":"source-h-291"},{"level":3,"title":"AP.3. Temperature does not reverse the phase clock","line":5880,"id":"source-h-292"},{"level":3,"title":"AP.4. Melting delay and evidence boundary","line":5915,"id":"source-h-293"},{"level":2,"title":"Appendix AQ. Electromagnetic correction ladder before higher-dimensional forces","line":5936,"id":"source-h-294"},{"level":3,"title":"AQ.1. Correction: electromagnetism was already present","line":5938,"id":"source-h-295"},{"level":3,"title":"AQ.2. Frozen H0/H1/H2 ladder","line":5959,"id":"source-h-296"},{"level":3,"title":"AQ.3. Result","line":6001,"id":"source-h-297"},{"level":3,"title":"AQ.4. Residual budget and higher-dimensional admission rule","line":6022,"id":"source-h-298"},{"level":2,"title":"Appendix AR. Fixed-grid and fixed-tick falsification engine","line":6051,"id":"source-h-299"},{"level":3,"title":"AR.1. Two hypotheses that must not be conflated","line":6053,"id":"source-h-300"},{"level":3,"title":"AR.2. Interval decision and non-identification theorem","line":6079,"id":"source-h-301"},{"level":3,"title":"AR.3. Frozen hydrogen-spectroscopy example","line":6112,"id":"source-h-302"},{"level":3,"title":"AR.4. Exact four-coordinate discrete string","line":6142,"id":"source-h-303"},{"level":3,"title":"AR.5. Failure criterion and next physical gate","line":6175,"id":"source-h-304"},{"level":2,"title":"Appendix AS. Geometry, phase boundaries, and conductivity collisions","line":6195,"id":"source-h-305"},{"level":3,"title":"AS.1. Scope and type discipline","line":6197,"id":"source-h-306"},{"level":3,"title":"AS.2. A representation-collision bound","line":6214,"id":"source-h-307"},{"level":3,"title":"AS.3. Frozen same-formula molecular test","line":6237,"id":"source-h-308"},{"level":3,"title":"AS.4. Counterexamples to one-dimensional harmony","line":6272,"id":"source-h-309"},{"level":3,"title":"AS.5. Verification, interpretation, and next test","line":6292,"id":"source-h-310"},{"level":2,"title":"Appendix AT. Property-specific transfer across alkane isomers","line":6321,"id":"source-h-311"},{"level":3,"title":"AT.1. Scope and frozen split","line":6323,"id":"source-h-312"},{"level":3,"title":"AT.2. Held-out boiling result","line":6360,"id":"source-h-313"},{"level":3,"title":"AT.3. Fusion counterexample","line":6377,"id":"source-h-314"},{"level":3,"title":"AT.4. What a residual can and cannot establish","line":6399,"id":"source-h-315"},{"level":3,"title":"AT.5. Verification and next test","line":6422,"id":"source-h-316"},{"level":2,"title":"Appendix AU. Latent rotation matrices and the inverse-projection boundary","line":6443,"id":"source-h-317"},{"level":3,"title":"AU.1. Question and evidence types","line":6445,"id":"source-h-318"},{"level":3,"title":"AU.2. Explicit five-coordinate dynamics and 3D projection","line":6467,"id":"source-h-319"},{"level":3,"title":"AU.3. Property coordinates and the relabeling counterexample","line":6529,"id":"source-h-320"},{"level":3,"title":"AU.4. Two independent non-identifiability theorems","line":6553,"id":"source-h-321"},{"level":3,"title":"AU.5. Result, limitations, and next test","line":6585,"id":"source-h-322"},{"level":2,"title":"Appendix AV. Water harmonics as a coupled projection experiment","line":6619,"id":"source-h-323"},{"level":3,"title":"AV.1. Scope and calibrated three-dimensional inputs","line":6621,"id":"source-h-324"},{"level":3,"title":"AV.2. Five coordinates per molecule and a norm-preserving coupling","line":6653,"id":"source-h-325"},{"level":3,"title":"AV.3. Three-dimensional rendering and the hidden-null control","line":6696,"id":"source-h-326"},{"level":3,"title":"AV.4. Executed evidence and its limits","line":6730,"id":"source-h-327"},{"level":2,"title":"Appendix AW. Water origami and the oscilloscope observation boundary","line":6769,"id":"source-h-328"},{"level":3,"title":"AW.1. Ordinary charge and dielectric baseline","line":6771,"id":"source-h-329"},{"level":3,"title":"AW.2. Origami as a many-to-one observation map","line":6817,"id":"source-h-330"},{"level":3,"title":"AW.3. Executed oscilloscope and counterexamples","line":6855,"id":"source-h-331"},{"level":3,"title":"AW.4. Evidence type, limitations, and next test","line":6881,"id":"source-h-332"},{"level":2,"title":"Appendix AX. Sunlight, moving water, and a finite visual observer","line":6916,"id":"source-h-333"},{"level":3,"title":"AX.1. Bounded question and ordinary optical baseline","line":6918,"id":"source-h-334"},{"level":3,"title":"AX.2. Spectral observation and the metamer counterexample","line":6965,"id":"source-h-335"},{"level":3,"title":"AX.3. Why the animation is not a hologram","line":7000,"id":"source-h-336"},{"level":3,"title":"AX.4. Executed evidence, limits, and next test","line":7025,"id":"source-h-337"},{"level":2,"title":"Appendix AY. Water-drop acoustics and the observer-rate boundary","line":7067,"id":"source-h-338"},{"level":3,"title":"AY.1. Bounded question and declared impact","line":7069,"id":"source-h-339"},{"level":3,"title":"AY.2. Entrained-bubble pitch and airborne pressure","line":7102,"id":"source-h-340"},{"level":3,"title":"AY.3. Why neither frame rate nor pitch is a unique inverse","line":7141,"id":"source-h-341"},{"level":3,"title":"AY.4. Executed evidence, limits, and next test","line":7168,"id":"source-h-342"},{"level":2,"title":"Appendix AZ. Bubble hidden-variable inverse and observation fibers","line":7211,"id":"source-h-343"},{"level":3,"title":"AZ.1. Bounded question and correction of scope","line":7213,"id":"source-h-344"},{"level":3,"title":"AZ.2. Exact radius--thermal-response observation fiber","line":7261,"id":"source-h-345"},{"level":3,"title":"AZ.3. Rank statement and what measurement must add","line":7324,"id":"source-h-346"},{"level":3,"title":"AZ.4. Evidence ledger, limitations, and next test","line":7360,"id":"source-h-347"},{"level":2,"title":"Appendix BA. Collective vibrational families and thermodynamic phase","line":7407,"id":"source-h-348"},{"level":3,"title":"BA.1. The bounded question and an exact counterexample","line":7409,"id":"source-h-349"},{"level":3,"title":"BA.2. A collective spectrum that can express both diffusion and vibration","line":7445,"id":"source-h-350"},{"level":3,"title":"BA.3. What was checked and what remains empirical","line":7497,"id":"source-h-351"},{"level":2,"title":"Appendix BB. Five-dimensional harmonies and a finite three-dimensional observer","line":7544,"id":"source-h-352"},{"level":3,"title":"BB.1. Bounded model and complete linear harmony theorem","line":7546,"id":"source-h-353"},{"level":3,"title":"BB.2. A product taxonomy rather than one “harmony” label","line":7596,"id":"source-h-354"},{"level":3,"title":"BB.3. What a finite observer does","line":7639,"id":"source-h-355"},{"level":3,"title":"BB.4. Hidden-basis gauge and the inverse boundary","line":7674,"id":"source-h-356"},{"level":3,"title":"BB.5. Finite validation and the next falsification","line":7705,"id":"source-h-357"},{"level":2,"title":"Appendix BC — Hydrogen spectroscopy gate for the two-harmony observer (revision 1.54)","line":7746,"id":"source-h-358"},{"level":2,"title":"Appendix BD — Multidimensional vector observers (revision 1.55)","line":7800,"id":"source-h-359"},{"level":3,"title":"BD.1. What one observer cannot see","line":7822,"id":"source-h-360"},{"level":3,"title":"BD.2. When several observers recover one common state","line":7842,"id":"source-h-361"},{"level":3,"title":"BD.3. Observers do not manufacture harmonies","line":7866,"id":"source-h-362"},{"level":3,"title":"BD.4. Evidence boundary","line":7895,"id":"source-h-363"},{"level":2,"title":"Appendix BE — Hydrogen transition holdout (revision 1.56)","line":7912,"id":"source-h-364"},{"level":3,"title":"BE.1. Frozen data split and conversion","line":7921,"id":"source-h-365"},{"level":3,"title":"BE.2. Two bounded laws","line":7949,"id":"source-h-366"},{"level":3,"title":"BE.3. Held-out result","line":7975,"id":"source-h-367"},{"level":3,"title":"BE.4. Exact finite-prefix counterexample","line":7998,"id":"source-h-368"},{"level":3,"title":"BE.5. Evidence boundary and next gate","line":8024,"id":"source-h-369"},{"level":2,"title":"Appendix BF — Hydrogen isotope correction ladder (revision 1.57)","line":8055,"id":"source-h-370"},{"level":3,"title":"BF.1. Frozen measured target and ordinary reference","line":8062,"id":"source-h-371"},{"level":3,"title":"BF.2. Explicit finite-range proxy","line":8113,"id":"source-h-372"},{"level":3,"title":"BF.3. Exact range/coupling non-identifiability","line":8148,"id":"source-h-373"},{"level":3,"title":"BF.4. Decision, limitations, and next test","line":8171,"id":"source-h-374"},{"level":2,"title":"Appendix BG — Frozen hydrogen-isotope holdout (revision 1.58)","line":8197,"id":"source-h-375"},{"level":3,"title":"BG.1. Frozen operator and historical target","line":8204,"id":"source-h-376"},{"level":3,"title":"BG.2. Ordinary reference and correlated uncertainty","line":8246,"id":"source-h-377"},{"level":3,"title":"BG.3. Decision and resolution limit","line":8283,"id":"source-h-378"},{"level":2,"title":"Appendix BH — Conserved quantum flow and observable harmonics (revision 1.59)","line":8320,"id":"source-h-379"},{"level":3,"title":"BH.1. Electromagnetic evolution and continuity","line":8327,"id":"source-h-380"},{"level":3,"title":"BH.2. Dipole harmonic and ideal rate","line":8385,"id":"source-h-381"},{"level":3,"title":"BH.3. Selection rules filter raw harmonics","line":8430,"id":"source-h-382"},{"level":3,"title":"BH.4. Evidence classes, decision, and next gate","line":8454,"id":"source-h-383"},{"level":2,"title":"Appendix BI — Golden-ratio exactness and coincidence audit (revision 1.60)","line":8495,"id":"source-h-384"},{"level":3,"title":"BI.1. Canonical golden quantities","line":8502,"id":"source-h-385"},{"level":3,"title":"BI.2. Where \\(\\varphi\\) is exact","line":8560,"id":"source-h-386"},{"level":3,"title":"BI.3. Exact exclusion from the ideal hydrogen gap ratios","line":8617,"id":"source-h-387"},{"level":3,"title":"BI.4. Fixed grids cannot contain the exact golden turn","line":8656,"id":"source-h-388"},{"level":3,"title":"BI.5. Measured manifestations do not transfer automatically","line":8685,"id":"source-h-389"},{"level":2,"title":"Appendix BJ. Forward observable compiler and the quantum light boundary","line":8730,"id":"source-h-390"},{"level":3,"title":"BJ.1. From “display everything” to a typed forward map","line":8732,"id":"source-h-391"},{"level":3,"title":"BJ.2. Coherent electromagnetic projection","line":8766,"id":"source-h-392"},{"level":3,"title":"BJ.3. Exact counterexample to a complete classical projection","line":8815,"id":"source-h-393"},{"level":3,"title":"BJ.4. Verification, evidence type, and boundary","line":8856,"id":"source-h-394"},{"level":2,"title":"Appendix BR. Primary-equation CW/LD truth-tower benchmark","line":8893,"id":"source-h-395"},{"level":3,"title":"BR.1. Bounded question and frozen assumptions","line":8895,"id":"source-h-396"},{"level":3,"title":"BR.2. Radius, masses, and couplings","line":8924,"id":"source-h-397"},{"level":3,"title":"BR.3. Conditional widths and channel ratios","line":8964,"id":"source-h-398"},{"level":3,"title":"BR.4. What changed in the recast inventory","line":9029,"id":"source-h-399"},{"level":3,"title":"BR.5. Verification, evidence classes, and next test","line":9051,"id":"source-h-400"},{"level":2,"title":"Appendix BS. Measured HEPData constraint on the compiled benchmark","line":9094,"id":"source-h-401"},{"level":3,"title":"BS.1. Source and bounded question","line":9096,"id":"source-h-402"},{"level":3,"title":"BS.2. Local contour calculation","line":9113,"id":"source-h-403"},{"level":3,"title":"BS.3. Correction and scope","line":9155,"id":"source-h-404"},{"level":3,"title":"BS.4. Submission inventory and recast boundary","line":9177,"id":"source-h-405"},{"level":3,"title":"BS.5. Verification and next test","line":9200,"id":"source-h-406"},{"level":2,"title":"Appendix BP. Retrospective ATLAS cross-channel dimension-evidence audit","line":9236,"id":"source-h-407"},{"level":3,"title":"BP.1. Bounded question and source","line":9238,"id":"source-h-408"},{"level":3,"title":"BP.2. Frozen necessary screen","line":9269,"id":"source-h-409"},{"level":3,"title":"BP.3. Result and counterexamples","line":9301,"id":"source-h-410"},{"level":3,"title":"BP.4. Exact procedural correction and limits","line":9333,"id":"source-h-411"},{"level":2,"title":"Appendix BO: Dimension evidence requires a distinguishing physical constraint (revision 1.66)","line":9377,"id":"source-h-412"},{"level":3,"title":"BO.1. The bounded question","line":9379,"id":"source-h-413"},{"level":3,"title":"BO.2. Projection-equivalence theorem","line":9394,"id":"source-h-414"},{"level":3,"title":"BO.3. What a constrained extra-dimensional signature can look like","line":9435,"id":"source-h-415"},{"level":3,"title":"BO.4. Executable checks and counterexample","line":9466,"id":"source-h-416"},{"level":3,"title":"BO.5. Physical-dimension evidence gate","line":9488,"id":"source-h-417"},{"level":3,"title":"BO.6. Current measured status","line":9510,"id":"source-h-418"},{"level":3,"title":"BO.7. Next experiment and retained boundaries","line":9535,"id":"source-h-419"},{"level":2,"title":"Appendix BK. All-element atomic projection atlas","line":9554,"id":"source-h-420"},{"level":3,"title":"BK.1. The word “shape” needs an observer","line":9556,"id":"source-h-421"},{"level":3,"title":"BK.2. Exact angular result","line":9582,"id":"source-h-422"},{"level":3,"title":"BK.3. All-118 finite atlas","line":9611,"id":"source-h-423"},{"level":3,"title":"BK.4. Verification and counterexample","line":9652,"id":"source-h-424"},{"level":2,"title":"Appendix BL. Bulk gold and silver color observer","line":9703,"id":"source-h-425"},{"level":3,"title":"BL.1. The corrected object of study","line":9705,"id":"source-h-426"},{"level":3,"title":"BL.2. Measured-input Fresnel map","line":9723,"id":"source-h-427"},{"level":3,"title":"BL.3. Finite result and counterexample","line":9772,"id":"source-h-428"},{"level":3,"title":"BL.4. Verification, evidence type, and boundary","line":9803,"id":"source-h-429"},{"level":2,"title":"Appendix BM. Frozen interband-response holdout","line":9852,"id":"source-h-430"},{"level":3,"title":"BM.1. The bounded question","line":9854,"id":"source-h-431"},{"level":3,"title":"BM.2. Frozen equations and split","line":9869,"id":"source-h-432"},{"level":3,"title":"BM.3. Held-out result","line":9915,"id":"source-h-433"},{"level":3,"title":"BM.4. Counterexamples and model strain","line":9938,"id":"source-h-434"},{"level":3,"title":"BM.5. Verification and evidence type","line":9962,"id":"source-h-435"},{"level":2,"title":"Appendix BN. Frozen gold/silver external-validation contract","line":10012,"id":"source-h-436"},{"level":3,"title":"BN.1. What is frozen","line":10014,"id":"source-h-437"},{"level":3,"title":"BN.2. Evaluation-only rule","line":10041,"id":"source-h-438"},{"level":3,"title":"BN.3. Verification and boundary","line":10065,"id":"source-h-439"},{"level":2,"title":"Appendix BQ. Exact-recast completeness before dimensional interpretation","line":10099,"id":"source-h-440"},{"level":3,"title":"BQ.1. Bounded question","line":10101,"id":"source-h-441"},{"level":3,"title":"BQ.2. The forward equation and exact ambiguity","line":10124,"id":"source-h-442"},{"level":3,"title":"BQ.3. Frozen readiness gate","line":10170,"id":"source-h-443"},{"level":3,"title":"BQ.4. Verification, evidence classes, and consequence","line":10199,"id":"source-h-444"},{"level":2,"title":"Appendix BT. Complete HEPData contour audit of the unchanged benchmark","line":10244,"id":"source-h-445"},{"level":3,"title":"BT.1. Bounded question and provenance","line":10246,"id":"source-h-446"},{"level":3,"title":"BT.2. Input inventory and geometry","line":10265,"id":"source-h-447"},{"level":3,"title":"BT.3. Checked observed result","line":10291,"id":"source-h-448"},{"level":3,"title":"BT.4. Verification and remaining reconstruction gap","line":10316,"id":"source-h-449"},{"level":3,"title":"BT.5. Evidence classes, correction, and next test","line":10339,"id":"source-h-450"},{"level":2,"title":"Appendix BU. Guarded exploration of published contour sides","line":10367,"id":"source-h-451"},{"level":3,"title":"BU.1. A map is not a new likelihood","line":10369,"id":"source-h-452"},{"level":3,"title":"BU.2. Counterexamples to overconfident mapping","line":10394,"id":"source-h-453"},{"level":3,"title":"BU.3. Verification and evidence class","line":10410,"id":"source-h-454"},{"level":3,"title":"BU.4. Sources and next bounded test","line":10439,"id":"source-h-455"},{"level":2,"title":"Appendix BV. Explicit detector losses and source–efficiency non-identifiability","line":10460,"id":"source-h-456"},{"level":3,"title":"BV.1. Observation map and declared synthetic experiment","line":10462,"id":"source-h-457"},{"level":3,"title":"BV.2. Fixed-background fitting and exact ambiguity","line":10498,"id":"source-h-458"},{"level":3,"title":"BV.3. Checked finite results and negative control","line":10536,"id":"source-h-459"},{"level":3,"title":"BV.4. Sources, remaining limits and next test","line":10574,"id":"source-h-460"},{"level":2,"title":"Appendix BW. Primitive crystal cells, projected views and sunlight color","line":10596,"id":"source-h-461"},{"level":3,"title":"BW.1. Smallest repeating pattern versus smallest stable object","line":10598,"id":"source-h-462"},{"level":3,"title":"BW.2. Optical observation requires an electronic response","line":10630,"id":"source-h-463"},{"level":3,"title":"BW.3. Two geometric checks","line":10669,"id":"source-h-464"},{"level":3,"title":"BW.4. Validation, provenance and next test","line":10693,"id":"source-h-465"},{"level":2,"title":"Appendix BX. Complete element records and source-qualified crystal/optical coverage","line":10733,"id":"source-h-466"},{"level":2,"title":"Coverage","line":10738,"id":"source-h-467"},{"level":2,"title":"Reference sources and their limits","line":10761,"id":"source-h-468"},{"level":2,"title":"Geometry and display","line":10803,"id":"source-h-469"},{"level":2,"title":"Optical expansion","line":10825,"id":"source-h-470"},{"level":2,"title":"Verification and next work","line":10850,"id":"source-h-471"},{"level":2,"title":"Appendix BY. Crystal interference, finite size and exact inverse ambiguity","line":10875,"id":"source-h-472"},{"level":2,"title":"Forward model","line":10881,"id":"source-h-473"},{"level":2,"title":"Published reference check","line":10919,"id":"source-h-474"},{"level":2,"title":"Finite crystal interference","line":10939,"id":"source-h-475"},{"level":2,"title":"Exact ambiguity that the engine must preserve","line":10953,"id":"source-h-476"},{"level":2,"title":"Scope and verification","line":10972,"id":"source-h-477"},{"level":2,"title":"Run","line":11013,"id":"source-h-478"},{"level":2,"title":"Appendix BZ. 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The two functions have exactly the same past but different smooth futures. An algorithm whose only input is that past must make the same prediction for both. By the triangle inequality,","label":"B. A rigorous limit on unconstrained gap filling","source":"archive/2711bdafd755-Higher_Dimension_Wave_Audit.md","sectionId":"source-h-44","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":0,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Anthony Michael Collado's Theory of Reality project · 22 September 2026 Inputs: Theory of Reality v1.70, especially BH, BK, BO and BS; Wave Chemistry Lab build 9. Status: Added controlled-intervention detection limits (1,920 repeated trials), multi-source phase/force predictions (160 paired datasets), exact feedback equivalence and a phase-work identity. Previous research is preserved. 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Read its methods, assumptions and original source before treating a claim as checked.","label":"Locate the checks","source":"archive/2ab60a5f99b1-THEORY_V16.md","sectionId":"source-record","provenance":"Editorial reading guide"},"nextQuestion":{"text":"Predicate invention in inductive logic programming is explicitly concerned with inventing new relations, and the literature identifies deciding the number and ordering of invented predicate arguments as a longstanding difficulty.","label":"Prior-art boundary","source":"archive/2ab60a5f99b1-THEORY_V16.md","sectionId":"source-h-7","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":7,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"v15 assumed that the missing primitive was binary.","words":552},"archive/2aeab23576cd-THEORY_V18.md":{"url":"archive/2aeab23576cd-THEORY_V18.md","title":"DRCT v18 — Learning the Equivalence Relation Between Concepts","kind":"Research manuscript","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/THEORY_V18.md","bytes":5173,"sha256":"2aeab23576cdddc5e834298ba92604be35b5b2414ad668d0abd197823c3fb35e","savedDate":"2026-08-23","date":"2026-08-23","dateKind":"Saved source date","declaredDates":[],"projectId":"drct","projectIds":["drct"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"DRCT v18 — Learning the Equivalence Relation Between Concepts","line":1,"id":"source-h-1"},{"level":2,"title":"Problem","line":3,"id":"source-h-2"},{"level":2,"title":"Exact mapping tomography","line":48,"id":"source-h-3"},{"level":2,"title":"MDL rule learning","line":66,"id":"source-h-4"},{"level":2,"title":"Learned result in the v18 laboratory","line":103,"id":"source-h-5"},{"level":2,"title":"Theorem 44 — Orbit Sameness Is an Equivalence Relation","line":136,"id":"source-h-6"},{"level":3,"title":"Proof","line":148,"id":"source-h-7"},{"level":2,"title":"Over-flexibility trap","line":163,"id":"source-h-8"},{"level":2,"title":"Prospective transfer","line":187,"id":"source-h-9"},{"level":2,"title":"Prior-art boundary","line":199,"id":"source-h-10"}],"journey":{"question":{"text":"What does “DRCT v18 — Learning the Equivalence Relation Between Concepts” establish within its declared scope?","label":"The reading question","source":"archive/2aeab23576cd-THEORY_V18.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The hidden source corpus is generated by one common carrier relabeling acting on row, column, and output coordinates, with optional argument reversal: The learner is not told this equality.","label":"Learned result in the v18 laboratory","source":"archive/2aeab23576cd-THEORY_V18.md","sectionId":"source-h-5","provenance":"Source excerpt"},"checks":{"text":"Reflexive: the identity \\(e\\in G\\) gives \\(T=e\\cdot T\\).","label":"Proof","source":"archive/2aeab23576cd-THEORY_V18.md","sectionId":"source-h-7","provenance":"Source excerpt"},"nextQuestion":{"text":"Symmetry discovery is an active field. Recent work studies learning unknown invariance groups from data, including exact subgroup recovery, unknown continuous symmetries, and unsupervised symmetry discovery.","label":"Prior-art boundary","source":"archive/2aeab23576cd-THEORY_V18.md","sectionId":"source-h-10","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":7,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"v17 learned a reusable concept only after being told which transformations should count as superficial coordinate changes.","words":722},"archive/2b014f84d8bb-RESULTS_0.11.md":{"url":"archive/2b014f84d8bb-RESULTS_0.11.md","title":"Element Projection Lab 0.11.0 — guarded parameter explorer","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Element Projection Lab/RESULTS_0.11.md","bytes":5143,"sha256":"2b014f84d8bb10775afa371b0e236b1dc59210e062b82246810488b5fc4c79e1","savedDate":"2026-09-20","date":"2026-09-20","dateKind":"Saved source date","declaredDates":[],"projectId":"elements","projectIds":["elements"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Element Projection Lab 0.11.0 — guarded parameter explorer","line":1,"id":"source-h-1"},{"level":2,"title":"Completed capability","line":3,"id":"source-h-2"},{"level":2,"title":"Checked result and counterexample","line":15,"id":"source-h-3"},{"level":2,"title":"What the display does","line":45,"id":"source-h-4"},{"level":2,"title":"Limits and next test","line":70,"id":"source-h-5"}],"journey":{"question":{"text":"What does “Element Projection Lab 0.11.0 — guarded parameter explorer” establish within its declared scope?","label":"The reading question","source":"archive/2b014f84d8bb-RESULTS_0.11.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"All 48,396 grid classifications and 2,916 off-grid classifications (729 probe records, 712 distinct coordinates, each checked in four tables) agree with an independent source-decimal exact-rational implementation. Maximum displayed-boundary discrepancy is 3e-12 GeV; a 1e-8 GeV tolerance is used only for float serialization, never to compare classifications or interpret experimental precision. The independent audit passes 54,586 checks, including 20 synthetic controls. All 162 unit tests pass, including all 120 prior tests and 42 new engine/view tests.","label":"Checked result and counterexample","source":"archive/2b014f84d8bb-RESULTS_0.11.md","sectionId":"source-h-3","provenance":"Source excerpt"},"checks":{"text":"All 48,396 grid classifications and 2,916 off-grid classifications (729 probe records, 712 distinct coordinates, each checked in four tables) agree with an independent source-decimal exact-rational implementation. Maximum displayed-boundary discrepancy is 3e-12 GeV; a 1e-8 GeV tolerance is used only for float serialization, never to compare classifications or interpret experimental precision. The independent audit passes 54,586 checks, including 20 synthetic controls. All 162 unit tests pass, including all 120 prior tests and 42 new engine/view tests.","label":"Checked result and counterexample","source":"archive/2b014f84d8bb-RESULTS_0.11.md","sectionId":"source-h-3","provenance":"Source excerpt"},"nextQuestion":{"text":"These are finite calculations from externally measured exclusion curves, plus synthetic tests—not new measured evidence, an independent likelihood reconstruction, a joint confidence region, or evidence for extra dimensions. Above-contour points need not lie within a supplied two-dimensional likelihood grid; the archive does not contain one. The four analyses reuse data. The borrowed CW/LD parameters are not derived from this project's fixed-grid or string-rotation hypothesis, and no unexplained residual identifies a unique physical or theological cause.","label":"Limits and next test","source":"archive/2b014f84d8bb-RESULTS_0.11.md","sectionId":"source-h-5","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":5,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The engine now provides an offline four-panel explorer and an off-grid query CLI for the four observed ATLAS CW/LD contours. It preserves the original k=500 GeV, M5=6000 GeV benchmark, which is still below all four boundaries. Moving the exploratory selection does not move or replace that benchmark.","words":699},"archive/2f8e1d2a9608-STRUCTURAL_REFINEMENT.md":{"url":"archive/2f8e1d2a9608-STRUCTURAL_REFINEMENT.md","title":"Applying the RE engine to the structure inside SAT","kind":"Research note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/STRUCTURAL_REFINEMENT.md","bytes":14945,"sha256":"2f8e1d2a9608195b24804ae863df567022d7eaf8ac1d0a5681d0207137360891","savedDate":"2026-09-05","date":"2026-09-05","dateKind":"Saved source date","declaredDates":["Date: 2026-09-05. Research companion to the Reality Bit Engine and RRLS audit."],"projectId":"rrls","projectIds":["rrls"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Applying the RE engine to the structure inside SAT","line":1,"id":"source-h-1"},{"level":2,"title":"1. 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Verification scope","line":197,"id":"source-h-10"}],"journey":{"question":{"text":"What does “Applying the RE engine to the structure inside SAT” establish within its declared scope?","label":"The reading question","source":"archive/2f8e1d2a9608-STRUCTURAL_REFINEMENT.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The new re_sat.py uses the existing RRLS exact factor-elimination engine. dispatcher.py also uses the existing v0.19/v0.20 Python DPLL solver. Unmodified copies are included with source hashes in vendor/ORIGINS.json.","label":"2. What was implemented","source":"archive/2f8e1d2a9608-STRUCTURAL_REFINEMENT.md","sectionId":"source-h-3","provenance":"Source excerpt"},"checks":{"text":"All 15 test groups passed. Checks include every three-variable Boolean relation, completeness of its affine consequence basis, fresh CNF counts, full reduced-assignment reconstruction, explicit nonlinear remainder preservation, parity contradictions, empty domains, arbitrary-precision counts, budget handling, and ten corrupted reduction variants.","label":"9. Verification scope","source":"archive/2f8e1d2a9608-STRUCTURAL_REFINEMENT.md","sectionId":"source-h-10","provenance":"Source excerpt"},"nextQuestion":{"text":"The two-variable clause \\(x\\lor y\\) has three satisfying assignments: The image of any nonempty affine set under an affine projection is affine. Every finite affine set over GF(2) has a power-of-two number of elements. Consequently:","label":"5. A boundary that cannot be removed by adding affine coordinates","source":"archive/2f8e1d2a9608-STRUCTURAL_REFINEMENT.md","sectionId":"source-h-6","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Outcome: a new engine stage recovers affine relationships from ordinary CNF clauses, derives independent coordinates, preserves nonlinear residual constraints, and selects a fallback when the transformed representation is unsuitable. The mathematical result is an exact reduction with explicit limits. 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This release expands the current crystal table using"],"projectId":"elements","projectIds":["elements"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Element reference completion — Lab 0.14.0","line":1,"id":"source-h-1"},{"level":2,"title":"Coverage","line":6,"id":"source-h-2"},{"level":2,"title":"Reference sources and their limits","line":29,"id":"source-h-3"},{"level":2,"title":"Geometry and display","line":71,"id":"source-h-4"},{"level":2,"title":"Optical expansion","line":93,"id":"source-h-5"},{"level":2,"title":"Verification and next work","line":118,"id":"source-h-6"}],"journey":{"question":{"text":"What does “Element reference completion — Lab 0.14.0” establish within its declared scope?","label":"The reading question","source":"archive/33deacfda028-RESULTS_0.14.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The 226 null property fields include 34 elements for which CIAAW assigns no standard atomic weight; these are marked not defined, not zero mass or an ordinary missing measurement. Other blanks mean this source snapshot does not supply a value. All 118 identities and property records are present, but this is not a claim that all properties of all elements have been measured.","label":"The source’s opening statement","source":"archive/33deacfda028-RESULTS_0.14.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"All 259 unit tests passed, including the 228 previous tests. Independent raw-CIF reconstructions checked 10 light-region phase records (including the two alternatives), nine middle-region cells and six heavy-region cells. The middle audit additionally confirms 1,793 periodic site comparisons in the integrated data. Independent scalar optics reproduced 7,619 reflectances, 15,238 interpolated n/k values and 38 Sun/D65 colors. All hex colors matched; maximum reflectance discrepancy was 6.67e-16. All 11 original optical records and 67 original crystal geometries remained unchanged.","label":"Verification and next work","source":"archive/33deacfda028-RESULTS_0.14.md","sectionId":"source-h-6","provenance":"Source excerpt"},"nextQuestion":{"text":"All 259 unit tests passed, including the 228 previous tests. Independent raw-CIF reconstructions checked 10 light-region phase records (including the two alternatives), nine middle-region cells and six heavy-region cells. The middle audit additionally confirms 1,793 periodic site comparisons in the integrated data. Independent scalar optics reproduced 7,619 reflectances, 15,238 interpolated n/k values and 38 Sun/D65 colors. All hex colors matched; maximum reflectance discrepancy was 6.67e-16. All 11 original optical records and 67 original crystal geometries remained unchanged.","label":"Verification and next work","source":"archive/33deacfda028-RESULTS_0.14.md","sectionId":"source-h-6","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":5,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The 226 null property fields include 34 elements for which CIAAW assigns no standard atomic weight; these are marked not defined, not zero mass or an ordinary missing measurement. Other blanks mean this source snapshot does not supply a value. 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Every finite real matrix can be reconstructed exactly by a finite collection of these rotors. The number needed is a useful, computable basis-dependent complexity measure, but it is not a universal measure of pattern or randomness.","label":"Executive conclusion","source":"archive/350b255f3242-THEORY_AND_RESULTS.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"- Matrix size: 64 × 64 (4,096 values). - Available conjugate rotor groups: 2,050. - Energy targets: 50%, 90%, 95%, 99%, and 99.9%. - Controls: constant, one sinusoid, four sinusoids, checkerboard, and square-wave stripes. - Geometry: Gaussian blob, binary disk, and binary square. - Counterexamples: random rank-one outer product and single spatial impulse. - Randomness: Gaussian noise, random signs, and a short-rule 32-bit LCG. - Random trials: 40 seeds for each distribution at 16², 32², 64², and 128². - Comparator: SVD components needed for the same retained-energy targets.","label":"Benchmark design","source":"archive/350b255f3242-THEORY_AND_RESULTS.md","sectionId":"source-h-4","provenance":"Source excerpt"},"nextQuestion":{"text":"Which additional test would distinguish the claim in “Rotational Complexity of Matrices — Theory and Experimental Results” from the alternatives allowed by its assumptions?","label":"The next reading question","source":"archive/350b255f3242-THEORY_AND_RESULTS.md","sectionId":"source-record","provenance":"Editorial reading question"}},"figures":[],"illustrationIndex":0,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The proposed idea is mathematically valid when a “rotating circle” is defined as one real conjugate pair of two-dimensional Fourier coefficients. 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Then freeze one complete tower model before genuinely independent future collision data are opened. A failed fit may indicate a wrong model, omitted conventional physics, miscalibration, or fluctuation; it is not automatic evidence for hidden variables or extra dimensions.","label":"Next test","source":"archive/3636ed2ff4b1-RESULTS_0.6.md","sectionId":"source-h-6","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":5,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The published ATLAS periodic dielectron/diphoton search does not pass the project's necessary cross-channel evidence screen for a physical extra dimension.","words":510},"archive/370642ea780a-THEORY.md":{"url":"archive/370642ea780a-THEORY.md","title":"Dimensional PRNG Tomography v4 — Formal Core","kind":"Research manuscript","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/THEORY.md","bytes":4742,"sha256":"370642ea780a956479ad68440ca8b6f4f5843d83a32b106bbe30491a3315a986","savedDate":"2026-08-23","date":"2026-08-23","dateKind":"Saved source date","declaredDates":[],"projectId":"prng-markets","projectIds":["prng-markets"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Dimensional PRNG Tomography v4 — Formal Core","line":2,"id":"source-h-1"},{"level":2,"title":"Scope","line":4,"id":"source-h-2"},{"level":2,"title":"1. 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The fitted factor improved the training sample slightly but did not improve the held-out elements. This is a negative result for this particular mapping and objective, not a denial of genuine quantum structure in atomic spectra or a test of every possible harmonic model.","label":"Result","source":"archive/435b7200338e-Element_Harmonic_Report.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"Python 3.10+ and NumPy are required. This bundle is offline: no downloads or credentials are needed. From its directory: The analysis refuses an existing output directory. The audit reads the shipped release_corrected/ and prints its verification; it preserves the saved audit record rather than overwriting it. LINES.json contains all source entries and their exclusions, not only successful matches. PER_ELEMENT.json contains all 118 coverage rows. 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Molecular/condensed-matter spectra need a separate declared dataset and physical conditions, not invented atomic compositions.","label":"Next test","source":"archive/435b7200338e-Element_Harmonic_Report.md","sectionId":"source-h-10","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"21 September 2026 · HARMONIC-ELEMENTS-01 · Corrected and independently audited","words":1763},"archive/441b2e8db915-RESULTS_0.2.md":{"url":"archive/441b2e8db915-RESULTS_0.2.md","title":"Fixed Grid String Lab 0.2.0 — bounded results","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Fixed Grid String Lab/RESULTS_0.2.md","bytes":5864,"sha256":"441b2e8db9159766c882bca11e717ba58a7d40b8412b078752aeec137f6b972b","savedDate":"2026-09-21","date":"2026-09-21","dateKind":"Saved source date","declaredDates":[],"projectId":"gauge","projectIds":["gauge"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Fixed Grid String Lab 0.2.0 — bounded results","line":1,"id":"source-h-1"},{"level":2,"title":"Corrected memory and stochastic claims","line":12,"id":"source-h-2"},{"level":2,"title":"Frozen spatial result","line":35,"id":"source-h-3"},{"level":2,"title":"Time equivalence and alias control","line":69,"id":"source-h-4"},{"level":2,"title":"Independent replay and claim ceiling","line":84,"id":"source-h-5"}],"journey":{"question":{"text":"What does “Fixed Grid String Lab 0.2.0 — bounded results” establish within its declared scope?","label":"The reading question","source":"archive/441b2e8db915-RESULTS_0.2.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The derivation and prior-work attribution are in FOUNDATION_DERIVATION.md. 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Next attack","line":468,"id":"source-h-21"}],"journey":{"question":{"text":"What does “RRLS v0.28 — Adversarial Generator Compiler” establish within its declared scope?","label":"The reading question","source":"archive/49eed9439785-RRLS_v28_ADVERSARIAL_GENERATOR_REPORT.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"v0.28 deliberately changes the research objective from \"make RRLS look good\" to \"construct formulas that break RRLS, preserve the breakage, classify why it breaks, and refuse to confuse finite success with a complexity theorem.\"","label":"Status","source":"archive/49eed9439785-RRLS_v28_ADVERSARIAL_GENERATOR_REPORT.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"The gate requires all of the following simultaneously: one fixed uniform deterministic exact algorithm for arbitrary SAT; rigorous worst-case polynomial time and intermediate-size proof; concrete proof artifact; independent verification.","label":"1. 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Next dimensional ladder","line":177,"id":"source-h-11"}],"journey":{"question":{"text":"What does “Dimensional Chess Experiment C1” establish within its declared scope?","label":"The reading question","source":"archive/6875140b9128-Dimensional_Chess_Experiment.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"Chess is finite once its complete rules and history-dependent draw state are fixed, so its initial position has a definite game-theoretic value: White win, draw, or Black win. Finiteness proves that an exhaustive solution exists in principle. It does not prove that the solution has a physically feasible computation or a compact polynomial representation.","label":"1. Verdict","source":"archive/6875140b9128-Dimensional_Chess_Experiment.md","sectionId":"source-h-3","provenance":"Source excerpt"},"checks":{"text":"verify_dimensional_chess.py imports no production function. It independently reconstructs: 1. all 399,112 raw legal positions; 2. all 50,015 symmetry orbits; 3. every legal transition and checkmate/stalemate condition; 4. all 400,120 symmetry-closure comparisons; 5. every win/loss/draw Bellman equation; 6. every shortest-mate and longest-defense distance; 7. every stored optimal policy edge; 8. all 32 concrete moves in the longest principal variation; 9. the certificate and principal-variation digests.","label":"6. 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Next test","line":164,"id":"source-h-7"}],"journey":{"question":{"text":"What does “Reality Render Engine — mathematical checkpoint” establish within its declared scope?","label":"The reading question","source":"archive/6df375e4347b-Reality_Render_Math_Check.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"I injected +1 cm⁻¹ into each of the 59 transitions separately: - 26 altered transitions break a cycle and are detected as inconsistent. - 33 are graph bridges; changing them leaves every cycle consistent.","label":"4. Counterexamples: what a passing checker cannot establish","source":"archive/6df375e4347b-Reality_Render_Math_Check.md","sectionId":"source-h-5","provenance":"Source excerpt"},"checks":{"text":"Every signed closed loop telescopes to zero. For a graph with \\(m\\) transitions, \\(n\\) level labels and \\(c\\) connected components, there are \\(m-n+c\\) independent linear cycle constraints. Each component retains an undetermined additive energy origin. These are graph-theoretic statements; they do not reconstruct spatial electron density or identify physical dimensions.","label":"3. New reusable check: energy-difference loops","source":"archive/6df375e4347b-Reality_Render_Math_Check.md","sectionId":"source-h-4","provenance":"Source excerpt"},"nextQuestion":{"text":"Freeze one hydrogen emission case: specify the state preparation, interaction, line profile, observer and numerical/physical error budget. Predict its line positions and transition strengths before comparing with an independently sourced measured spectrum. Include the reduced-mass, relativistic and radiative terms required by the chosen precision; do not treat numerical error as new physics. Preserve the outcome and reserve fresh data after any model repair.","label":"6. Next test","source":"archive/6df375e4347b-Reality_Render_Math_Check.md","sectionId":"source-h-7","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"21 September 2026 · SPECTRAL-CONSISTENCY-01 · standalone checker 0.1.0","words":1185},"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md":{"url":"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md","title":"Dimensional Chess C8: Movement-Frequency Relations","kind":"Research note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/Dimensional_Chess_Movement_Frequency_C8.md","bytes":6611,"sha256":"709ba3d90a0c3bb881ccf93be06a2c1d8ea5f7aa364d9de90e3c57a40c0f3e3a","savedDate":"2026-09-15","date":"2026-09-15","dateKind":"Saved source date","declaredDates":["Date: 15 September 2026"],"projectId":"chess","projectIds":["chess"],"associationBasis":"Explicit project source citation","status":"Original saved source","headings":[{"level":1,"title":"Dimensional Chess C8: Movement-Frequency Relations","line":1,"id":"source-h-1"},{"level":2,"title":"Result","line":7,"id":"source-h-2"},{"level":2,"title":"Frequency coordinate","line":37,"id":"source-h-3"},{"level":2,"title":"Patterns in the learned patterns","line":67,"id":"source-h-4"},{"level":2,"title":"Seven-ply transfer and repeatability","line":88,"id":"source-h-5"},{"level":2,"title":"Falsified variants","line":103,"id":"source-h-6"},{"level":2,"title":"Audit","line":132,"id":"source-h-7"},{"level":2,"title":"Consequence","line":142,"id":"source-h-8"}],"journey":{"question":{"text":"What does “Dimensional Chess C8: Movement-Frequency Relations” establish within its declared scope?","label":"The reading question","source":"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"C8 tests the proposal that chess pieces exhibit reusable relational movement rhythms. A move is mapped to a class describing piece type, displacement, capture status, square-color phase, distance changes to both kings, geometric relations to both kings, edge-to-center motion, and home-relative rank phase. The learner records which defender classes terminate bounded mating claims in eight deterministic phase-shuffled five-ply searches. A later exact search orders defender moves by the frozen empirical score.","label":"Result","source":"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"The C8 result agrees with the separately implemented and independently verified C7 certificate that neither side can force mate within nine plies. A structural audit samples 960 deterministically reachable states and checks seven ordering schemes over 168,882 legal-move instances. Every ordered list is exactly a permutation of the corresponding legal list. Of the state/scheme cases, 6,720 actually change order, establishing that the test is not a lexical no-op. Audit status: PASS.","label":"Audit","source":"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md","sectionId":"source-h-7","provenance":"Source excerpt"},"nextQuestion":{"text":"Which additional test would distinguish the claim in “Dimensional Chess C8: Movement-Frequency Relations” from the alternatives allowed by its assumptions?","label":"The next reading question","source":"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md","sectionId":"source-record","provenance":"Editorial reading question"}},"figures":[],"illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"C8 tests the proposal that chess pieces exhibit reusable relational movement rhythms. 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It does not prove that physical collisions work this way, that ordinary space has exactly these hidden coordinates, or that information automatically moves to another dimension without an encoding law.","label":"What the theorem does and does not prove","source":"archive/7a9c23a3a539-projective-ripple-reality.md","sectionId":"source-h-16","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":0,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"This document formalizes the idea that an observer at one descriptive layer sees a projection of a richer state, while information invisible at that layer remains in the fiber above the observed state. 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Revision 1.58 freezes a single member of that family and asks whether it predicts a second transition.","label":"The source’s opening statement","source":"archive/7c616040c25f-Reality_Revision_1.58.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"This record does not separate a verification section. 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Revision 1.58 freezes a single member of that family and asks whether it predicts a second transition.","words":295},"archive/81b60f656540-RESULTS_0.5.md":{"url":"archive/81b60f656540-RESULTS_0.5.md","title":"Hydrogen Matrix Lab 0.5.0 — electromagnetic correction ladder","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/RESULTS_0.5.md","bytes":3563,"sha256":"81b60f6565400e1019ae0b55accb4995e85b45bd42b62db823c422a56481deea","savedDate":"2026-09-20","date":"2026-09-20","dateKind":"Saved source date","declaredDates":[],"projectId":"hydrogen","projectIds":["hydrogen"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Hydrogen Matrix Lab 0.5.0 — electromagnetic correction ladder","line":1,"id":"source-h-1"},{"level":2,"title":"Bounded question","line":3,"id":"source-h-2"},{"level":2,"title":"Frozen ladder and real-data comparison","line":15,"id":"source-h-3"},{"level":2,"title":"What the residual does and does not mean","line":29,"id":"source-h-4"},{"level":2,"title":"Next test","line":41,"id":"source-h-5"},{"level":2,"title":"Sources","line":45,"id":"source-h-6"}],"journey":{"question":{"text":"The old fixed-proton Schrödinger clock missed the NIST Lyman-alpha centroid by about -0.05325%. Does that discrepancy require a new force, or is it mostly the result of standard electromagnetic structure omitted from the baseline?","label":"Bounded question","source":"archive/81b60f656540-RESULTS_0.5.md","sectionId":"source-h-2","provenance":"Source excerpt"},"answer":{"text":"The old fixed-proton Schrödinger clock missed the NIST Lyman-alpha centroid by about -0.05325%. Does that discrepancy require a new force, or is it mostly the result of standard electromagnetic structure omitted from the baseline?","label":"The source’s opening statement","source":"archive/81b60f656540-RESULTS_0.5.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"Add the complete standard precision ladder—recoil, Lamb/QED, finite-size, and hyperfine contributions—and validate it against multiple independently sourced hydrogen transitions, not only Lyman-alpha. Only then freeze one explicit higher-dimensional operator and test whether it predicts a state-dependent residual pattern that cannot be absorbed by the standard constants.","label":"Next test","source":"archive/81b60f656540-RESULTS_0.5.md","sectionId":"source-h-5","provenance":"Source excerpt"},"nextQuestion":{"text":"Add the complete standard precision ladder—recoil, Lamb/QED, finite-size, and hyperfine contributions—and validate it against multiple independently sourced hydrogen transitions, not only Lyman-alpha. Only then freeze one explicit higher-dimensional operator and test whether it predicts a state-dependent residual pattern that cannot be absorbed by the standard constants.","label":"Next test","source":"archive/81b60f656540-RESULTS_0.5.md","sectionId":"source-h-5","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":4,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The old fixed-proton Schrödinger clock missed the NIST Lyman-alpha centroid by about -0.05325%. Does that discrepancy require a new force, or is it mostly the result of standard electromagnetic structure omitted from the baseline?","words":460},"archive/876994ae70a5-Reality_Revision_1.47.md":{"url":"archive/876994ae70a5-Reality_Revision_1.47.md","title":"Reality Revision 1.47 — water harmonics without hidden-dimension inflation","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Matter Harmony Lab/Reality_Revision_1.47.md","bytes":2197,"sha256":"876994ae70a5d900bb56986e6bd16557f7f52025248416c2537a4a25de755cc3","savedDate":"2026-09-20","date":"2026-09-20","dateKind":"Saved source date","declaredDates":[],"projectId":"matter","projectIds":["matter"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Reality Revision 1.47 — water harmonics without hidden-dimension inflation","line":1,"id":"source-h-1"},{"level":2,"title":"Concrete addition","line":3,"id":"source-h-2"},{"level":2,"title":"Result and counterexample","line":19,"id":"source-h-3"},{"level":2,"title":"Limits","line":32,"id":"source-h-4"}],"journey":{"question":{"text":"What does “Reality Revision 1.47 — water harmonics without hidden-dimension inflation” establish within its declared scope?","label":"The reading question","source":"archive/876994ae70a5-Reality_Revision_1.47.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The 64-frame computation preserves state norm to 2.220e-16, rigid molecular geometry to below 1.2e-13 degrees and 1.4e-15 Å, and the calibrated density to reported precision. Forty-one unit tests pass. A separately implemented audit checks 36,864 atomic-coordinate scalars and the principal invariants.","label":"Result and counterexample","source":"archive/876994ae70a5-Reality_Revision_1.47.md","sectionId":"source-h-3","provenance":"Source excerpt"},"checks":{"text":"The 64-frame computation preserves state norm to 2.220e-16, rigid molecular geometry to below 1.2e-13 degrees and 1.4e-15 Å, and the calibrated density to reported precision. Forty-one unit tests pass. A separately implemented audit checks 36,864 atomic-coordinate scalars and the principal invariants.","label":"Result and counterexample","source":"archive/876994ae70a5-Reality_Revision_1.47.md","sectionId":"source-h-3","provenance":"Source excerpt"},"nextQuestion":{"text":"Which additional test would distinguish the claim in “Reality Revision 1.47 — water harmonics without hidden-dimension inflation” from the alternatives allowed by its assumptions?","label":"The next reading question","source":"archive/876994ae70a5-Reality_Revision_1.47.md","sectionId":"source-record","provenance":"Editorial reading question"}},"figures":[],"illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Matter Harmony Lab 0.4.0 adds an executable many-molecule water animation. Sixty-four rigid H2O geometries are placed on an ordered periodic tetrahedral scaffold whose box volume matches the declared 298.15 K water density. A 320-coordinate skew system couples 192 visible displacement coordinates to 128 hidden coordinates and projects only the visible block into the rendered three-dimensional positions.","words":308},"archive/88c2103b5c5b-Dimensional_Chess_Tension_Field_C5.md":{"url":"archive/88c2103b5c5b-Dimensional_Chess_Tension_Field_C5.md","title":"Dimensional Chess C5: Tension Fields and Tactical Entry Ordering","kind":"Research note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/Dimensional_Chess_Tension_Field_C5.md","bytes":6839,"sha256":"88c2103b5c5b93f522207ecfafe57e01221a23600d9c52ee3f1cdbd634716179","savedDate":"2026-09-15","date":"2026-09-15","dateKind":"Saved source date","declaredDates":["Date: 15 September 2026"],"projectId":"chess","projectIds":["chess"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Dimensional Chess C5: Tension Fields and Tactical Entry Ordering","line":1,"id":"source-h-1"},{"level":2,"title":"Result","line":7,"id":"source-h-2"},{"level":2,"title":"1. Square field","line":32,"id":"source-h-3"},{"level":2,"title":"2. Tension-breaking entries","line":73,"id":"source-h-4"},{"level":2,"title":"3. Search allocation","line":103,"id":"source-h-5"},{"level":2,"title":"4. Frozen fixture results","line":129,"id":"source-h-6"},{"level":2,"title":"5. What survived and what failed","line":150,"id":"source-h-7"},{"level":2,"title":"6. Next falsifiable experiment","line":169,"id":"source-h-8"}],"journey":{"question":{"text":"What does “Dimensional Chess C5: Tension Fields and Tactical Entry Ordering” establish within its declared scope?","label":"The reading question","source":"archive/88c2103b5c5b-Dimensional_Chess_Tension_Field_C5.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The proposed attacker/defender heat map is a useful way to allocate search. It identifies where opposing geometric dependencies overlap, distinguishes raw interaction density from control imbalance, and orders tension-breaking entries before quiet alternatives. It does not establish that the hottest move is best.","label":"Result","source":"archive/88c2103b5c5b-Dimensional_Chess_Tension_Field_C5.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"This record does not separate a verification section. Read its methods, assumptions and original source before treating a claim as checked.","label":"Locate the checks","source":"archive/88c2103b5c5b-Dimensional_Chess_Tension_Field_C5.md","sectionId":"source-record","provenance":"Editorial reading guide"},"nextQuestion":{"text":"Freeze a tactically diverse corpus before scoring it: mates, quiet defensive moves, sacrifices, overloaded defenders, pins, discovered attacks, promotion races, zugzwangs, and deliberately misleading hot squares. Compare at equal node budgets: 1. unordered alpha-beta; 2. checks/captures-first ordering; 3. C5 tension ordering; 4. a standard engine ordering baseline.","label":"6. Next falsifiable experiment","source":"archive/88c2103b5c5b-Dimensional_Chess_Tension_Field_C5.md","sectionId":"source-h-8","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The proposed attacker/defender heat map is a useful way to allocate search. It identifies where opposing geometric dependencies overlap, distinguishes raw interaction density from control imbalance, and orders tension-breaking entries before quiet alternatives. It does not establish that the hottest move is best.","words":971},"archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md":{"url":"archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md","title":"Physical coverage and the electromagnetic wave foundation","kind":"Mathematical note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/Physical_Coverage_And_Gauge_Derivation.md","bytes":21709,"sha256":"88d96126ec54660cfa707f915a74f5197cd669616e10a78ce0f2a4edabf3e8e1","savedDate":"2026-09-21","date":"2026-09-21","dateKind":"Saved source date","declaredDates":[],"projectId":"theory","projectIds":["theory"],"associationBasis":"Explicit project source citation","status":"Original saved source","headings":[{"level":1,"title":"Physical coverage and the electromagnetic wave foundation","line":1,"id":"source-h-1"},{"level":2,"title":"CG.1 — What physical completeness would require","line":5,"id":"source-h-2"},{"level":2,"title":"CG.2 — Coverage ledger and acceptance obligations","line":46,"id":"source-h-3"},{"level":2,"title":"CG.3 — Conditional electromagnetic coupling on a grid","line":77,"id":"source-h-4"},{"level":3,"title":"Assumptions and orientation","line":79,"id":"source-h-5"},{"level":3,"title":"Static and time-dependent gauge covariance","line":124,"id":"source-h-6"},{"level":3,"title":"Probability and charge continuity","line":147,"id":"source-h-7"},{"level":3,"title":"Continuum relation and closed-loop phase","line":171,"id":"source-h-8"},{"level":2,"title":"CG.4 — A field law still needs its own action","line":219,"id":"source-h-9"},{"level":2,"title":"CG.5 — Frozen computation and independent verification","line":270,"id":"source-h-10"},{"level":2,"title":"CG.6 — Release boundary and next work","line":328,"id":"source-h-11"},{"level":2,"title":"CG.7 — Sources and provenance","line":358,"id":"source-h-12"}],"journey":{"question":{"text":"What does “Physical coverage and the electromagnetic wave foundation” establish within its declared scope?","label":"The reading question","source":"archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"Theory of Reality 1.84 · Fixed Grid String Lab 0.9.0 · 21 September 2026","label":"The source’s opening statement","source":"archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"The production implementation assembles an incidence-matrix energy and evolves by a matrix exponential. Three synthetic rings have N=5,9,16, fixed seeds, real potentials, unit-modulus links and normalized complex initial states. The ring spectrum and refinement examples are specified separately. No measured data or fitted physical parameter is used. Units are dimensionless with hbar=1.","label":"CG.5 — Frozen computation and independent verification","source":"archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md","sectionId":"source-h-10","provenance":"Source excerpt"},"nextQuestion":{"text":"This release advances PC-05 and documents the conditional action behind PC-06. It supplies a local continuity law and a consistent charged-wave connection. It does not derive the Standard Model, general relativity, all material properties, the fine-structure constant, or a unique higher-dimensional origin. There is no new measured physical evidence in this release.","label":"CG.6 — Release boundary and next work","source":"archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md","sectionId":"source-h-11","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":0,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Theory of Reality 1.84 · Fixed Grid String Lab 0.9.0 · 21 September 2026","words":2938},"archive/8932ff1185c8-Theory_of_Reality_v1.70_draft.md":{"url":"archive/8932ff1185c8-Theory_of_Reality_v1.70_draft.md","title":"Theory of Reality","kind":"Research manuscript","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/Theory_of_Reality_v1.70_draft.md","bytes":634113,"sha256":"8932ff1185c821eba3fe63458d7cc7fef42724cfc80e3b110aab1566da55f489","savedDate":"2026-09-21","date":"2026-09-21","dateKind":"Saved source date","declaredDates":["Date: 20 September 2026"],"projectId":"hydrogen","projectIds":["hydrogen"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Theory of Reality","line":1,"id":"source-h-1"},{"level":2,"title":"A Projective Seven-Layer Framework for Hidden State, Time, Quantum Observation, Computation, and Testable Physics","line":3,"id":"source-h-2"},{"level":2,"title":"Abstract","line":127,"id":"source-h-3"},{"level":2,"title":"1. Claim discipline","line":143,"id":"source-h-4"},{"level":3,"title":"1.1 Meaning of “prove”","line":167,"id":"source-h-5"},{"level":2,"title":"2. Primitive structure","line":179,"id":"source-h-6"},{"level":3,"title":"Axiom A1: projection coherence","line":202,"id":"source-h-7"},{"level":3,"title":"Axiom A2: coordinate covariance","line":211,"id":"source-h-8"},{"level":3,"title":"Axiom A3: measured probabilities require a measure","line":221,"id":"source-h-9"},{"level":3,"title":"Definition 2.1: fiber","line":233,"id":"source-h-10"},{"level":3,"title":"Definition 2.2: complete compatible state","line":243,"id":"source-h-11"},{"level":2,"title":"3. The seven typed layers","line":262,"id":"source-h-12"},{"level":3,"title":"3.1 Canonical serialization","line":283,"id":"source-h-13"},{"level":3,"title":"Theorem 3.1: canonical projection coherence [M]","line":313,"id":"source-h-14"},{"level":3,"title":"3.2 Is \\(D_7\\) a wall?","line":323,"id":"source-h-15"},{"level":3,"title":"Theorem 3.2: completeness of the finite compatible diagram [M]","line":337,"id":"source-h-16"},{"level":2,"title":"4. Law descent: how an upper layer confines a lower law","line":349,"id":"source-h-17"},{"level":3,"title":"Theorem 4.1: factorization or law-descent theorem [M]","line":353,"id":"source-h-18"},{"level":3,"title":"4.1 Stochastic lower behavior","line":393,"id":"source-h-19"},{"level":3,"title":"4.2 The hidden-mechanism theorem","line":406,"id":"source-h-20"},{"level":3,"title":"Theorem 4.2: coarsest deterministic repair [M]","line":426,"id":"source-h-21"},{"level":3,"title":"Corollary 4.3: operational proof of hidden state [M/E boundary]","line":440,"id":"source-h-22"},{"level":3,"title":"4.3 Conservation-law descent","line":446,"id":"source-h-23"},{"level":2,"title":"5. Effects, causes, and the limit of inverse inference","line":464,"id":"source-h-24"},{"level":3,"title":"5.1 Linear effect model","line":466,"id":"source-h-25"},{"level":3,"title":"5.2 Exact Boolean inverse","line":498,"id":"source-h-26"},{"level":3,"title":"Theorem 5.1: latent relabeling non-identifiability [M]","line":517,"id":"source-h-27"},{"level":3,"title":"5.3 Why an unconstrained \\(G\\) destroys science","line":543,"id":"source-h-28"},{"level":2,"title":"6. Reversible hidden-coordinate transport","line":561,"id":"source-h-29"},{"level":3,"title":"Theorem 6.1: visible-to-hidden ripple [M]","line":579,"id":"source-h-30"},{"level":3,"title":"Theorem 6.2: generic collision-capacity bound [M]","line":597,"id":"source-h-31"},{"level":2,"title":"7. Time, process, loop, and helix","line":619,"id":"source-h-32"},{"level":3,"title":"7.1 A state is not a process","line":621,"id":"source-h-33"},{"level":3,"title":"7.2 Linear and cyclic time","line":651,"id":"source-h-34"},{"level":3,"title":"7.3 Infinite cyclic dimension addressing","line":674,"id":"source-h-35"},{"level":3,"title":"7.4 Cycle twist or monodromy","line":694,"id":"source-h-36"},{"level":3,"title":"7.5 Polarity","line":714,"id":"source-h-37"},{"level":2,"title":"8. Exact increments, ULPs, and computation in bits","line":739,"id":"source-h-38"},{"level":3,"title":"8.1 Typed dyadic scalar","line":741,"id":"source-h-39"},{"level":3,"title":"8.2 Default increments","line":765,"id":"source-h-40"},{"level":3,"title":"8.3 Observer-relative reality ULP","line":781,"id":"source-h-41"},{"level":3,"title":"8.4 Precision towers","line":806,"id":"source-h-42"},{"level":2,"title":"9. Schrödinger's cat in the language","line":830,"id":"source-h-43"},{"level":3,"title":"9.1 Decoherence","line":886,"id":"source-h-44"},{"level":2,"title":"10. Two-slit observation","line":901,"id":"source-h-45"},{"level":2,"title":"11. Quantum computing","line":968,"id":"source-h-46"},{"level":3,"title":"11.1 Layer interpretation for a circuit","line":1003,"id":"source-h-47"},{"level":2,"title":"12. Temperature, quanta, and selective entropy removal","line":1019,"id":"source-h-48"},{"level":3,"title":"12.1 Concrete 5 GHz scale","line":1059,"id":"source-h-49"},{"level":3,"title":"12.2 “Inverse microwave” as anti-Stokes conversion","line":1079,"id":"source-h-50"},{"level":3,"title":"12.3 Active reset","line":1107,"id":"source-h-51"},{"level":3,"title":"12.4 Optimization target","line":1129,"id":"source-h-52"},{"level":2,"title":"13. Typed higher-layer frequencies, magnets, and energy","line":1154,"id":"source-h-53"},{"level":2,"title":"14. Exact mathematical discovery","line":1216,"id":"source-h-54"},{"level":3,"title":"Theorem 14.1: invariant-language completeness [M]","line":1233,"id":"source-h-55"},{"level":2,"title":"15. Real measured prediction","line":1257,"id":"source-h-56"},{"level":3,"title":"15.1 Holdout results [E/C]","line":1285,"id":"source-h-57"},{"level":2,"title":"16. What would constitute evidence for a hidden mechanism?","line":1298,"id":"source-h-58"},{"level":3,"title":"16.1 The target signature","line":1300,"id":"source-h-59"},{"level":3,"title":"16.2 Intervention requirement","line":1316,"id":"source-h-60"},{"level":3,"title":"16.3 Tomography requirement","line":1332,"id":"source-h-61"},{"level":3,"title":"16.4 Model contest","line":1344,"id":"source-h-62"},{"level":2,"title":"17. Can seven-dimensional physics be proved?","line":1371,"id":"source-h-63"},{"level":3,"title":"Theorem 17.1 (replacement): deterministic closure is idempotent [M]","line":1375,"id":"source-h-64"},{"level":3,"title":"17.1 A decisive physical success criterion","line":1391,"id":"source-h-65"},{"level":2,"title":"18. Optional Christian metaphysical interpretation","line":1410,"id":"source-h-66"},{"level":3,"title":"18.1 God as ground, not coordinate","line":1414,"id":"source-h-67"},{"level":3,"title":"18.2 Trinity guardrail","line":1426,"id":"source-h-68"},{"level":3,"title":"18.3 Free choice and authorization","line":1454,"id":"source-h-69"},{"level":3,"title":"18.4 Miracles","line":1483,"id":"source-h-70"},{"level":3,"title":"18.5 Biblical time","line":1493,"id":"source-h-71"},{"level":3,"title":"18.6 Scripture as a finite observer","line":1537,"id":"source-h-72"},{"level":2,"title":"19. Adversarial tests and resolutions","line":1543,"id":"source-h-73"},{"level":2,"title":"20. Computational verification record","line":1567,"id":"source-h-74"},{"level":2,"title":"21. Compact formal statement","line":1603,"id":"source-h-75"},{"level":2,"title":"22. Conclusions","line":1637,"id":"source-h-76"},{"level":2,"title":"References","line":1651,"id":"source-h-77"},{"level":2,"title":"Reproducibility companion [C]","line":1670,"id":"source-h-78"},{"level":2,"title":"Appendix A: Relativity integration [M/C]","line":1676,"id":"source-h-79"},{"level":2,"title":"Appendix B: Three Millennium laboratories [C]","line":1707,"id":"source-h-80"},{"level":2,"title":"Appendix C: D0 polarity and frozen errors [M/C]","line":1746,"id":"source-h-81"},{"level":2,"title":"Appendix D: Independent falsification and the limits of D0 [C]","line":1818,"id":"source-h-82"},{"level":3,"title":"D.1 Exact finite RH certificate [C]","line":1835,"id":"source-h-83"},{"level":3,"title":"D.2 Independent SAT check [C]","line":1851,"id":"source-h-84"},{"level":3,"title":"D.3 Fault recovery with a frozen bias [M/C]","line":1859,"id":"source-h-85"},{"level":3,"title":"D.4 Residual is not distance to solution [M]","line":1889,"id":"source-h-86"},{"level":2,"title":"Appendix E. Restricted proofs and rejected universal estimates [M/C]","line":1911,"id":"source-h-87"},{"level":3,"title":"E.1 A restricted Lagarias theorem [M/C]","line":1919,"id":"source-h-88"},{"level":3,"title":"E.2 All-size pigeonhole error formulas [M/C]","line":1946,"id":"source-h-89"},{"level":3,"title":"E.3 Exact fluid counterexamples to proposed estimates [M]","line":1973,"id":"source-h-90"},{"level":3,"title":"E.4 The meaning of a frozen failure [M/C]","line":2017,"id":"source-h-91"},{"level":2,"title":"Appendix F. Independent certificates and exact counting projections [C]","line":2032,"id":"source-h-92"},{"level":3,"title":"F.1 Rational lower witnesses [M/C]","line":2039,"id":"source-h-93"},{"level":3,"title":"F.2 A counting law that survives projection [M/C]","line":2059,"id":"source-h-94"},{"level":3,"title":"F.3 Independent fluid algebra [C]","line":2100,"id":"source-h-95"},{"level":3,"title":"F.4 Rejection tests and remaining trust [C]","line":2110,"id":"source-h-96"},{"level":2,"title":"Appendix G. Arguments at the remaining proof gaps [M/C]","line":2132,"id":"source-h-97"},{"level":3,"title":"G.1 Removing the prime-count restriction from a bounded RH verification [M/C, finite coverage to 1e24 conditional on unpublished exact-arithmetic run]","line":2139,"id":"source-h-98"},{"level":3,"title":"G.2 A lower-bound extension that cannot work [M]","line":2193,"id":"source-h-99"},{"level":3,"title":"G.3 An exact continuation-summary bound [M]","line":2216,"id":"source-h-100"},{"level":3,"title":"G.4 Why the quadratic fluid strategy fails more generally [M]","line":2236,"id":"source-h-101"},{"level":3,"title":"G.5 Evidence boundary [C]","line":2267,"id":"source-h-102"},{"level":2,"title":"Appendix H. A computable sufficient condition for all-time fluid smoothness [M/C]","line":2276,"id":"source-h-103"},{"level":3,"title":"H.1 The conditional all-time statement [M]","line":2287,"id":"source-h-104"},{"level":3,"title":"H.2 The estimate and its continuation argument [M]","line":2312,"id":"source-h-105"},{"level":3,"title":"H.3 What the computer verifies [C]","line":2351,"id":"source-h-106"},{"level":3,"title":"H.4 The boundary that remains [M/C]","line":2372,"id":"source-h-107"},{"level":2,"title":"Appendix I. Relative error control beyond the total-smallness condition [M/C]","line":2392,"id":"source-h-108"},{"level":3,"title":"I.1 A reference trajectory and its full error [M]","line":2401,"id":"source-h-109"},{"level":3,"title":"I.2 An all-time specialization the engine computes [M/C]","line":2427,"id":"source-h-110"},{"level":3,"title":"I.3 The next engineering prerequisite [C]","line":2467,"id":"source-h-111"},{"level":2,"title":"Appendix J. Computed references with continuous-time and full-mode certificates [C, conditional on unpublished certificate]","line":2489,"id":"source-h-112"},{"level":3,"title":"J.1 Continuous-time polynomial bounds [M]","line":2498,"id":"source-h-113"},{"level":3,"title":"J.2 Every omitted output mode of the reference residual [M/C]","line":2519,"id":"source-h-114"},{"level":3,"title":"J.3 An affine supersolution checked by algebra [M]","line":2537,"id":"source-h-115"},{"level":3,"title":"J.4 Executed evidence and its limits [C, conditional on unpublished certificate]","line":2569,"id":"source-h-116"},{"level":2,"title":"Appendix K. A sharper error estimate that certifies a previously unresolved input [M/C, conditional on unpublished certificate]","line":2604,"id":"source-h-117"},{"level":3,"title":"K.1 The same input before and after the changes [C]","line":2611,"id":"source-h-118"},{"level":3,"title":"K.2 Exact constrained quadratic optimization [M]","line":2637,"id":"source-h-119"},{"level":3,"title":"K.3 Nonlinear references with accounted-for rounding [C]","line":2687,"id":"source-h-120"},{"level":3,"title":"K.4 Checked outcome and the next failure [C, conditional on unpublished certificate]","line":2707,"id":"source-h-121"},{"level":2,"title":"Appendix L. Directing the engine toward valid extension arguments [C, conditional on unpublished certificate]","line":2743,"id":"source-h-122"},{"level":3,"title":"L.1 The shared objective [H]","line":2748,"id":"source-h-123"},{"level":3,"title":"L.2 A finite certificate with unbounded path-length coverage [M/C]","line":2763,"id":"source-h-124"},{"level":3,"title":"L.3 Refine the distinctions responsible for the fluid residual [C]","line":2800,"id":"source-h-125"},{"level":3,"title":"L.4 Local error budgets [M]","line":2822,"id":"source-h-126"},{"level":3,"title":"L.5 The new accepted input and the common audit [C, conditional on unpublished certificate]","line":2856,"id":"source-h-127"},{"level":2,"title":"Appendix M. Hypothetical universes and checked proof transfer [M/C]","line":2908,"id":"source-h-128"},{"level":3,"title":"M.1. A contracting comparison can close an error loop [M]","line":2928,"id":"source-h-129"},{"level":3,"title":"M.2. A finite dynamics-to-SAT bridge with complete coverage [M/C]","line":2962,"id":"source-h-130"},{"level":3,"title":"M.3. Transfer through a verified state map [M/C]","line":2991,"id":"source-h-131"},{"level":2,"title":"Appendix N. Null-axis probes, observability, and a fluid projection obstruction [M/C]","line":3023,"id":"source-h-132"},{"level":3,"title":"N.1. Linear hidden directions and allowed transformations [M]","line":3031,"id":"source-h-133"},{"level":3,"title":"N.2. Signed recovery from paired squared-distance readings [M]","line":3062,"id":"source-h-134"},{"level":3,"title":"N.3. No autonomous law for any fixed energy-derivative jet of all shears [M]","line":3091,"id":"source-h-135"},{"level":3,"title":"N.4. Two further shortcut failures and validation [M/C]","line":3136,"id":"source-h-136"},{"level":2,"title":"Appendix O. Active experiments, model rejection, and correction of the hierarchy [M/C]","line":3166,"id":"source-h-137"},{"level":3,"title":"O.1. Intervention-relative cause classes [M]","line":3170,"id":"source-h-138"},{"level":3,"title":"O.2. Choose a discriminating experiment before seeing its outcome [M/C]","line":3185,"id":"source-h-139"},{"level":3,"title":"O.3. A concrete intervention that breaks an exact delay ambiguity [M/H]","line":3198,"id":"source-h-140"},{"level":3,"title":"O.4. Evidence and limits of this release [C]","line":3215,"id":"source-h-141"},{"level":3,"title":"O.5. A revisable theory [H/T]","line":3225,"id":"source-h-142"},{"level":2,"title":"Appendix P. Capture, generator discovery, and the limits of an observed cycle [M/C]","line":3231,"id":"source-h-143"},{"level":3,"title":"P.1. Keep the event model's semantics explicit [M]","line":3235,"id":"source-h-144"},{"level":3,"title":"P.2. Finite observations do not select a universal generator language [M]","line":3249,"id":"source-h-145"},{"level":3,"title":"P.3. Positive theorem: continuation in a bounded recurrence class [M]","line":3261,"id":"source-h-146"},{"level":3,"title":"P.4. New computation and repaired failures [C]","line":3273,"id":"source-h-147"},{"level":2,"title":"Appendix Q. Repeated model checks with a bounded false-rejection budget [M/C]","line":3287,"id":"source-h-148"},{"level":3,"title":"Q.1. A single-observation cutoff is not an investigation-wide guarantee [M]","line":3291,"id":"source-h-149"},{"level":3,"title":"Q.2. Written guarantee and its exact assumptions [M]","line":3301,"id":"source-h-150"},{"level":3,"title":"Q.3. Fresh synthetic evidence and an independent check [C]","line":3322,"id":"source-h-151"},{"level":3,"title":"Q.4. Research context, model revision, and next test [H]","line":3336,"id":"source-h-152"},{"level":2,"title":"Appendix R. Accumulating weak residual evidence without optional-stopping inflation","line":3342,"id":"source-h-153"},{"level":3,"title":"R.1. Bounded target and assumptions","line":3346,"id":"source-h-154"},{"level":3,"title":"R.2. Written anytime-valid guarantee","line":3373,"id":"source-h-155"},{"level":3,"title":"R.3. Frozen synthetic validation","line":3391,"id":"source-h-156"},{"level":3,"title":"R.4. Relation to current primary research","line":3408,"id":"source-h-157"},{"level":3,"title":"R.5. What changed and what remains open","line":3412,"id":"source-h-158"},{"level":2,"title":"Appendix S. Unknown fixed scale without pretending to know the variance","line":3418,"id":"source-h-159"},{"level":3,"title":"S.1. Bounded question and exact model class","line":3422,"id":"source-h-160"},{"level":3,"title":"S.2. Established theorem and a crucial filtration boundary","line":3446,"id":"source-h-161"},{"level":3,"title":"S.3. Frozen finite computation and synthetic tests","line":3460,"id":"source-h-162"},{"level":3,"title":"S.4. Result, limits, and next test","line":3479,"id":"source-h-163"},{"level":2,"title":"Appendix T. One shared error budget for complementary model checks","line":3485,"id":"source-h-164"},{"level":3,"title":"T.1. The composition problem","line":3489,"id":"source-h-165"},{"level":3,"title":"T.2. Written joint guarantee","line":3495,"id":"source-h-166"},{"level":3,"title":"T.3. Frozen synthetic validation","line":3517,"id":"source-h-167"},{"level":3,"title":"T.4. Supported change and next test","line":3539,"id":"source-h-168"},{"level":2,"title":"Appendix U. Accumulating moderate Gaussian scale evidence","line":3545,"id":"source-h-169"},{"level":3,"title":"U.1. Bounded question and fixed alternatives","line":3549,"id":"source-h-170"},{"level":3,"title":"U.2. Written anytime guarantee and interpretation boundary","line":3578,"id":"source-h-171"},{"level":3,"title":"U.3. Frozen synthetic test and independent replay","line":3592,"id":"source-h-172"},{"level":3,"title":"U.4. Supported change, limitations, and next test","line":3612,"id":"source-h-173"},{"level":2,"title":"Appendix V. A common-filtration mean-plus-variance process","line":3618,"id":"source-h-174"},{"level":3,"title":"V.1. Why this is not a detector substitution","line":3622,"id":"source-h-175"},{"level":3,"title":"V.2. Written fixed-mixture guarantee","line":3628,"id":"source-h-176"},{"level":3,"title":"V.3. Frozen paired comparison","line":3653,"id":"source-h-177"},{"level":3,"title":"V.4. Supported change and unresolved design choice","line":3676,"id":"source-h-178"},{"level":2,"title":"Appendix W. A trained, frozen mean/variance/point allocation","line":3685,"id":"source-h-179"},{"level":3,"title":"W.1. Bounded question and predeclared separation","line":3689,"id":"source-h-180"},{"level":3,"title":"W.2. Written anytime bound","line":3699,"id":"source-h-181"},{"level":3,"title":"W.3. One held-out synthetic validation","line":3730,"id":"source-h-182"},{"level":3,"title":"W.4. Supported change, limits, and next test","line":3752,"id":"source-h-183"},{"level":2,"title":"Appendix X. Allocation-selection stability and a boundary warning","line":3762,"id":"source-h-184"},{"level":3,"title":"X.1. Bounded question and sealed-data rule","line":3766,"id":"source-h-185"},{"level":3,"title":"X.2. Finite stability results","line":3774,"id":"source-h-186"},{"level":3,"title":"X.3. Separate synthetic reference and counterexample to optimality","line":3791,"id":"source-h-187"},{"level":3,"title":"X.4. Supported correction, evidence classes, and next test","line":3808,"id":"source-h-188"},{"level":2,"title":"Appendix Y. Expanded allocation boundaries refute the released grid optimum","line":3818,"id":"source-h-189"},{"level":3,"title":"Y.1. Assumptions and frozen training-only protocol","line":3822,"id":"source-h-190"},{"level":3,"title":"Y.2. Finite results and counterexamples","line":3842,"id":"source-h-191"},{"level":3,"title":"Y.3. Supported correction, limits, and next test","line":3862,"id":"source-h-192"},{"level":2,"title":"Appendix Z. Fresh paired validation rejects a universal allocation replacement","line":3874,"id":"source-h-193"},{"level":3,"title":"Z.1. Frozen question, assumptions, and decision rule","line":3878,"id":"source-h-194"},{"level":3,"title":"Z.2. Fresh synthetic results and counterexample","line":3893,"id":"source-h-195"},{"level":3,"title":"Z.3. Supported correction, evidence classes, and next test","line":3915,"id":"source-h-196"},{"level":2,"title":"Appendix AA. An anytime-valid sign process for a declared heavy-tail class","line":3925,"id":"source-h-197"},{"level":3,"title":"AA.1. The bounded question and null class","line":3929,"id":"source-h-198"},{"level":3,"title":"AA.2. Written probability proof","line":3943,"id":"source-h-199"},{"level":3,"title":"AA.3. Frozen finite synthetic validation","line":3974,"id":"source-h-200"},{"level":3,"title":"AA.4. Counterexamples and interpretation","line":3996,"id":"source-h-201"},{"level":3,"title":"AA.5. Supported change, evidence classes, and next test","line":4004,"id":"source-h-202"},{"level":2,"title":"Appendix AB. Composite Born prediction, coded lift search, and projection collisions","line":4012,"id":"source-h-203"},{"level":3,"title":"AB.1. One theory, three different uses of seven and eight","line":4016,"id":"source-h-204"},{"level":3,"title":"AB.2. Exact and composite Born walls","line":4030,"id":"source-h-205"},{"level":3,"title":"AB.3. Prefix-coded dimensional lifts","line":4068,"id":"source-h-206"},{"level":3,"title":"AB.4. Projection collisions are universal decoder failures","line":4105,"id":"source-h-207"},{"level":3,"title":"AB.5. Foundational assumption map","line":4141,"id":"source-h-208"},{"level":3,"title":"AB.6. Executed evidence, preserved failures, and next test","line":4165,"id":"source-h-209"},{"level":2,"title":"Appendix AC. Information rate, adversarial tripwires, and the wall ledger","line":4190,"id":"source-h-210"},{"level":3,"title":"AC.1. General Born-evidence decomposition","line":4194,"id":"source-h-211"},{"level":3,"title":"AC.2. No finite data determine an unrestricted continuation","line":4264,"id":"source-h-212"},{"level":3,"title":"AC.3. Three-channel tripwire","line":4272,"id":"source-h-213"},{"level":3,"title":"AC.4. Bell, contextuality, and measurement-independence routes","line":4306,"id":"source-h-214"},{"level":3,"title":"AC.5. The thirteen walls and the next physical test","line":4324,"id":"source-h-215"},{"level":2,"title":"Appendix AD. P3-R1: an executable single-device hardware frontier","line":4346,"id":"source-h-216"},{"level":3,"title":"AD.1. Bounded physical question and claim ceiling","line":4348,"id":"source-h-217"},{"level":3,"title":"AD.2. An exactly marginal-preserving eight-cycle grammar","line":4362,"id":"source-h-218"},{"level":3,"title":"AD.3. Composite-null score and delayed-setting tripwire","line":4398,"id":"source-h-219"},{"level":3,"title":"AD.4. Executed adversarial software evidence","line":4418,"id":"source-h-220"},{"level":3,"title":"AD.5. Activation boundary and next honest wall","line":4430,"id":"source-h-221"},{"level":2,"title":"Appendix AE. Dimensional Chess C1: exact solution of a closed game universe","line":4438,"id":"source-h-222"},{"level":3,"title":"AE.1. Finite does not mean computationally feasible","line":4440,"id":"source-h-223"},{"level":3,"title":"AE.2. A collision-free symmetry lift","line":4452,"id":"source-h-224"},{"level":3,"title":"AE.3. Time cycles become a least fixed point","line":4472,"id":"source-h-225"},{"level":3,"title":"AE.4. Exact result and proof certificate","line":4488,"id":"source-h-226"},{"level":3,"title":"AE.5. The wall exposed by chess","line":4502,"id":"source-h-227"},{"level":2,"title":"Appendix AF. Dimensional Chess C2: interval bounds, certified pruning, and the full-chess gate","line":4518,"id":"source-h-228"},{"level":3,"title":"AF.1. Freeze the target before optimizing it","line":4520,"id":"source-h-229"},{"level":3,"title":"AF.2. D-/D+ becomes interval minimax","line":4551,"id":"source-h-230"},{"level":3,"title":"AF.3. Exact Disadvantage Pruning Theorem","line":4576,"id":"source-h-231"},{"level":3,"title":"AF.4. Exact KQK extension","line":4603,"id":"source-h-232"},{"level":3,"title":"AF.5. Strong future-law identity fails as the large quotient","line":4628,"id":"source-h-233"},{"level":3,"title":"AF.6. Measured ceiling of disadvantage pruning","line":4648,"id":"source-h-234"},{"level":3,"title":"AF.7. Counterexample-guided dimensional refinement","line":4664,"id":"source-h-235"},{"level":3,"title":"AF.8. Chess, quantum algorithms, and physical dimensions are separate gates","line":4683,"id":"source-h-236"},{"level":3,"title":"AF.9. Claim gate and next rung","line":4703,"id":"source-h-237"},{"level":2,"title":"Appendix AG. Dimensional Chess C3: the complete state reaches the initial position","line":4720,"id":"source-h-238"},{"level":3,"title":"AG.1. The legal-transition wall is crossed, not the solution wall","line":4722,"id":"source-h-239"},{"level":3,"title":"AG.2. Move-generation audit","line":4751,"id":"source-h-240"},{"level":3,"title":"AG.3. First exact interval probe of the normal start","line":4774,"id":"source-h-241"},{"level":3,"title":"AG.4. Forcing dominance formalizes ignored legal moves","line":4814,"id":"source-h-242"},{"level":3,"title":"AG.5. Updated wall and claim gate","line":4869,"id":"source-h-243"},{"level":2,"title":"Appendix AH. Dimensional Chess C4: constraint waves and relational phase","line":4892,"id":"source-h-244"},{"level":3,"title":"AH.1. Human search is selective constraint propagation","line":4894,"id":"source-h-245"},{"level":3,"title":"AH.2. Table-hidden geometric language","line":4934,"id":"source-h-246"},{"level":3,"title":"AH.3. Exact table-hidden results","line":4955,"id":"source-h-247"},{"level":3,"title":"AH.4. Predictive success does not equal scaling","line":4982,"id":"source-h-248"},{"level":3,"title":"AH.5. Constraint-delta lift","line":4995,"id":"source-h-249"},{"level":2,"title":"Appendix AI. Dimensional Chess C5: local tension and tactical entry","line":5038,"id":"source-h-250"},{"level":3,"title":"AI.1. Attack multiplicity is a field, not a verdict","line":5040,"id":"source-h-251"},{"level":3,"title":"AI.2. Tension-breaking entry","line":5079,"id":"source-h-252"},{"level":3,"title":"AI.3. Adversarial ordering","line":5103,"id":"source-h-253"},{"level":3,"title":"AI.4. Executable fixture and independent audit","line":5119,"id":"source-h-254"},{"level":3,"title":"AI.5. Counterexample and boundary","line":5148,"id":"source-h-255"},{"level":2,"title":"Appendix AJ. Dimensional Chess C6: legal exchange dependencies","line":5168,"id":"source-h-256"},{"level":3,"title":"AJ.1. From simultaneous counts to ordered interactions","line":5170,"id":"source-h-257"},{"level":3,"title":"AJ.2. Exact bounded proof layer","line":5209,"id":"source-h-258"},{"level":3,"title":"AJ.3. Deterministic recapture corpus","line":5230,"id":"source-h-259"},{"level":3,"title":"AJ.4. Independent audit","line":5252,"id":"source-h-260"},{"level":3,"title":"AJ.5. Consequence for the full-chess program","line":5262,"id":"source-h-261"},{"level":2,"title":"Appendix AK. Initial-position mate frontier R1","line":5277,"id":"source-h-262"},{"level":3,"title":"AK.1. Direct run on the orthodox root","line":5279,"id":"source-h-263"},{"level":3,"title":"AK.2. Measured frontier","line":5301,"id":"source-h-264"},{"level":3,"title":"AK.3. Independent result and ordering falsification","line":5312,"id":"source-h-265"},{"level":3,"title":"AK.4. Dual proof direction","line":5329,"id":"source-h-266"},{"level":2,"title":"Appendix AL. Dimensional Chess C7: horizon-safe projection","line":5352,"id":"source-h-267"},{"level":3,"title":"AL.1. Repetition coordinates have a finite activation horizon","line":5354,"id":"source-h-268"},{"level":3,"title":"AL.2. Polarity-aware ordering test","line":5386,"id":"source-h-269"},{"level":3,"title":"AL.3. Seven-ply quotient check","line":5401,"id":"source-h-270"},{"level":3,"title":"AL.4. Independently verified nine-ply frontier","line":5415,"id":"source-h-271"},{"level":3,"title":"AL.5. Boundary of the result","line":5437,"id":"source-h-272"},{"level":2,"title":"Appendix AM. Dimensional Chess C8: movement-frequency relations","line":5469,"id":"source-h-273"},{"level":3,"title":"AM.1. Relational move phase","line":5471,"id":"source-h-274"},{"level":3,"title":"AM.2. Learned pattern","line":5499,"id":"source-h-275"},{"level":3,"title":"AM.3. Transfer to seven and nine plies","line":5512,"id":"source-h-276"},{"level":3,"title":"AM.4. Counterexamples to stronger frequency claims","line":5537,"id":"source-h-277"},{"level":3,"title":"AM.5. Audit and boundary","line":5552,"id":"source-h-278"},{"level":2,"title":"Appendix AN. Dependent-sign evidence under a declared Markov null","line":5573,"id":"source-h-279"},{"level":3,"title":"AN.1. The bounded question","line":5575,"id":"source-h-280"},{"level":3,"title":"AN.2. Predictive likelihood-ratio martingale","line":5599,"id":"source-h-281"},{"level":3,"title":"AN.3. Fresh finite synthetic validation","line":5644,"id":"source-h-282"},{"level":3,"title":"AN.4. Counterexamples and boundary","line":5670,"id":"source-h-283"},{"level":2,"title":"Appendix AO. Hydrogen spectroscopy clock and tangent-rotor holdout","line":5689,"id":"source-h-284"},{"level":3,"title":"AO.1. What real data can calibrate","line":5691,"id":"source-h-285"},{"level":3,"title":"AO.2. Frozen spatial discrimination protocol","line":5726,"id":"source-h-286"},{"level":3,"title":"AO.3. Held-out result and counterexample","line":5741,"id":"source-h-287"},{"level":3,"title":"AO.4. Verification and evidence boundary","line":5763,"id":"source-h-288"},{"level":2,"title":"Appendix AP. Temperature, phase direction, and bounded missing components","line":5790,"id":"source-h-289"},{"level":3,"title":"AP.1. Why a failed model does not select one cause","line":5792,"id":"source-h-290"},{"level":3,"title":"AP.2. Frozen latent-component rescue","line":5809,"id":"source-h-291"},{"level":3,"title":"AP.3. Temperature does not reverse the phase clock","line":5833,"id":"source-h-292"},{"level":3,"title":"AP.4. Melting delay and evidence boundary","line":5868,"id":"source-h-293"},{"level":2,"title":"Appendix AQ. Electromagnetic correction ladder before higher-dimensional forces","line":5889,"id":"source-h-294"},{"level":3,"title":"AQ.1. Correction: electromagnetism was already present","line":5891,"id":"source-h-295"},{"level":3,"title":"AQ.2. Frozen H0/H1/H2 ladder","line":5912,"id":"source-h-296"},{"level":3,"title":"AQ.3. Result","line":5954,"id":"source-h-297"},{"level":3,"title":"AQ.4. Residual budget and higher-dimensional admission rule","line":5975,"id":"source-h-298"},{"level":2,"title":"Appendix AR. Fixed-grid and fixed-tick falsification engine","line":6004,"id":"source-h-299"},{"level":3,"title":"AR.1. Two hypotheses that must not be conflated","line":6006,"id":"source-h-300"},{"level":3,"title":"AR.2. Interval decision and non-identification theorem","line":6032,"id":"source-h-301"},{"level":3,"title":"AR.3. Frozen hydrogen-spectroscopy example","line":6065,"id":"source-h-302"},{"level":3,"title":"AR.4. Exact four-coordinate discrete string","line":6095,"id":"source-h-303"},{"level":3,"title":"AR.5. Failure criterion and next physical gate","line":6128,"id":"source-h-304"},{"level":2,"title":"Appendix AS. Geometry, phase boundaries, and conductivity collisions","line":6148,"id":"source-h-305"},{"level":3,"title":"AS.1. Scope and type discipline","line":6150,"id":"source-h-306"},{"level":3,"title":"AS.2. A representation-collision bound","line":6167,"id":"source-h-307"},{"level":3,"title":"AS.3. Frozen same-formula molecular test","line":6190,"id":"source-h-308"},{"level":3,"title":"AS.4. Counterexamples to one-dimensional harmony","line":6225,"id":"source-h-309"},{"level":3,"title":"AS.5. Verification, interpretation, and next test","line":6249,"id":"source-h-310"},{"level":2,"title":"Appendix AT. Property-specific transfer across alkane isomers","line":6278,"id":"source-h-311"},{"level":3,"title":"AT.1. Scope and frozen split","line":6280,"id":"source-h-312"},{"level":3,"title":"AT.1a. The frozen data table (added in revision 1.69)","line":6317,"id":"source-h-313"},{"level":3,"title":"AT.2. Held-out boiling result","line":6385,"id":"source-h-314"},{"level":3,"title":"AT.3. Fusion counterexample","line":6402,"id":"source-h-315"},{"level":3,"title":"AT.4. What a residual can and cannot establish","line":6424,"id":"source-h-316"},{"level":3,"title":"AT.5. Verification and next test","line":6447,"id":"source-h-317"},{"level":2,"title":"Appendix AU. Latent rotation matrices and the inverse-projection boundary","line":6468,"id":"source-h-318"},{"level":3,"title":"AU.1. Question and evidence types","line":6470,"id":"source-h-319"},{"level":3,"title":"AU.2. Explicit five-coordinate dynamics and 3D projection","line":6493,"id":"source-h-320"},{"level":3,"title":"AU.3. Property coordinates and the relabeling counterexample","line":6555,"id":"source-h-321"},{"level":3,"title":"AU.4. Two independent non-identifiability theorems","line":6579,"id":"source-h-322"},{"level":3,"title":"AU.5. Result, limitations, and next test","line":6611,"id":"source-h-323"},{"level":2,"title":"Appendix AV. Water harmonics as a coupled projection experiment","line":6645,"id":"source-h-324"},{"level":3,"title":"AV.1. Scope and calibrated three-dimensional inputs","line":6647,"id":"source-h-325"},{"level":3,"title":"AV.2. Five coordinates per molecule and a norm-preserving coupling","line":6679,"id":"source-h-326"},{"level":3,"title":"AV.3. Three-dimensional rendering and the hidden-null control","line":6722,"id":"source-h-327"},{"level":3,"title":"AV.4. Executed evidence and its limits","line":6756,"id":"source-h-328"},{"level":2,"title":"Appendix AW. Water origami and the oscilloscope observation boundary","line":6795,"id":"source-h-329"},{"level":3,"title":"AW.1. Ordinary charge and dielectric baseline","line":6797,"id":"source-h-330"},{"level":3,"title":"AW.2. Origami as a many-to-one observation map","line":6843,"id":"source-h-331"},{"level":3,"title":"AW.3. Executed oscilloscope and counterexamples","line":6881,"id":"source-h-332"},{"level":3,"title":"AW.4. Evidence type, limitations, and next test","line":6907,"id":"source-h-333"},{"level":2,"title":"Appendix AX. Sunlight, moving water, and a finite visual observer","line":6942,"id":"source-h-334"},{"level":3,"title":"AX.1. Bounded question and ordinary optical baseline","line":6944,"id":"source-h-335"},{"level":3,"title":"AX.2. Spectral observation and the metamer counterexample","line":6991,"id":"source-h-336"},{"level":3,"title":"AX.3. Why the animation is not a hologram","line":7026,"id":"source-h-337"},{"level":3,"title":"AX.4. Executed evidence, limits, and next test","line":7051,"id":"source-h-338"},{"level":2,"title":"Appendix AY. Water-drop acoustics and the observer-rate boundary","line":7093,"id":"source-h-339"},{"level":3,"title":"AY.1. Bounded question and declared impact","line":7095,"id":"source-h-340"},{"level":3,"title":"AY.2. Entrained-bubble pitch and airborne pressure","line":7128,"id":"source-h-341"},{"level":3,"title":"AY.3. Why neither frame rate nor pitch is a unique inverse","line":7167,"id":"source-h-342"},{"level":3,"title":"AY.4. Executed evidence, limits, and next test","line":7194,"id":"source-h-343"},{"level":2,"title":"Appendix AZ. Bubble hidden-variable inverse and observation fibers","line":7237,"id":"source-h-344"},{"level":3,"title":"AZ.1. Bounded question and correction of scope","line":7239,"id":"source-h-345"},{"level":3,"title":"AZ.2. Exact radius--thermal-response observation fiber","line":7287,"id":"source-h-346"},{"level":3,"title":"AZ.3. Rank statement and what measurement must add","line":7350,"id":"source-h-347"},{"level":3,"title":"AZ.4. Evidence ledger, limitations, and next test","line":7386,"id":"source-h-348"},{"level":2,"title":"Appendix BA. Collective vibrational families and thermodynamic phase","line":7433,"id":"source-h-349"},{"level":3,"title":"BA.1. The bounded question and an exact counterexample","line":7435,"id":"source-h-350"},{"level":3,"title":"BA.2. A collective spectrum that can express both diffusion and vibration","line":7471,"id":"source-h-351"},{"level":3,"title":"BA.3. What was checked and what remains empirical","line":7523,"id":"source-h-352"},{"level":2,"title":"Appendix BB. Five-dimensional harmonies and a finite three-dimensional observer","line":7570,"id":"source-h-353"},{"level":3,"title":"BB.1. Bounded model and complete linear harmony theorem","line":7572,"id":"source-h-354"},{"level":3,"title":"BB.2. A product taxonomy rather than one “harmony” label","line":7622,"id":"source-h-355"},{"level":3,"title":"BB.3. What a finite observer does","line":7665,"id":"source-h-356"},{"level":3,"title":"BB.4. Hidden-basis gauge and the inverse boundary","line":7700,"id":"source-h-357"},{"level":3,"title":"BB.5. Finite validation and the next falsification","line":7731,"id":"source-h-358"},{"level":2,"title":"Appendix BC — Hydrogen spectroscopy gate for the two-harmony observer (revision 1.54)","line":7772,"id":"source-h-359"},{"level":2,"title":"Appendix BD — Multidimensional vector observers (revision 1.55)","line":7826,"id":"source-h-360"},{"level":3,"title":"BD.1. What one observer cannot see","line":7848,"id":"source-h-361"},{"level":3,"title":"BD.2. When several observers recover one common state","line":7868,"id":"source-h-362"},{"level":3,"title":"BD.3. Observers do not manufacture harmonies","line":7892,"id":"source-h-363"},{"level":3,"title":"BD.4. Evidence boundary","line":7921,"id":"source-h-364"},{"level":2,"title":"Appendix BE — Hydrogen transition holdout (revision 1.56)","line":7938,"id":"source-h-365"},{"level":3,"title":"BE.1. Frozen data split and conversion","line":7947,"id":"source-h-366"},{"level":3,"title":"BE.2. Two bounded laws","line":7975,"id":"source-h-367"},{"level":3,"title":"BE.3. Held-out result","line":8001,"id":"source-h-368"},{"level":3,"title":"BE.4. Exact finite-prefix counterexample","line":8024,"id":"source-h-369"},{"level":3,"title":"BE.5. Evidence boundary and next gate","line":8050,"id":"source-h-370"},{"level":2,"title":"Appendix BF — Hydrogen isotope correction ladder (revision 1.57)","line":8081,"id":"source-h-371"},{"level":3,"title":"BF.1. Frozen measured target and ordinary reference","line":8088,"id":"source-h-372"},{"level":3,"title":"BF.2. Explicit finite-range proxy","line":8139,"id":"source-h-373"},{"level":3,"title":"BF.3. Exact range/coupling non-identifiability","line":8174,"id":"source-h-374"},{"level":3,"title":"BF.4. Decision, limitations, and next test","line":8197,"id":"source-h-375"},{"level":2,"title":"Appendix BG — Frozen hydrogen-isotope holdout (revision 1.58)","line":8223,"id":"source-h-376"},{"level":3,"title":"BG.1. Frozen operator and historical target","line":8230,"id":"source-h-377"},{"level":3,"title":"BG.2. Ordinary reference and correlated uncertainty","line":8272,"id":"source-h-378"},{"level":3,"title":"BG.3. Decision and resolution limit","line":8309,"id":"source-h-379"},{"level":2,"title":"Appendix BH — Conserved quantum flow and observable harmonics (revision 1.59)","line":8346,"id":"source-h-380"},{"level":3,"title":"BH.1. Electromagnetic evolution and continuity","line":8353,"id":"source-h-381"},{"level":3,"title":"BH.2. Dipole harmonic and ideal rate","line":8411,"id":"source-h-382"},{"level":3,"title":"BH.3. Selection rules filter raw harmonics","line":8456,"id":"source-h-383"},{"level":3,"title":"BH.4. Evidence classes, decision, and next gate","line":8480,"id":"source-h-384"},{"level":2,"title":"Appendix BI — Golden-ratio exactness and coincidence audit (revision 1.60)","line":8521,"id":"source-h-385"},{"level":3,"title":"BI.1. Canonical golden quantities","line":8528,"id":"source-h-386"},{"level":3,"title":"BI.2. Where \\(\\varphi\\) is exact","line":8586,"id":"source-h-387"},{"level":3,"title":"BI.3. Exact exclusion from the ideal hydrogen gap ratios","line":8643,"id":"source-h-388"},{"level":3,"title":"BI.4. Fixed grids cannot contain the exact golden turn","line":8682,"id":"source-h-389"},{"level":3,"title":"BI.5. Measured manifestations do not transfer automatically","line":8711,"id":"source-h-390"},{"level":2,"title":"Appendix BJ. Forward observable compiler and the quantum light boundary","line":8756,"id":"source-h-391"},{"level":3,"title":"BJ.1. From “display everything” to a typed forward map","line":8758,"id":"source-h-392"},{"level":3,"title":"BJ.2. Coherent electromagnetic projection","line":8792,"id":"source-h-393"},{"level":3,"title":"BJ.3. Exact counterexample to a complete classical projection","line":8841,"id":"source-h-394"},{"level":3,"title":"BJ.4. Verification, evidence type, and boundary","line":8882,"id":"source-h-395"},{"level":2,"title":"Appendix BK. All-element atomic projection atlas","line":8919,"id":"source-h-396"},{"level":3,"title":"BK.1. The word “shape” needs an observer","line":8921,"id":"source-h-397"},{"level":3,"title":"BK.2. Exact angular result","line":8947,"id":"source-h-398"},{"level":3,"title":"BK.3. All-118 finite atlas","line":8976,"id":"source-h-399"},{"level":3,"title":"BK.4. Verification and counterexample","line":9017,"id":"source-h-400"},{"level":2,"title":"Appendix BL. Bulk gold and silver color observer","line":9068,"id":"source-h-401"},{"level":3,"title":"BL.1. The corrected object of study","line":9070,"id":"source-h-402"},{"level":3,"title":"BL.2. Measured-input Fresnel map","line":9088,"id":"source-h-403"},{"level":3,"title":"BL.3. Finite result and counterexample","line":9137,"id":"source-h-404"},{"level":3,"title":"BL.4. Verification, evidence type, and boundary","line":9168,"id":"source-h-405"},{"level":2,"title":"Appendix BM. Frozen interband-response holdout","line":9217,"id":"source-h-406"},{"level":3,"title":"BM.1. The bounded question","line":9219,"id":"source-h-407"},{"level":3,"title":"BM.2. Frozen equations and split","line":9234,"id":"source-h-408"},{"level":3,"title":"BM.3. Held-out result","line":9280,"id":"source-h-409"},{"level":3,"title":"BM.4. Counterexamples and model strain","line":9303,"id":"source-h-410"},{"level":3,"title":"BM.5. Verification and evidence type","line":9327,"id":"source-h-411"},{"level":2,"title":"Appendix BN. Frozen gold/silver external-validation contract","line":9377,"id":"source-h-412"},{"level":3,"title":"BN.1. What is frozen","line":9379,"id":"source-h-413"},{"level":3,"title":"BN.2. Evaluation-only rule","line":9406,"id":"source-h-414"},{"level":3,"title":"BN.3. Verification and boundary","line":9430,"id":"source-h-415"},{"level":2,"title":"Appendix BO: Dimension evidence requires a distinguishing physical constraint (revision 1.66)","line":9464,"id":"source-h-416"},{"level":3,"title":"BO.1. The bounded question","line":9466,"id":"source-h-417"},{"level":3,"title":"BO.2. Projection-equivalence theorem","line":9481,"id":"source-h-418"},{"level":3,"title":"BO.3. What a constrained extra-dimensional signature can look like","line":9522,"id":"source-h-419"},{"level":3,"title":"BO.4. Executable checks and counterexample","line":9553,"id":"source-h-420"},{"level":3,"title":"BO.5. Physical-dimension evidence gate","line":9575,"id":"source-h-421"},{"level":3,"title":"BO.6. Current measured status","line":9597,"id":"source-h-422"},{"level":3,"title":"BO.7. Next experiment and retained boundaries","line":9622,"id":"source-h-423"},{"level":2,"title":"Appendix BP. Retrospective ATLAS cross-channel dimension-evidence audit","line":9641,"id":"source-h-424"},{"level":3,"title":"BP.1. Bounded question and source","line":9643,"id":"source-h-425"},{"level":3,"title":"BP.2. Frozen necessary screen","line":9674,"id":"source-h-426"},{"level":3,"title":"BP.3. Result and counterexamples","line":9706,"id":"source-h-427"},{"level":3,"title":"BP.4. Exact procedural correction and limits","line":9738,"id":"source-h-428"},{"level":2,"title":"Appendix BQ. Exact-recast completeness before dimensional interpretation","line":9782,"id":"source-h-429"},{"level":3,"title":"BQ.1. Bounded question","line":9784,"id":"source-h-430"},{"level":3,"title":"BQ.2. The forward equation and exact ambiguity","line":9807,"id":"source-h-431"},{"level":3,"title":"BQ.3. Frozen readiness gate","line":9853,"id":"source-h-432"},{"level":3,"title":"BQ.4. Verification, evidence classes, and consequence","line":9882,"id":"source-h-433"},{"level":3,"title":"BQ.5. Independent replay of the benchmark truth tower (revision 1.69) [C]","line":9919,"id":"source-h-434"},{"level":3,"title":"BQ.6. HEPData inventory: the record holds limit contours, not spectra (revision 1.69) [E on the record, M on the consequence]","line":9923,"id":"source-h-435"},{"level":2,"title":"Appendix BR. Scripture as a finite observer (revision 1.69)","line":9943,"id":"source-h-436"},{"level":3,"title":"BR.1. A text is a projection","line":9947,"id":"source-h-437"},{"level":3,"title":"BR.2. Job 38 read as an observer-limit text [T]","line":9956,"id":"source-h-438"},{"level":3,"title":"BR.3. Genesis 1 and the seven typed layers [M on the count, T on the mapping]","line":9974,"id":"source-h-439"},{"level":3,"title":"BR.4. The sky: raqia and \"stretched out\" [T]","line":9987,"id":"source-h-440"},{"level":3,"title":"BR.5. Sanctuary geometry: every stated dimension, every ratio [M]","line":9996,"id":"source-h-441"},{"level":3,"title":"BR.6. The Bronze Sea and \\(\\pi\\) [M on the numbers, T on the rule]","line":10027,"id":"source-h-442"},{"level":3,"title":"BR.7. Sevens [M count, T meaning]","line":10041,"id":"source-h-443"},{"level":3,"title":"BR.8. What survives, by type","line":10045,"id":"source-h-444"},{"level":3,"title":"BR.9. On \"the Bible is the instruction manual\"","line":10061,"id":"source-h-445"},{"level":3,"title":"BR.10. The operation grammar of Genesis 1 and Job 38 [T, with M counts on the text]","line":10065,"id":"source-h-446"},{"level":4,"title":"BR.10.1. Genesis 1 has an explicit instruction set","line":10069,"id":"source-h-447"},{"level":4,"title":"BR.10.2. The heavens are described with a surveyor's verbs","line":10100,"id":"source-h-448"},{"level":4,"title":"BR.10.3. The sun's path is called a statute","line":10108,"id":"source-h-449"},{"level":4,"title":"BR.10.4. Creation is written in Tabernacle-building vocabulary","line":10124,"id":"source-h-450"},{"level":4,"title":"BR.10.5. What the wording tells you, exactly","line":10140,"id":"source-h-451"},{"level":3,"title":"BR.11. The operation grammar written in the framework's mathematics [M on the model, T on the identification]","line":10154,"id":"source-h-452"},{"level":4,"title":"BR.11.1. Primitives","line":10158,"id":"source-h-453"},{"level":4,"title":"BR.11.2. Genesis 1 as a program","line":10179,"id":"source-h-454"},{"level":4,"title":"BR.11.3. What the program proves about its own lower law","line":10207,"id":"source-h-455"},{"level":4,"title":"BR.11.4. The boundary, restated with the new objects","line":10221,"id":"source-h-456"},{"level":3,"title":"BR.12. \"Hebrew is mathematical code\": an exact audit [M on the numbers, T on the meanings]","line":10227,"id":"source-h-457"},{"level":4,"title":"BR.12.1. What the alphabet is, historically [E, from the epigraphic record]","line":10231,"id":"source-h-458"},{"level":4,"title":"BR.12.2. Gematria facts that are exactly true [M on the text]","line":10235,"id":"source-h-459"},{"level":4,"title":"BR.12.3. The \"π in Genesis 1:1\" formula [M on the arithmetic]","line":10262,"id":"source-h-460"},{"level":4,"title":"BR.12.4. Aleph–Tav [T, with exact textual facts]","line":10280,"id":"source-h-461"},{"level":4,"title":"BR.12.5. The Name is a verb [T, linguistically solid]","line":10284,"id":"source-h-462"},{"level":4,"title":"BR.12.6. YHWH and the genome [M on the counts]","line":10288,"id":"source-h-463"},{"level":4,"title":"BR.12.7. Equidistant letter sequences, \"Torah codes\" [E on the literature]","line":10302,"id":"source-h-464"},{"level":4,"title":"BR.12.8. Summary by claim type","line":10306,"id":"source-h-465"},{"level":2,"title":"Appendix BS. Inversion Theory: a falsifiable detector for one spatial dimension above the third (revision 1.70)","line":10324,"id":"source-h-466"},{"level":3,"title":"BS.0. The hat, stated exactly","line":10333,"id":"source-h-467"},{"level":3,"title":"BS.1. Definitions","line":10341,"id":"source-h-468"},{"level":3,"title":"BS.2. Theorems","line":10353,"id":"source-h-469"},{"level":3,"title":"BS.3. The hypothesis","line":10406,"id":"source-h-470"},{"level":3,"title":"BS.4. What a measurement is, and what it is not","line":10422,"id":"source-h-471"},{"level":3,"title":"BS.5. Existing measured status [E]","line":10441,"id":"source-h-472"},{"level":3,"title":"BS.6. The powered experiment","line":10452,"id":"source-h-473"},{"level":3,"title":"BS.7. What it would mean to measure it","line":10470,"id":"source-h-474"},{"level":3,"title":"BS.8. Relation to the parent manuscript","line":10480,"id":"source-h-475"},{"level":3,"title":"BS.A. The black sheep: definition, circle, explanation, shape","line":10486,"id":"source-h-476"},{"level":4,"title":"BS.A.1 The idea, stated in the framework","line":10488,"id":"source-h-477"},{"level":4,"title":"BS.A.2 The circle","line":10501,"id":"source-h-478"},{"level":4,"title":"BS.A.3 Why the family cannot discuss it","line":10510,"id":"source-h-479"},{"level":4,"title":"BS.A.4 The catalog, read through the definition","line":10520,"id":"source-h-480"},{"level":4,"title":"BS.A.5 The geometric shape of the black sheep","line":10534,"id":"source-h-481"},{"level":4,"title":"BS.A.6 Two consequences for the detector","line":10553,"id":"source-h-482"},{"level":3,"title":"BS.B. The catalog","line":10562,"id":"source-h-483"},{"level":4,"title":"BS.B.1 Family 1. Proven to exist. No one will ever meet them.","line":10566,"id":"source-h-484"},{"level":4,"title":"BS.B.2 Family 2. Well defined. 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What are we actually trying to solve?","line":7,"id":"source-h-2"},{"level":2,"title":"2. The common algebraic contract","line":31,"id":"source-h-3"},{"level":2,"title":"3. An executable refinement method for finite systems","line":66,"id":"source-h-4"},{"level":3,"title":"Executed example","line":90,"id":"source-h-5"},{"level":2,"title":"4. Direct computation toward the actual missing fluid modes","line":102,"id":"source-h-6"},{"level":2,"title":"5. Reuse expensive work without trusting a cache as a proof","line":127,"id":"source-h-7"},{"level":2,"title":"6. Local error caps and their analytic justification","line":137,"id":"source-h-8"},{"level":2,"title":"7. The formerly unresolved input is now certified","line":192,"id":"source-h-9"},{"level":2,"title":"8. A director that keeps proof scope explicit","line":221,"id":"source-h-10"},{"level":2,"title":"9. Validation, limitations, and the next useful work","line":240,"id":"source-h-11"},{"level":2,"title":"10. 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The finite-system tests include 160 seeded comparisons against direct concrete reachability.","label":"9. Validation, limitations, and the next useful work","source":"archive/8cbc00e49b56-PROOF_SEARCH_DIRECTION.md","sectionId":"source-h-11","provenance":"Source excerpt"},"nextQuestion":{"text":"Twenty-three targeted test methods cover cache reuse and identity, forged caches with recomputed hashes, exact reference constraints and joins, local-cap inequalities and coverage, nonzero initial error, stale-output replacement, requested-input binding, finite-system refinement, concrete counterexamples, scope containment, isolated standalone execution, and rejection under optimized Python. The finite-system tests include 160 seeded comparisons against direct concrete reachability.","label":"9. 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A prespecified extension allowed up to four nonnegative phase-shifted copies chosen from twelve offsets. Global simplex weights and component choices were learned on the same eight training phases; the four-component rescue candidate was then evaluated on the sixteen previously untouched phases.","label":"Result 1: extra same-family rotors do not rescue the model","source":"archive/8da92f374f97-RESULTS_0.4.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"All 29 unit-test groups pass (23 inherited plus 6 new). A separate implementation reconstructs the spectroscopic gap, optical period, all three thermal population ratios, time-reversal sign, saved latent-component metrics, simplex weights, and the six-gate decision: 11/11 checks pass.","label":"Verification and evidence boundary","source":"archive/8da92f374f97-RESULTS_0.4.md","sectionId":"source-h-4","provenance":"Source excerpt"},"nextQuestion":{"text":"Do not add unconstrained components to this holdout. Specify a genuinely new interaction law—preferably a Hamiltonian or continuity equation—that predicts both spectral and spatial observables with a fixed parameter budget. Freeze it before using a new experimental preparation with a matching measured spatial observable.","label":"Next test","source":"archive/8da92f374f97-RESULTS_0.4.md","sectionId":"source-h-5","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":4,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The release-0.3 six-parameter geometry was frozen. A prespecified extension allowed up to four nonnegative phase-shifted copies chosen from twelve offsets. 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Quantum reference: exact non-relativistic hydrogen 1s and 2p_z basis functions, including a time-dependent coherent superposition stored as a four-dimensional (time, x, y, z) density matrix. 2. Geometric hypothesis: two tangent 3-spheres embedded in four spatial coordinates, rotated and projected into interacting 3D wave sources. This is synthetic and is not asserted to be hydrogen physics.","label":"The source’s opening statement","source":"archive/8f4bc9b887c3-README.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"- hydrogen_1s_density.npz: coordinates, the full density matrix, and sampled voxel centers. - hydrogen_1s_90pct.obj: static 3D probability envelope; coordinates are in Bohr radii. - summary.json: matrix configuration, moments, probability radii, and epistemic status. - independent_check.json: a separate SciPy quadrature and matrix audit. - hydrogen_1s_preview.png: static preview generated from the saved matrix samples. - hydrogen_1s_2pz_basis.npz: independently testable 1s and signed 2p_z basis matrices. - hydrogen_1s_2pz_4d_density.npz: 24 time-indexed 3D quantum density and interference frames.","label":"Run","source":"archive/8f4bc9b887c3-README.md","sectionId":"source-h-6","provenance":"Source excerpt"},"nextQuestion":{"text":"These are written analytic or synthetic models plus finite computation. They are not measurements of a particular atom. The spatial density reference still ignores proton recoil, spin, fine/hyperfine structure, Lamb shift, relativity, external fields, and finite proton size. The 0.5 spectroscopy ladder adds reduced mass and leading Dirac structure only to the energy comparison; it does not turn the old voxel animation into a precision-QED state. A density animation does not imply that a localized electron follows a trajectory. The synthetic rotor engine has not been derived from the hydrogen Hamiltonian and does not identify a deeper physical or theological cause.","label":"Interpretation boundary","source":"archive/8f4bc9b887c3-README.md","sectionId":"source-h-7","provenance":"Source excerpt"}},"figures":[{"url":"archive/a70d3edc91ba-golden_ratio_audit.png","caption":"golden ratio audit","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/golden_ratio_audit.png","reference":"golden_ratio_audit.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"a70d3edc91ba7216e75c8c078516aa55797715ea80edd4fa331d2e48f743f2df"},{"url":"archive/1f01305a37c5-hydrogen_1s_2pz_wave_frames.png","caption":"hydrogen 1s 2pz wave frames","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/hydrogen_1s_2pz_wave_frames.png","reference":"hydrogen_1s_2pz_wave_frames.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"1f01305a37c519f422ffdafe4b8fa4df0a354cdfcd5e76dfbb0430fe11158984"},{"url":"archive/2bd98d766cc8-hydrogen_1s_preview.png","caption":"hydrogen 1s preview","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/hydrogen_1s_preview.png","reference":"hydrogen_1s_preview.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"2bd98d766cc8a26dbd0d31e49d25413438bd939634fb152e5671cf948888fa62"},{"url":"archive/81054538955b-quantum_harmonic_current.png","caption":"quantum harmonic current","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/quantum_harmonic_current.png","reference":"quantum_harmonic_current.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"81054538955bb6faa47dde3de76db078a1e16189a3e7d38f4c9bbc62c7e42d95"},{"url":"archive/f58d9e2dfc82-reality_observer_map.png","caption":"reality observer map","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/reality_observer_map.png","reference":"reality_observer_map.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"f58d9e2dfc8265917a04c8fc3dcdcef5a81fc64e4356d1b3aab6a08c99864a34"},{"url":"archive/618f5922d17b-rotor_holdout_comparison.png","caption":"rotor holdout comparison","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/rotor_holdout_comparison.png","reference":"rotor_holdout_comparison.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"618f5922d17b4233d858c4d575b3fb571cecf1accbf7db60ba45d78b46202d5f"}],"illustrationIndex":4,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"This lab contains two explicitly separated engines: 1. 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This is synthetic and is not asserted to be hydrogen physics.","words":1866},"archive/8f54278510af-THEORY_V11.md":{"url":"archive/8f54278510af-THEORY_V11.md","title":"DRCT v11 — Gauge, Measurement Ports, and Identifiable Subspaces","kind":"Research manuscript","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/THEORY_V11.md","bytes":2328,"sha256":"8f54278510af9086530b382b0c5b7f4ea2c29362d5926ef397601fb1ce99dab3","savedDate":"2026-08-23","date":"2026-08-23","dateKind":"Saved source date","declaredDates":[],"projectId":"drct","projectIds":["drct"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"DRCT v11 — Gauge, Measurement Ports, and Identifiable Subspaces","line":1,"id":"source-h-1"},{"level":2,"title":"Theorem 1 — Hidden-basis gauge","line":3,"id":"source-h-2"},{"level":2,"title":"Theorem 2 — One internal measurement port fixes the gauge when reachable","line":34,"id":"source-h-3"},{"level":2,"title":"Theorem 3 — Reachable-subspace observability","line":68,"id":"source-h-4"},{"level":2,"title":"Consequence for transformers","line":107,"id":"source-h-5"}],"journey":{"question":{"text":"What does “DRCT v11 — Gauge, Measurement Ports, and Identifiable Subspaces” establish within its declared scope?","label":"The reading question","source":"archive/8f54278510af-THEORY_V11.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"For every invertible hidden-coordinate transform \\(S\\),","label":"The source’s opening statement","source":"archive/8f54278510af-THEORY_V11.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"This record does not separate a verification section. Read its methods, assumptions and original source before treating a claim as checked.","label":"Locate the checks","source":"archive/8f54278510af-THEORY_V11.md","sectionId":"source-record","provenance":"Editorial reading guide"},"nextQuestion":{"text":"Which additional test would distinguish the claim in “DRCT v11 — Gauge, Measurement Ports, and Identifiable Subspaces” from the alternatives allowed by its assumptions?","label":"The next reading question","source":"archive/8f54278510af-THEORY_V11.md","sectionId":"source-record","provenance":"Editorial reading question"}},"figures":[],"illustrationIndex":7,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"For every invertible hidden-coordinate transform \\(S\\),","words":325},"archive/90009b9e2f31-RRLS_EXCLUSIVITY_LIFT.md":{"url":"archive/90009b9e2f31-RRLS_EXCLUSIVITY_LIFT.md","title":"RRLS exact-cover lift: exclusivity, certificates, and a measured limit","kind":"Research note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/RRLS_EXCLUSIVITY_LIFT.md","bytes":17043,"sha256":"90009b9e2f31eef8559e8378e9d6cd895969cc0165abd51aaf03ee2fce24da11","savedDate":"2026-09-05","date":"2026-09-05","dateKind":"Saved source date","declaredDates":[],"projectId":"rrls","projectIds":["rrls"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"RRLS exact-cover lift: exclusivity, certificates, and a measured limit","line":1,"id":"source-h-1"},{"level":2,"title":"1. 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Scope of the result","line":235,"id":"source-h-12"}],"journey":{"question":{"text":"What does “RRLS exact-cover lift: exclusivity, certificates, and a measured limit” establish within its declared scope?","label":"The reading question","source":"archive/90009b9e2f31-RRLS_EXCLUSIVITY_LIFT.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"Every triple in T_n satisfies i+j-k = 0 modulo n. If a perfect matching existed, summing over its triples would give","label":"8. A checked counting rule modulo eight","source":"archive/90009b9e2f31-RRLS_EXCLUSIVITY_LIFT.md","sectionId":"source-h-10","provenance":"Source excerpt"},"checks":{"text":"The new runner tries the cheap cyclic-sum certificate first, then parity degree 1 and bounded exclusivity lifts. Its default maximum degree is 2. Optional exact boundary solving supplies a checked SAT or UNSAT result when the filters leave the instance unresolved. A SAT result includes the decoded selected triples.","label":"9. Runnable route and verification","source":"archive/90009b9e2f31-RRLS_EXCLUSIVITY_LIFT.md","sectionId":"source-h-11","provenance":"Source excerpt"},"nextQuestion":{"text":"5 September 2026. Extension to the RRLS proof-audit engine.","label":"RRLS exact-cover lift: exclusivity, certificates, and a measured limit","source":"archive/90009b9e2f31-RRLS_EXCLUSIVITY_LIFT.md","sectionId":"source-h-1","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"5 September 2026. Extension to the RRLS proof-audit engine.","words":2499},"archive/92f68f02a2fa-Circular_Structure_Report.md":{"url":"archive/92f68f02a2fa-Circular_Structure_Report.md","title":"Does the nearly uniform spectrum-offset histogram hide a cylinder?","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/Circular_Structure_Report.md","bytes":11358,"sha256":"92f68f02a2fa72e6a1d24db0d0ea4ac667a73eb56bfcda1d33df7f94b2365730","savedDate":"2026-09-21","date":"2026-09-21","dateKind":"Saved source date","declaredDates":[],"projectId":"matter","projectIds":["matter"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Does the nearly uniform spectrum-offset histogram hide a cylinder?","line":1,"id":"source-h-1"},{"level":2,"title":"Outcome","line":5,"id":"source-h-2"},{"level":2,"title":"Four controlled comparisons","line":13,"id":"source-h-3"},{"level":3,"title":"1. Flatness is ordinary under a pattern-preserving control","line":26,"id":"source-h-4"},{"level":3,"title":"2. Individual-element variation needs a dependence control","line":44,"id":"source-h-5"},{"level":3,"title":"3. The best fitted helix does not predict convincingly","line":60,"id":"source-h-6"},{"level":2,"title":"What the cylinder does—and does not—mean mathematically","line":78,"id":"source-h-7"},{"level":2,"title":"Scope, sources and evidence status","line":94,"id":"source-h-8"},{"level":2,"title":"Verification and reproducibility","line":108,"id":"source-h-9"},{"level":2,"title":"Next test","line":125,"id":"source-h-10"}],"journey":{"question":{"text":"Does the nearly uniform spectrum-offset histogram hide a cylinder?","label":"The reading question","source":"archive/92f68f02a2fa-Circular_Structure_Report.md","sectionId":"source-record","provenance":"Source title"},"answer":{"text":"The near-uniform pooled distribution is confirmed, but these checks do not support a shared cylinder-like winding law. This is a bounded negative result for the explicitly tested phase statistics and linear winding rule, not a proof that atomic spectra have no structure or that every geometric model fails.","label":"Outcome","source":"archive/92f68f02a2fa-Circular_Structure_Report.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"Ten unit tests passed. A separate numerical implementation imported none of the main analysis helpers. It recomputed all 11,729 offsets from the saved vacuum wavelengths, rebuilt all 6,907 proximity blocks, rechecked every one of the 512 candidate slopes, reproduced all 39,996 simulated reference statistics, and matched every tail count. This is independent calculation on the same data, not independent measurements.","label":"Verification and reproducibility","source":"archive/92f68f02a2fa-Circular_Structure_Report.md","sectionId":"source-h-9","provenance":"Source excerpt"},"nextQuestion":{"text":"Obtain a previously unused, transition-labeled observed-line sample, with actual multiplet/energy-level families and wavelength uncertainties. Fix one predicted relationship and a family-level holdout before looking at its phases. That can distinguish a reproducible element-dependent effect from strong-line selection, neighboring-line overcounting, and the geometry we imposed when wrapping the note offsets. Do not promote the fitted eight-element slope or modify the theory's physical claims on this result.","label":"Next test","source":"archive/92f68f02a2fa-Circular_Structure_Report.md","sectionId":"source-h-10","provenance":"Source excerpt"}},"figures":[{"url":"archive/1cfc2fb311ea-Element_Phase_Map.png","caption":"Element Phase Map","originalPath":"/Element_Phase_Map.png","reference":"Element_Phase_Map.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"1cfc2fb311ead6f0ca034cd627682cc07d9e9792bb7335ea837147aa19cab373"}],"illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"21 September 2026 · HARMONIC-CIRCLE-02 · Exploratory catalog reanalysis","words":1538},"archive/95573c01bc39-NULL_AXIS_OBSERVABILITY.md":{"url":"archive/95573c01bc39-NULL_AXIS_OBSERVABILITY.md","title":"Null-Axis Probes and the Limits of Projection","kind":"Research note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/NULL_AXIS_OBSERVABILITY.md","bytes":19163,"sha256":"95573c01bc3949e6c7c2c01a0d3ff54e09ee9334449102e5eabca8a6f7125ce7","savedDate":"2026-09-05","date":"2026-09-05","dateKind":"Saved source date","declaredDates":[],"projectId":"theory","projectIds":["theory"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Null-Axis Probes and the Limits of Projection","line":1,"id":"source-h-1"},{"level":2,"title":"1. 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But the seven-line pattern does not establish a special musical law: 23.5747% of common tuning shifts match the complete pattern at least as well as A4=440 Hz under the explicitly chosen reference comparison.","label":"Outcome","source":"archive/c69c23892b03-Harmonic_Alpha_Results.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"Ten unit tests passed. A separately written audit, importing none of the main implementation, reproduced the material calculations using 60-digit Decimal arithmetic, bisection for the air conversion, natural logarithms, and Machin's formula for pi. 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Current corrected results; all distances are cents (100 cents = one equal-tempered semitone).","label":"The source’s opening statement","source":"archive/c74f4adf9d1f-Element_By_Element.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"This record does not separate a verification section. 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Your “absolute zero” has a rigorous definition","words":3454},"archive/fde8fc6a803b-NEXT_WALL.md":{"url":"archive/fde8fc6a803b-NEXT_WALL.md","title":"The next proof obstacle and a first extension beyond it","kind":"Mathematical note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/NEXT_WALL.md","bytes":14414,"sha256":"fde8fc6a803bd3f21533fcd69c2e40b1355ed125b82b7adac6a91dcd26ec3e7e","savedDate":"2026-09-05","date":"2026-09-05","dateKind":"Saved source date","declaredDates":["Date: 5 September 2026"],"projectId":"rrls","projectIds":["rrls"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"The next proof obstacle and a first extension beyond it","line":1,"id":"source-h-1"},{"level":2,"title":"1. The obstacle worth targeting next","line":7,"id":"source-h-2"},{"level":2,"title":"2. A relative error inequality","line":15,"id":"source-h-3"},{"level":2,"title":"3. The general validation condition, still to be implemented","line":82,"id":"source-h-4"},{"level":2,"title":"4. An implemented all-time special case","line":129,"id":"source-h-5"},{"level":2,"title":"5. A field newly certified by the engine","line":187,"id":"source-h-6"},{"level":2,"title":"6. Reproduction and arithmetic","line":228,"id":"source-h-7"},{"level":2,"title":"7. What would accelerate useful progress most","line":248,"id":"source-h-8"}],"journey":{"question":{"text":"What does “The next proof obstacle and a first extension beyond it” establish within its declared scope?","label":"The reading question","source":"archive/fde8fc6a803b-NEXT_WALL.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"Engine: 0.15.0 Date: 5 September 2026 Status: An implemented sufficient theorem for perturbations of an exact shear; a development specification for general trajectory validation. No mathematical novelty or Millennium solution is claimed.","label":"The source’s opening statement","source":"archive/fde8fc6a803b-NEXT_WALL.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"Suppose a smooth reference \\(v\\), on a finite time interval \\([0,T]\\), has certified bounds \\(V(t)\\le\\overline V(t)\\) and \\(R(t)\\le\\overline R(t)\\). Put","label":"3. The general validation condition, still to be implemented","source":"archive/fde8fc6a803b-NEXT_WALL.md","sectionId":"source-h-4","provenance":"Source excerpt"},"nextQuestion":{"text":"Engine: 0.15.0 Date: 5 September 2026 Status: An implemented sufficient theorem for perturbations of an exact shear; a development specification for general trajectory validation. No mathematical novelty or Millennium solution is claimed.","label":"The next proof obstacle and a first extension beyond it","source":"archive/fde8fc6a803b-NEXT_WALL.md","sectionId":"source-h-1","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Engine: 0.15.0 Date: 5 September 2026 Status: An implemented sufficient theorem for perturbations of an exact shear; a development specification for general trajectory validation. No mathematical novelty or Millennium solution is claimed.","words":1854},"archive/fe52db8f3602-Reality_Revision_1.39.md":{"url":"archive/fe52db8f3602-Reality_Revision_1.39.md","title":"Reality Revision 1.39 — Anytime evidence for a declared Markov sign model","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Reality_Revision_1.39.md","bytes":2729,"sha256":"fe52db8f3602b8f2b596f623b687622a27d987d0f0169df692152b8dc108e1dd","savedDate":"2026-09-20","date":"2026-09-20","dateKind":"Saved source date","declaredDates":["Date: 20 September 2026"],"projectId":"rope","projectIds":["rope"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Reality Revision 1.39 — Anytime evidence for a declared Markov sign model","line":1,"id":"source-h-1"},{"level":2,"title":"Result","line":6,"id":"source-h-2"},{"level":2,"title":"Limitations and retained corrections","line":43,"id":"source-h-3"}],"journey":{"question":{"text":"What does “Reality Revision 1.39 — Anytime evidence for a declared Markov sign model” establish within its declared scope?","label":"The reading question","source":"archive/fe52db8f3602-Reality_Revision_1.39.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The v1.26 dependence counterexample is resolved only within one explicit model class. Conditional on the first nonzero sign, the nonzero projected-residual signs must form a fixed first-order homogeneous binary Markov chain. For a declared transition matrix (P_0), a past-only Krichevsky--Trofimov predictor (widehat Q_t) gives","label":"Result","source":"archive/fe52db8f3602-Reality_Revision_1.39.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"This record does not separate a verification section. Read its methods, assumptions and original source before treating a claim as checked.","label":"Locate the checks","source":"archive/fe52db8f3602-Reality_Revision_1.39.md","sectionId":"source-record","provenance":"Editorial reading guide"},"nextQuestion":{"text":"Which additional test would distinguish the claim in “Reality Revision 1.39 — Anytime evidence for a declared Markov sign model” from the alternatives allowed by its assumptions?","label":"The next reading question","source":"archive/fe52db8f3602-Reality_Revision_1.39.md","sectionId":"source-record","provenance":"Editorial reading question"}},"figures":[],"illustrationIndex":3,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"The v1.26 dependence counterexample is resolved only within one explicit model class. Conditional on the first nonzero sign, the nonzero projected-residual signs must form a fixed first-order homogeneous binary Markov chain. For a declared transition matrix (P_0), a past-only Krichevsky--Trofimov predictor (widehat Q_t) gives","words":366},"archive/fe6d26d12295-RESULTS_0.12.md":{"url":"archive/fe6d26d12295-RESULTS_0.12.md","title":"Element Projection Lab 0.12.0 — detector-response closure","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Element Projection Lab/RESULTS_0.12.md","bytes":5881,"sha256":"fe6d26d1229580788cf0c6d5d820d479e483ae94796a955f0b988408481e1ff0","savedDate":"2026-09-20","date":"2026-09-20","dateKind":"Saved source date","declaredDates":[],"projectId":"elements","projectIds":["elements"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Element Projection Lab 0.12.0 — detector-response closure","line":1,"id":"source-h-1"},{"level":2,"title":"Result","line":6,"id":"source-h-2"},{"level":2,"title":"Frozen assumptions and finite results","line":18,"id":"source-h-3"},{"level":2,"title":"Verification and preservation","line":70,"id":"source-h-4"},{"level":2,"title":"Sources, limitations and next test","line":92,"id":"source-h-5"}],"journey":{"question":{"text":"What does “Element Projection Lab 0.12.0 — detector-response closure” establish within its declared scope?","label":"The reading question","source":"archive/fe6d26d12295-RESULTS_0.12.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The engine now accounts separately for reconstructed and missed events and fits a nonnegative signal strength under a fixed response and known positive background. The counterexample is stronger than a poor fit: a wrong global efficiency can give an exactly identical fit with a wrong source strength.","label":"Result","source":"archive/fe6d26d12295-RESULTS_0.12.md","sectionId":"source-h-2","provenance":"Source excerpt"},"checks":{"text":"- All 192 unit tests pass, including 30 new response/protocol tests. - Independent scalar audit: 1,231,728 checks, zero failures; 9,384 response entries, 552,000 Poisson counts and 18,000 fitted strengths. - It imports no production module: Gaussian integrals use math.erf, sums use math.fsum, and a safeguarded scalar Newton solver replaces production vectorized bisection. Count replay uses the same specified NumPy PCG64 algorithm; it is reproducibility checking, not an independent randomness experiment. Maximum matrix difference is 1.39e-16 and maximum fitted-strength difference is 7.96e-13.","label":"Verification and preservation","source":"archive/fe6d26d12295-RESULTS_0.12.md","sectionId":"source-h-4","provenance":"Source excerpt"},"nextQuestion":{"text":"The forward-folding construction follows Koch, revised 21 March 2019. Zhu et al., revised 27 January 2026 separately study response-estimation uncertainty; their method is relevant to the next stage but is not implemented or tested here. Neither source supplies the missing ATLAS calibration. The published negative ATLAS result and all earlier contour classifications remain unchanged.","label":"Sources, limitations and next test","source":"archive/fe6d26d12295-RESULTS_0.12.md","sectionId":"source-h-5","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":5,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Theory revision 1.73. Evidence class: written conditional mathematics and finite synthetic computation. No new measured data or detector calibration.","words":823},"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md":{"url":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md","title":"Version 0.22.0 — paired-reference calibration boundary","kind":"Technical documentation","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md","bytes":17912,"sha256":"f2f7bd9d95991af39dc27f11a5903679f19b8e3aefd413c57808ce7770d3a82f","savedDate":null,"date":null,"dateKind":"Source date not separately recorded","declaredDates":[],"projectId":"gauge","projectIds":["gauge"],"associationBasis":"Explicit project source citation","status":"Original saved source","headings":[{"level":1,"title":"Version 0.22.0 — paired-reference calibration boundary","line":1,"id":"source-h-1"},{"level":1,"title":"Preserved version 0.21.0 — all-distance optical-tail countermodel","line":15,"id":"source-h-2"},{"level":1,"title":"Version 0.20.0 — mirror orientation, 3D shadows and causal delay","line":19,"id":"source-h-3"},{"level":1,"title":"Version 0.19.0 — local continuum comparator","line":23,"id":"source-h-4"},{"level":1,"title":"Version 0.18.0 — nonlinear sampled-field ambiguity","line":27,"id":"source-h-5"},{"level":1,"title":"Version 0.17.0 — dispersion discrimination and continuous countermodel","line":31,"id":"source-h-6"},{"level":1,"title":"Version 0.16.0 — smooth versus cusp regularity challenge","line":35,"id":"source-h-7"},{"level":1,"title":"Version 0.15.0 — longer unforced coupled trajectory","line":39,"id":"source-h-8"},{"level":1,"title":"Version 0.14.0 — exact driven coupled trajectory","line":43,"id":"source-h-9"},{"level":1,"title":"Version 0.13.0 — evolving coupled three-grid comparison","line":47,"id":"source-h-10"},{"level":1,"title":"Version 0.12.0 — corrected dispersion and interacting RHS refinement","line":51,"id":"source-h-11"},{"level":1,"title":"Fixed Grid String Lab 0.11.0","line":55,"id":"source-h-12"},{"level":2,"title":"Preserved 0.10.0 self-consistent ring","line":73,"id":"source-h-13"},{"level":2,"title":"Preserved 0.9.0 prescribed-field gauge module","line":94,"id":"source-h-14"},{"level":2,"title":"Preserved 0.8.0 wave formulation","line":117,"id":"source-h-15"},{"level":2,"title":"Preserved 0.7.0 dimensional-slice test","line":139,"id":"source-h-16"},{"level":2,"title":"Preserved 0.6.0 mathematical-exception audit","line":165,"id":"source-h-17"},{"level":2,"title":"Preserved 0.5.0 material-acoustics calculation","line":193,"id":"source-h-18"},{"level":2,"title":"Preserved 0.4.0 acoustic-support calculation","line":220,"id":"source-h-19"},{"level":2,"title":"Preserved 0.3.0 electric-dipole benchmark","line":251,"id":"source-h-20"},{"level":2,"title":"Preserved 0.2.0 foundation","line":273,"id":"source-h-21"}],"journey":{"question":{"text":"What does “Version 0.22.0 — paired-reference calibration boundary” establish within its declared scope?","label":"The reading question","source":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"Run python reference_calibration.py, python independent_reference_calibration_audit.py, and python -m unittest discover -p 'test_*.py' -q; inspect RESULTS_0.22.md. Under an exactly shared detector and optical-path kernel, the sample/reference Laplace-transform ratio identifies the material kernel. A sample-only path mismatch multiplies into the same ratio, and an exact counterexample replaces the entire 0.8 ns material delay with an observationally identical 0.8 ns excess-path delay. This is conditional mathematics plus finite synthetic checking, not a measured afterglow or evidence of an extra dimension.","label":"The source’s opening statement","source":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"Run python reference_calibration.py, python independent_reference_calibration_audit.py, and python -m unittest discover -p 'test_*.py' -q; inspect RESULTS_0.22.md. Under an exactly shared detector and optical-path kernel, the sample/reference Laplace-transform ratio identifies the material kernel. A sample-only path mismatch multiplies into the same ratio, and an exact counterexample replaces the entire 0.8 ns material delay with an observationally identical 0.8 ns excess-path delay. This is conditional mathematics plus finite synthetic checking, not a measured afterglow or evidence of an extra dimension.","label":"Version 0.22.0 — paired-reference calibration boundary","source":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md","sectionId":"source-h-1","provenance":"Source excerpt"},"nextQuestion":{"text":"Run python reference_calibration.py, python independent_reference_calibration_audit.py, and python -m unittest discover -p 'test_*.py' -q; inspect RESULTS_0.22.md. Under an exactly shared detector and optical-path kernel, the sample/reference Laplace-transform ratio identifies the material kernel. A sample-only path mismatch multiplies into the same ratio, and an exact counterexample replaces the entire 0.8 ns material delay with an observationally identical 0.8 ns excess-path delay. This is conditional mathematics plus finite synthetic checking, not a measured afterglow or evidence of an extra dimension.","label":"Version 0.22.0 — paired-reference calibration boundary","source":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md","sectionId":"source-h-1","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Run python reference_calibration.py, python independent_reference_calibration_audit.py, and python -m unittest discover -p 'test_*.py' -q; inspect RESULTS_0.22.md. Under an exactly shared detector and optical-path kernel, the sample/reference Laplace-transform ratio identifies the material kernel. A sample-only path mismatch multiplies into the same ratio, and an exact counterexample replaces the entire 0.8 ns material delay with an observationally identical 0.8 ns excess-path delay. This is conditional mathematics plus finite synthetic checking, not a measured afterglow or evidence of an extra dimension.","words":2099},"archive/grounded-wave-semantic-network-v0.1.md":{"url":"archive/grounded-wave-semantic-network-v0.1.md","title":"Grounded Wave Semantic Network Architecture and Theorem","kind":"Research manuscript","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"/The Theory of Reality/Grounded_Wave_Semantic_Network_Theorem_v0.1.md","bytes":24333,"sha256":"a1de2c115537f8492657694816a0c7c3a1ba3c5922930647b5cf779d611a3356","savedDate":"2026-09-30","date":"2026-09-30","dateKind":"Saved source date","declaredDates":["Date: 30 September 2026"],"projectId":"semantic","projectIds":["semantic"],"associationBasis":"Explicit project source citation","status":"Original saved source","headings":[{"level":1,"title":"Grounded Wave Semantic Network Architecture and Theorem","line":1,"id":"source-h-1"},{"level":2,"title":"Design objective","line":13,"id":"source-h-2"},{"level":2,"title":"Semantic states and declared equivalence","line":21,"id":"source-h-3"},{"level":2,"title":"Physical and semantic constraints","line":49,"id":"source-h-4"},{"level":2,"title":"An exact wave representation","line":65,"id":"source-h-5"},{"level":2,"title":"Proposition 1 Wave recoverability","line":82,"id":"source-h-6"},{"level":2,"title":"Proposed neural architecture","line":96,"id":"source-h-7"},{"level":2,"title":"Theorem 1 Conditional language invariance and certified semantic reasoning","line":137,"id":"source-h-8"},{"level":2,"title":"Certified and predictive operating modes","line":181,"id":"source-h-9"},{"level":2,"title":"Proposition 2 Capacity of a finite wave state","line":191,"id":"source-h-10"},{"level":2,"title":"Grounding examples and counterexamples","line":207,"id":"source-h-11"},{"level":2,"title":"Training objectives","line":222,"id":"source-h-12"},{"level":2,"title":"Evaluation and failure conditions","line":249,"id":"source-h-13"},{"level":2,"title":"Relationship to existing research","line":274,"id":"source-h-14"},{"level":2,"title":"Conclusion and theorem scope","line":282,"id":"source-h-15"},{"level":2,"title":"References","line":290,"id":"source-h-16"}],"journey":{"question":{"text":"What does “Grounded Wave Semantic Network Architecture and Theorem” establish within its declared scope?","label":"The reading question","source":"archive/grounded-wave-semantic-network-v0.1.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"The proposed architecture uses a canonical semantic interface, an auditable wave representation, a learned reasoning component, and explicit constraints. The proved statement is conditional: accepted equivalent inputs share a reasoning result when the representation is lossless, execution is faithful, and the selected operators preserve their declared contracts.","label":"Conclusion and theorem scope","source":"archive/grounded-wave-semantic-network-v0.1.md","sectionId":"source-h-15","provenance":"Source excerpt"},"checks":{"text":"For a literal physical description, the intended grounding process is to obtain observations or a declared model, construct typed properties, and enforce laws within their validity regime. The network does not derive arbitrary object properties merely by receiving a noun.","label":"Grounding examples and counterexamples","source":"archive/grounded-wave-semantic-network-v0.1.md","sectionId":"source-h-11","provenance":"Source excerpt"},"nextQuestion":{"text":"Which additional test would distinguish the claim in “Grounded Wave Semantic Network Architecture and Theorem” from the alternatives allowed by its assumptions?","label":"The next reading question","source":"archive/grounded-wave-semantic-network-v0.1.md","sectionId":"source-record","provenance":"Editorial reading question"}},"figures":[],"illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"This document proposes the Grounded Wave Semantic Network (GWSN), a neural architecture that separates language interpretation, structured meaning, wave encoding, reasoning, and output generation. Physical descriptions include composition, organization, state, and applicable laws; other meanings include agents, roles, context, and declared conventions.","words":3296},"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md":{"url":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md","title":"Hydrogen Matrix Lab 0.8.0","kind":"Technical documentation","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md","bytes":14987,"sha256":"8f4bc9b887c36850e10b1d3a67f4464230a3126fa253e01e10d56132e76e8413","savedDate":null,"date":null,"dateKind":"Source date not separately recorded","declaredDates":[],"projectId":"hydrogen","projectIds":["hydrogen"],"associationBasis":"Editorial topic association","status":"Original saved source","headings":[{"level":1,"title":"Hydrogen Matrix Lab 0.8.0","line":1,"id":"source-h-1"},{"level":2,"title":"Model","line":20,"id":"source-h-2"},{"level":2,"title":"Time-dependent quantum reference","line":34,"id":"source-h-3"},{"level":2,"title":"Conserved flow and observable harmonics","line":47,"id":"source-h-4"},{"level":2,"title":"Touching-rotor hypothesis","line":59,"id":"source-h-5"},{"level":2,"title":"Run","line":65,"id":"source-h-6"},{"level":2,"title":"Interpretation boundary","line":131,"id":"source-h-7"}],"journey":{"question":{"text":"What does “Hydrogen Matrix Lab 0.8.0” establish within its declared scope?","label":"The reading question","source":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md","sectionId":"source-record","provenance":"Editorial reading question"},"answer":{"text":"This lab contains two explicitly separated engines: 1. Quantum reference: exact non-relativistic hydrogen 1s and 2p_z basis functions, including a time-dependent coherent superposition stored as a four-dimensional (time, x, y, z) density matrix. 2. Geometric hypothesis: two tangent 3-spheres embedded in four spatial coordinates, rotated and projected into interacting 3D wave sources. This is synthetic and is not asserted to be hydrogen physics.","label":"The source’s opening statement","source":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"- hydrogen_1s_density.npz: coordinates, the full density matrix, and sampled voxel centers. - hydrogen_1s_90pct.obj: static 3D probability envelope; coordinates are in Bohr radii. - summary.json: matrix configuration, moments, probability radii, and epistemic status. - independent_check.json: a separate SciPy quadrature and matrix audit. - hydrogen_1s_preview.png: static preview generated from the saved matrix samples. - hydrogen_1s_2pz_basis.npz: independently testable 1s and signed 2p_z basis matrices. - hydrogen_1s_2pz_4d_density.npz: 24 time-indexed 3D quantum density and interference frames.","label":"Run","source":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md","sectionId":"source-h-6","provenance":"Source excerpt"},"nextQuestion":{"text":"These are written analytic or synthetic models plus finite computation. They are not measurements of a particular atom. The spatial density reference still ignores proton recoil, spin, fine/hyperfine structure, Lamb shift, relativity, external fields, and finite proton size. The 0.5 spectroscopy ladder adds reduced mass and leading Dirac structure only to the energy comparison; it does not turn the old voxel animation into a precision-QED state. A density animation does not imply that a localized electron follows a trajectory. The synthetic rotor engine has not been derived from the hydrogen Hamiltonian and does not identify a deeper physical or theological cause.","label":"Interpretation boundary","source":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md","sectionId":"source-h-7","provenance":"Source excerpt"}},"figures":[{"url":"archive/a70d3edc91ba-golden_ratio_audit.png","caption":"golden ratio audit","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/golden_ratio_audit.png","reference":"golden_ratio_audit.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"a70d3edc91ba7216e75c8c078516aa55797715ea80edd4fa331d2e48f743f2df"},{"url":"archive/1f01305a37c5-hydrogen_1s_2pz_wave_frames.png","caption":"hydrogen 1s 2pz wave frames","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/hydrogen_1s_2pz_wave_frames.png","reference":"hydrogen_1s_2pz_wave_frames.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"1f01305a37c519f422ffdafe4b8fa4df0a354cdfcd5e76dfbb0430fe11158984"},{"url":"archive/2bd98d766cc8-hydrogen_1s_preview.png","caption":"hydrogen 1s preview","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/hydrogen_1s_preview.png","reference":"hydrogen_1s_preview.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"2bd98d766cc8a26dbd0d31e49d25413438bd939634fb152e5671cf948888fa62"},{"url":"archive/81054538955b-quantum_harmonic_current.png","caption":"quantum harmonic current","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/quantum_harmonic_current.png","reference":"quantum_harmonic_current.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"81054538955bb6faa47dde3de76db078a1e16189a3e7d38f4c9bbc62c7e42d95"},{"url":"archive/f58d9e2dfc82-reality_observer_map.png","caption":"reality observer map","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/reality_observer_map.png","reference":"reality_observer_map.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"f58d9e2dfc8265917a04c8fc3dcdcef5a81fc64e4356d1b3aab6a08c99864a34"},{"url":"archive/618f5922d17b-rotor_holdout_comparison.png","caption":"rotor holdout comparison","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/rotor_holdout_comparison.png","reference":"rotor_holdout_comparison.png","provenance":"Image filename in source","basis":"Original source figure referenced by this document","sha256":"618f5922d17b4233d858c4d575b3fb571cecf1accbf7db60ba45d78b46202d5f"}],"illustrationIndex":4,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"This lab contains two explicitly separated engines: 1. 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These counts overlap: an asset can exist both as a standalone file and inside one or more release archives.","words":428},"journey/sources/octave-design-review.txt":{"url":"journey/sources/octave-design-review.txt","title":"POWM / OCTAVE — Eight-observer predictive memory architecture","kind":"Source note","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"journey/sources/octave-design-review.txt","bytes":11112,"sha256":"1b7da66e7aee221012919f6b7510caea02dc17ac7e2713d9ce0cc9a96fc10f7e","savedDate":"2026-09-30","date":"2026-09-30","dateKind":"Saved source date","declaredDates":["Design review, 30 September 2026"],"projectId":"octave","projectIds":["octave"],"associationBasis":"Explicit project source citation","status":"Original saved source","headings":[],"journey":{"question":{"text":"Build a causal probabilistic world model with eight communicating temporal slots, persistent memory and explicit uncertainty. Eight is the experimental hypothesis supplied by the project, not an established law of brains or reality. The system must be able to falsify the hypothesis. This package implements a small recurrent research baseline and correctness fixes; it does not implement the entire scaled design below or demonstrate frontier performance.","label":"Decision and hypothesis","source":"journey/sources/octave-design-review.txt","sectionId":"source-record","provenance":"Source excerpt"},"answer":{"text":"53,200 learned parameters. Eight observer identities and relative circular anchors; learned shared phase routing; gated fast and slow recurrent states; trainable communication and global feedback; three shared-backbone prediction heads; prioritized training replay. No generating period or physical phase is passed to the student. Verified exact 32-bit forecasts on all eight contexts of the fixed 11110000 pattern after 400 updates. Numerical gradient error below 0.000006. Streaming chunks reproduce full-window outputs. Hidden sensor NaNs and caller-supplied differences cannot affect inference.","label":"What the current implementation establishes","source":"journey/sources/octave-design-review.txt","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"Finite losses and gradients under 128+ ticks; bounded activations over long streams; input schema rejection tests; hidden-value invariance; no target leakage; deterministic resume with external RNG explicitly included by the trainer; replay cutoff audit; interrupted-save recovery; inference state reset rules. Evaluate latency and peak memory as observer count and history grow. 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Give learning curves against both observed samples and elapsed compute.","label":"Required comparisons before claims","source":"journey/sources/octave-design-review.txt","sectionId":"source-record","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":10,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"53,200 learned parameters. Eight observer identities and relative circular anchors; learned shared phase routing; gated fast and slow recurrent states; trainable communication and global feedback; three shared-backbone prediction heads; prioritized training replay. No generating period or physical phase is passed to the student. Verified exact 32-bit forecasts on all eight contexts of the fixed 11110000 pattern after 400 updates. Numerical gradient error below 0.000006. Streaming chunks reproduce full-window outputs. Hidden sensor NaNs and caller-supplied differences cannot affect inference.","words":1465},"journey/sources/octave-school-benchmark.txt":{"url":"journey/sources/octave-school-benchmark.txt","title":"OCTAVE — SCHOOL TRAINING AND BENCHMARK RESULTS","kind":"Research report","author":"Anthony Michael Collado","authorBasis":"Collection attribution; original record retains its own credits","originalPath":"journey/sources/octave-school-benchmark.txt","bytes":6635,"sha256":"288afeeb8dda6449f735745fb14913d78be023a16fdd1f330c6448e32d11811f","savedDate":"2026-10-01","date":"2026-10-01","dateKind":"Saved source date","declaredDates":[],"projectId":"octave","projectIds":["octave"],"associationBasis":"Explicit project source citation","status":"Original saved source","headings":[],"journey":{"question":{"text":"Can broader Level 2 training improve held-out forecasts and transfer back to Level 1 under the declared school protocol?","label":"The benchmark question","source":"journey/sources/octave-school-benchmark.txt","sectionId":"source-record","provenance":"Editorial question based on the source protocol"},"answer":{"text":"L2 improves held-out L1 bit accuracy in all three recurrent seeds: mean +1.66 percentage points. Exact L1 improves in seed 117 but declines in seeds 228 and 339: mean +2.34 points, driven by one seed. No reliable exact-transfer claim. Held-out L2 combined A+B bit accuracy: recurrent 92.70%, dense 84.16%; complete forecasts: recurrent 9.90%, dense 4.23%. Dense performs better on trained-band bit forecasts, and on exact L1 forecasts in its L1-only branch.","label":"Measured conclusions","source":"journey/sources/octave-school-benchmark.txt","sectionId":"source-record","provenance":"Source excerpt"},"checks":{"text":"Final exams did not select checkpoints, alter teaching or drive training. Train bands, held-out bands, noise protocol and reproduction commands are documented in README.txt. This is a preliminary fixed-budget experiment, not a mastery or frontier-performance certificate. More updates could change the comparison. Same data/update budget does not mean same compute: architectures, learning rates and gradient clipping differ. Eight-observer superiority requires matched observer-count ablations. Complete L2 forecasts require all 64 A+B bits correct, whereas complete L1 forecasts require 32 A bits. Log loss and Brier scores appear in raw results. No uncertainty calibration is claimed. Historical recurrence/copy reference uses strong integer-lag structure and separately trained weights.","label":"Final exam protocol and interpretation limits","source":"journey/sources/octave-school-benchmark.txt","sectionId":"source-record","provenance":"Source excerpt"},"nextQuestion":{"text":"This is a preliminary fixed-budget experiment, not a mastery or frontier-performance certificate. More updates could change the comparison. Same data/update budget does not mean same compute: architectures, learning rates and gradient clipping differ. Eight-observer superiority requires matched observer-count ablations. Complete L2 forecasts require all 64 A+B bits correct, whereas complete L1 forecasts require 32 A bits. Log loss and Brier scores appear in raw results. No uncertainty calibration is claimed. Historical recurrence/copy reference uses strong integer-lag structure and separately trained weights.","label":"Interpretation limits","source":"journey/sources/octave-school-benchmark.txt","sectionId":"source-record","provenance":"Source excerpt"}},"figures":[],"illustrationIndex":10,"illustrationLabel":"Explanatory illustration · not a reported measurement","abstract":"Actual execution: 800.8 seconds recurrent experiment; 2.5 seconds dense comparison. Training plus final evaluation, excluding added diagnostics. 53,200 recurrent parameters; 74,306 dense parameters. Three training seeds. 600 base L1 updates + 600 per cloned branch; batch 16. 5,400 gradient updates / 86,400 example presentations per architecture across the experiment. Both branches consume the same fresh worlds; 57,600 unique generated training worlds per architecture. The existing runnable model was trained from scratch on the broader school. The scaled world-model proposal is not implemented or trained.","words":921}},"projects":{"theory":{"id":"theory","title":"Theory of Reality","area":"Framework","version":"Theory 2.42 / reviewed 15 Oct 2026","status":"Revisable framework · empirical validation open","question":"How can a richer state, its dynamics, and an observer be expressed in one explicit modelling architecture?","build":["A versioned seven-layer projective framework, a 20-sector physical coverage ledger, and the Wave–Observer Formulation.","The central pipeline is state → mode dynamics → interaction → observer → checked prediction.","The manuscript retains derivations, synthetic benchmarks, countermodels, failed trials, and correction history."],"results":["15 October update: 57 engine records mapped; recorded native replay passes 1,365 tests in 31 groups. 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Every neighbouring experiment tests a particular part of that architecture.","recordDates":["2026-09-21","2026-09-26"],"dateLabel":"4 Sep – 15 Oct 2026","dateKind":"Current manuscript source window","sources":[{"label":"Current 15 October audit and next test","url":"research/state-of-the-theory.html"},{"label":"Theory_of_Reality.md","url":"archive/1d8715c179d2-Theory_of_Reality.md"},{"label":"Wave_Observer_Formulation.md","url":"archive/cae4bcf2f553-Wave_Observer_Formulation.md"},{"label":"Physical_Coverage_And_Gauge_Derivation.md","url":"archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md"}],"lab":null,"measurement":"v1.97 · 84 revision entries","group":"Foundation","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":0,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which independently distinguishing measurement can separate a material delay from a sample-only optical-path delay?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/034529e4bc8c-benchmark_v28_all_unknown_full_market_minimized.cnf.txt","archive/1d8715c179d2-Theory_of_Reality.md","archive/2711bdafd755-Higher_Dimension_Wave_Audit.md","archive/350b255f3242-THEORY_AND_RESULTS.md","archive/7a9c23a3a539-projective-ripple-reality.md","archive/88d96126ec54-Physical_Coverage_And_Gauge_Derivation.md","archive/95573c01bc39-NULL_AXIS_OBSERVABILITY.md","archive/9c556a0548e7-Dimensional_Reality_Court_Audit.md","archive/be3eaac1ae3c-BS_AUDIT.md","archive/cae4bcf2f553-Wave_Observer_Formulation.md","archive/edfdb0a56bf4-UNIVERSES_AND_PROOF_BRIDGES.md","archive/fb5c05cfc8ce-Eingef-gter-Text.txt","archive/snapshot-readme.md"],"checks":[{"text":"Reality Bit Engine 0.10.0 has a standard-library-only C++17 core and an optional Python 3.10+ standard-library independent audit. 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The general RH, P-vs-NP, and Navier–Stokes problems remain open.","origin":"The modelling architecture becomes a canonical finite state and a library of declared operators that can be compiled and checked.","contribution":"The framework becomes executable: a canonical state and declared operators turn modelling choices into finite computations that can be checked.","recordDates":["2026-09-05"],"dateLabel":"Saved 5 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/state-of-the-theory.html"},{"label":"Reality Bit Engine 0.20.0 · README","url":"archive/reality-bit-engine-v0.20.0-README.md"},{"label":"reality-bit-engine-v0.20.0.zip","url":"archive/1a23cf011c55-reality-bit-engine-v0.20.0.zip"}],"lab":null,"measurement":"848-bit state · 101 capabilities","group":"Foundation","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which additional capability can be supported by a portable, independently replayed certificate within a declared mathematical scope?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/reality-bit-engine-v0.20.0-README.md"],"checks":[],"journey":{"question":{"text":"Which parts of the proposed framework can be compiled into exact, inspectable computation?","label":"Research question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"Exact finite-state witnesses and counterexamples distinguish a closed projection from a same-effect/different-future collision. 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Python 3.10+ is required; execution here used Linux and Python 3.12.13. Windows commands are supplied but were not independently run on Windows.","label":"7. Reproduce and inspect","source":"archive/089c94a4ecca-RRLS_PNP_COMPOSITION_PROOF.md","sectionId":"source-h-8","provenance":"Source excerpt"}],"journey":{"question":{"text":"When does recognizing the right relation remove unnecessary search?","label":"Research question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The v0.27 repair checks 1,200 rational modular worlds, 500 generated sequences, and 14,000 values excluded from fitting. A learned Fibonacci recurrence evaluates a(10^96) = 160 mod 257, independently checked by fast doubling. 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Windows commands are supplied but were not independently run on Windows.","label":"Checks and conditions","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Can recognition, rewriting and solving together remain efficient on a declared family once every part of the cost is counted?","label":"The next question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"rrls","figures":[]},"drct":{"id":"drct","title":"DRCT: black-box reconstruction & invented concepts","area":"AI & inference","version":"v1 → v21","status":"Finite-domain reconstruction","question":"What structure can an oracle reveal, and how can a learner invent reusable relation classes?","build":["A progression from observable closure and blind reconstruction to interventions, exact module tomography, sensor synthesis, operator invention, and ontology induction.","The v6 transformer experiment queries the complete declared domain of a five-token, four-position teacher.","v21 removes the fixed morphism-class menu and learns anonymous concepts from generic degree predicates and finite combinatorial code length."],"results":["The v6 lookup clone covers all 780 possible contexts, with zero maximum oracle-logit difference and zero argmax mismatches.","A head-permuted teacher has different parameters but the same input/output function; this separates functional reconstruction from weight identifiability.","v21 learns four concepts from 50 source worlds; its frozen ontology scores 500/500 unseen post-hoc types and rejects 200/200 novel structural controls.","Across 50 Monte Carlo labs, the expected concept basis is recovered in all 50."],"boundary":"The v6 clone is exhaustive on its small finite domain. v21 still assumes a primitive predicate language; neither result establishes arbitrary-scale model reconstruction or ontology from no prior structure.","origin":"Black-box reconstruction separates functional equality from hidden-parameter identity. Small complete domains give a controlled reference for that distinction.","contribution":"An exact observable clone need not identify unique hidden parameters. Anonymous-concept tests then ask which internal descriptions transfer to unseen worlds.","recordDates":["2026-08-23"],"dateLabel":"Saved 23 Aug 2026","dateKind":"Saved source window","sources":[{"label":"DRCT v6 · complete-domain record","url":"archive/d4ca6f5515b8-README.md"},{"label":"THEORY_V21.md","url":"archive/519566f74c0d-THEORY_V21.md"},{"label":"DRCT v21 · results","url":"archive/drct_morphism_ontology_induction_v21-results.json"},{"label":"drct_morphism_ontology_induction_v21.zip","url":"archive/8e95cf5667dd-drct_morphism_ontology_induction_v21.zip"}],"lab":null,"measurement":"780/780 contexts cloned","group":"Inference","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":7,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which larger held-out system can be reconstructed when the query budget and primitive relation language are fixed in advance?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/17fae99d3cec-THEORY_V3.md","archive/1abe41bc67c3-THEORY_V2.md","archive/1becea26408c-THEORY_V9.md","archive/2ab60a5f99b1-THEORY_V16.md","archive/2aeab23576cd-THEORY_V18.md","archive/341d6e48b548-THEORY_V14.md","archive/515974945d3b-THEORY_V17.md","archive/519566f74c0d-THEORY_V21.md","archive/6692434a8200-THEORY_V19.md","archive/7a6adf9e99db-THEORY_V15.md","archive/8f54278510af-THEORY_V11.md","archive/9a6ff68abec1-THEORY_V12.md","archive/9f79fa0d0806-THEORY-1-.md","archive/a76d46a48686-THEORY_V13.md","archive/ab7a8225476b-THEORY_V5.md","archive/b590d28cd189-THEORY_V4.md","archive/b6069be05c7f-THEORY_V10.md","archive/c94337709c96-P3_Hardware_Runbook_R1.md","archive/d0801d0f81e1-THEORY_V20.md","archive/d1230f150e39-P3_Hardware_Audit_Report.md","archive/d4ca6f5515b8-README.md","archive/ef2aa36ff943-Wallbreaker_Protocol_P3.md"],"checks":[{"text":"A trained two-head causal transformer was hidden behind a logit-query oracle.","label":"DRCT Black-Box Transformer Stress Test v6","source":"archive/d4ca6f5515b8-README.md","sectionId":"source-h-1","provenance":"Source excerpt"}],"journey":{"question":{"text":"What structure can an oracle reveal, and how can a learner invent reusable relation classes?","label":"Research question","source":"archive/d4ca6f5515b8-README.md","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The v6 lookup clone covers all 780 possible contexts, with zero maximum oracle-logit difference and zero argmax mismatches. A head-permuted teacher has different parameters but the same input/output function; this separates functional reconstruction from weight identifiability. v21 learns four concepts from 50 source worlds; its frozen ontology scores 500/500 unseen post-hoc types and rejects 200/200 novel structural controls. Across 50 Monte Carlo labs, the expected concept basis is recovered in all 50.","label":"Reported findings","source":"archive/d4ca6f5515b8-README.md","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"A trained two-head causal transformer was hidden behind a logit-query oracle.","label":"Checks and conditions","source":"archive/d4ca6f5515b8-README.md","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which larger held-out system can be reconstructed when the query budget and primitive relation language are fixed in advance?","label":"The next question","source":"archive/d4ca6f5515b8-README.md","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"drct","figures":[]},"rope":{"id":"rope","title":"Rope Tomography & sequential validation","area":"Dynamics","version":"0.14.0","status":"Synthetic system identification","question":"Can causal delays and local responses be recovered from a boundary-driven wave?","build":["A causal string model with local attachment response, multi-frequency fitting, withheld prediction, and source-calibration ambiguity controls.","The lab evolves through intervention design and independently budgeted sequential adequacy tests.","Later detectors distinguish conditional Gaussian, conditionally balanced-sign, and fixed Markov-sign assumptions."],"results":["The original program includes three wave-equation grids, 72 noisy fits and 72 unmodelled-echo fits, with six withheld frequencies per fit.","The Markov-sign release crosses on 39/5,000 declared 90%-persistence null histories and detects 4,629/5,000 97%-persistence alternatives.","An independent replay reproduces 24,000,000 decisions; the 0.14.0 README records 110 passing tests."],"boundary":"All lab observations are synthetic. A detector crossing supports a correction under its declared conditional null; it does not uniquely identify a physical mechanism.","origin":"The forward string model opens an inverse question: which causal delays can be identified from observations and withheld predictions?","contribution":"The inverse problem asks what can be recovered from delayed signals. Held-out frequencies and sequential controls turn that question into bounded evidence for a declared model.","recordDates":["2026-09-05"],"dateLabel":"Saved 5 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/identifiability.html"},{"label":"Universal_Cycle_Tomography.md","url":"archive/128270b32cd4-Universal_Cycle_Tomography.md"},{"label":"Rope Tomography Lab 0.14.0 · README (saved 20 Sep)","url":"archive/rope-tomography-lab-rope-tomography-lab-README.md"}],"lab":null,"measurement":"72 response fits · 24M replayed decisions","group":"Dynamics","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":3,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which calibrated physical intervention can distinguish the proposed response mechanism from alternatives that share the same observed signal?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/068ce17145c0-Reality_Revision_1.14.md","archive/128270b32cd4-Universal_Cycle_Tomography.md","archive/58da85d88c36-RRLS_v24_UNIVERSAL_CYCLE_REPORT.md","archive/fe52db8f3602-Reality_Revision_1.39.md","archive/rope-tomography-lab-rope-tomography-lab-README.md"],"checks":[{"text":"The next empirical step is a defined physical system with a calibrated actuator and synchronized sensors. Specify the propagation law, admissible attachment responses, noise model, and competing models before fitting. Vary the input deliberately, fit on one set of trials, and predict withheld frequencies or time sequences without refitting. Use physically justified bounds on delay, gain, and local response; retain alternative parameterizations that remain observationally equivalent.","label":"9. What would make this a test of nature?","source":"archive/128270b32cd4-Universal_Cycle_Tomography.md","sectionId":"source-h-14","provenance":"Source excerpt"},{"text":"Tested on Python 3.12.13, NumPy 2.3.5, and SciPy 1.17.0. Install the pinned environment, then run: On Linux/macOS, use python3 in place of py -3.12. Re-running the experiment overwrites results/. The recorded run used OPENBLAS_NUM_THREADS=1 and OMP_NUM_THREADS=1. Timings and floating-point rounding can vary across machines and numerical libraries.","label":"Run on a PC","source":"archive/rope-tomography-lab-rope-tomography-lab-README.md","sectionId":"source-h-14","provenance":"Source excerpt"}],"journey":{"question":{"text":"Can causal delays and local responses be recovered from a boundary-driven wave?","label":"Research question","source":"research/identifiability.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The original program includes three wave-equation grids, 72 noisy fits and 72 unmodelled-echo fits, with six withheld frequencies per fit. The Markov-sign release crosses on 39/5,000 declared 90%-persistence null histories and detects 4,629/5,000 97%-persistence alternatives. An independent replay reproduces 24,000,000 decisions; the 0.14.0 README records 110 passing tests.","label":"Reported findings","source":"research/identifiability.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The next empirical step is a defined physical system with a calibrated actuator and synchronized sensors. Specify the propagation law, admissible attachment responses, noise model, and competing models before fitting. Vary the input deliberately, fit on one set of trials, and predict withheld frequencies or time sequences without refitting. Use physically justified bounds on delay, gain, and local response; retain alternative parameterizations that remain observationally equivalent. Tested on Python 3.12.13, NumPy 2.3.5, and SciPy 1.17.0. Install the pinned environment, then run: On Linux/macOS, use python3 in place of py -3.12. Re-running the experiment overwrites results/. The recorded run used OPENBLAS_NUM_THREADS=1 and OMP_NUM_THREADS=1. Timings and floating-point rounding can vary across machines and numerical libraries.","label":"Checks and conditions","source":"research/identifiability.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which calibrated physical intervention can distinguish the proposed response mechanism from alternatives that share the same observed signal?","label":"The next question","source":"research/identifiability.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"rope","figures":[]},"hydrogen":{"id":"hydrogen","title":"Hydrogen Matrix Lab","area":"Matter & chemistry","version":"0.8.0","status":"Quantum reference & hypothesis tests","question":"Can projected rotor geometry reproduce a declared quantum reference, and which harmonics reach an observable?","build":["A 129³ hydrogen 1s probability matrix and a 24 × 49³ time-indexed 1s + 2p_z density sequence.","Independent density/current audits, a reduced-mass/Dirac spectroscopy ladder, golden-ratio controls, and an observable compiler.","Separate touching-4D-rotor geometry is calibrated and tested against unseen quantum phases."],"results":["The proposed rotor fails four of five preregistered gates; a four-component rescue improves held-out Hellinger error by only 0.34% and still fails five of six.","Reduced mass removes 97.77% of the old centroid error. The reduced-mass Dirac comparison leaves a 3.303 ppm residual in the stated ladder.","The exhaustive n ≤ 40 scan checks 303,809 distinct pairs among 780 ideal transitions; exact golden-gap ratios are excluded by the written rationality argument.","The observable compiler carries density into conserved current, dipole, radiation, and operator-filtered harmonics."],"boundary":"Quantum references use imported standard assumptions. Probability envelopes are not hard electron shells; a classical expectation dipole does not supply the whole spontaneous-photon channel.","origin":"Hydrogen supplies an explicit reference against which projected rotor hypotheses and observable constructions can fail or improve.","contribution":"Density, current, and spectral observables are compiled from a declared atomic state. Failed rotor gates expose which geometric descriptions do not recover the quantum reference.","recordDates":["2026-09-20"],"dateLabel":"Saved 20 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/measurement.html"},{"label":"/The Theory of Reality/Hydrogen Matrix Lab/README.md","url":"archive/8f4bc9b887c3-README.md"},{"label":"Hydrogen Matrix Lab · observable compiler","url":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-RESULTS_0.8.md"},{"label":"hydrogen-matrix-lab.zip","url":"archive/6094e1c15325-hydrogen-matrix-lab.zip"}],"lab":"atoms","measurement":"129³ density · 24 time slices","group":"Matter & light","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":4,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which frozen holdout can distinguish the geometric rotor model from the declared quantum reference without refitting the model?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/12135221929f-RESULTS_0.6.md","archive/249244afa345-RESULTS_0.3.md","archive/26ff0912ad26-RESULTS.md","archive/4d178b10ff09-release_0.6_test_log.txt","archive/51077294ef69-RESULTS_0.7.md","archive/5238c9f96c50-release_0.7_test_log.txt","archive/62fcd117c532-RESULTS_0.2.md","archive/81b60f656540-RESULTS_0.5.md","archive/8932ff1185c8-Theory_of_Reality_v1.70_draft.md","archive/8da92f374f97-RESULTS_0.4.md","archive/8f4bc9b887c3-README.md","archive/9c0d442dad18-CLAIM_LEDGER.md","archive/hydrogen-matrix-lab-hydrogen-matrix-lab-README.md","archive/hydrogen-matrix-lab-hydrogen-matrix-lab-RESULTS_0.8.md"],"checks":[{"text":"- hydrogen_1s_density.npz: coordinates, the full density matrix, and sampled voxel centers. - hydrogen_1s_90pct.obj: static 3D probability envelope; coordinates are in Bohr radii. - summary.json: matrix configuration, moments, probability radii, and epistemic status. - independent_check.json: a separate SciPy quadrature and matrix audit. - hydrogen_1s_preview.png: static preview generated from the saved matrix samples. - hydrogen_1s_2pz_basis.npz: independently testable 1s and signed 2p_z basis matrices. - hydrogen_1s_2pz_4d_density.npz: 24 time-indexed 3D quantum density and interference frames.","label":"Run","source":"archive/8f4bc9b887c3-README.md","sectionId":"source-h-6","provenance":"Source excerpt"},{"text":"A separate implementation imports none of the production compiler modules and passes 12 checks against independently reconstructed constants and saved arrays. The ten new unit tests pass. The full package regression is recorded in outputs/release_0.8_test_log.txt.","label":"Independent verification and limits","source":"archive/hydrogen-matrix-lab-hydrogen-matrix-lab-RESULTS_0.8.md","sectionId":"source-h-5","provenance":"Source excerpt"}],"journey":{"question":{"text":"Can projected rotor geometry reproduce a declared quantum reference, and which harmonics reach an observable?","label":"Research question","source":"research/measurement.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The proposed rotor fails four of five preregistered gates; a four-component rescue improves held-out Hellinger error by only 0.34% and still fails five of six. Reduced mass removes 97.77% of the old centroid error. The reduced-mass Dirac comparison leaves a 3.303 ppm residual in the stated ladder. The exhaustive n ≤ 40 scan checks 303,809 distinct pairs among 780 ideal transitions; exact golden-gap ratios are excluded by the written rationality argument. The observable compiler carries density into conserved current, dipole, radiation, and operator-filtered harmonics.","label":"Reported findings","source":"research/measurement.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"- hydrogen_1s_density.npz: coordinates, the full density matrix, and sampled voxel centers. - hydrogen_1s_90pct.obj: static 3D probability envelope; coordinates are in Bohr radii. - summary.json: matrix configuration, moments, probability radii, and epistemic status. - independent_check.json: a separate SciPy quadrature and matrix audit. - hydrogen_1s_preview.png: static preview generated from the saved matrix samples. - hydrogen_1s_2pz_basis.npz: independently testable 1s and signed 2p_z basis matrices. - hydrogen_1s_2pz_4d_density.npz: 24 time-indexed 3D quantum density and interference frames. A separate implementation imports none of the production compiler modules and passes 12 checks against independently reconstructed constants and saved arrays. The ten new unit tests pass. The full package regression is recorded in outputs/release_0.8_test_log.txt.","label":"Checks and conditions","source":"research/measurement.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which frozen holdout can distinguish the geometric rotor model from the declared quantum reference without refitting the model?","label":"The next question","source":"research/measurement.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"hydrogen","figures":[{"url":"archive/2bd98d766cc8-hydrogen_1s_preview.png","caption":"hydrogen_1s_preview.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/hydrogen_1s_preview.png","sha256":"2bd98d766cc8a26dbd0d31e49d25413438bd939634fb152e5671cf948888fa62"}],"figure":{"url":"archive/2bd98d766cc8-hydrogen_1s_preview.png","caption":"hydrogen_1s_preview.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Hydrogen Matrix Lab/hydrogen_1s_preview.png","sha256":"2bd98d766cc8a26dbd0d31e49d25413438bd939634fb152e5671cf948888fa62"}},"elements":{"id":"elements","title":"Element Projection & crystal interference","area":"Matter & chemistry","version":"0.16.0","status":"Reference-backed numerical models","question":"What atom, crystal, and optical geometry can be built from explicit, sourced inputs?","build":["All 118 identities, 92 crystal phase records, 30 sourced optical datasets, and browser observers for atoms, local faces, primitive cells, and finite specimens.","Reciprocal lattices, geometry-only structure factors, powder shells, finite-crystal sums, and explicit homometric ambiguity controls.","Density level sets and wave-defined crossing surfaces, with reference geometry kept separate from display constructions."],"results":["The diffraction release computes 56,656 reciprocal points, 4,766 numerically suppressed points, and 5,962 powder shells.","An independent NIST SRM640g geometry check reproduces eleven tabulated computed angles to within 0.000435607°.","Two different point arrangements have exactly identical intensity for every real q within the equal-scatterer model."],"boundary":"These are point-scatterer geometry weights. The NIST angle check concerns tabulated computed values, not eleven independent measured peaks. Growth habits and multielectron densities have separate approximation limits.","origin":"Reference density and geometry lead into the Atom & Crystal Observer. Structure factors connect declared basis sites to diffraction.","contribution":"Atomic references become finite specimens and interference observables. Exact intensity ambiguities test how much structure a particular observer can actually identify.","recordDates":["2026-09-21"],"dateLabel":"Saved 21 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/measurement.html"},{"label":"Atom_Crystal_Observer_Method.md","url":"archive/c60f72e23a0b-Atom_Crystal_Observer_Method.md"},{"label":"/The Theory of Reality/Element Projection Lab/RESULTS_0.15.md","url":"archive/a00a6dab1f40-RESULTS_0.15.md"},{"label":"element-projection-lab.zip","url":"archive/bb9b23d8100b-element-projection-lab.zip"}],"lab":"crystals","measurement":"56,656 reciprocal points · 92 phases","group":"Matter & light","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":5,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which calibrated independent observation can check the point-scatterer geometry and material-response approximations?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/2b014f84d8bb-RESULTS_0.11.md","archive/33deacfda028-RESULTS_0.14.md","archive/3636ed2ff4b1-RESULTS_0.6.md","archive/49a533cb5852-release_0.4_test_log.txt","archive/5860aee36113-RESULTS_0.13.1.md","archive/615550862b88-RESULTS_0.10.md","archive/634ff256fff3-release_0.3_test_log.txt","archive/9bcf81fa9421-RESULTS_0.13.md","archive/a00a6dab1f40-RESULTS_0.15.md","archive/bb51103f7acd-CLAIM_LEDGER.md","archive/c60f72e23a0b-Atom_Crystal_Observer_Method.md","archive/fe6d26d12295-RESULTS_0.12.md"],"checks":[{"text":"Seven new unit groups verify all 92 phase-coordinate records, known neighbor polyhedra, oriented hull volumes and Euler topology, compatibility with the previous nearest-site environments, hydrogen normalization/orthogonality, normal-incidence color preservation and graphite's planar-shell boundary.","label":"Executed checks and preserved limitations","source":"archive/c60f72e23a0b-Atom_Crystal_Observer_Method.md","sectionId":"source-h-7","provenance":"Source excerpt"},{"text":"The model is elastic, coherent, kinematic scattering from identical points. It omits element-dependent atomic form factors, thermal displacement, absorption, multiple scattering, texture, background and instrument response. Consequently the displayed weights are geometry-only interference weights, not calibrated detector counts or material-color predictions. A real diffraction measurement can require physics that the point model omits.","label":"Scope and verification","source":"archive/a00a6dab1f40-RESULTS_0.15.md","sectionId":"source-h-6","provenance":"Source excerpt"}],"journey":{"question":{"text":"What atom, crystal, and optical geometry can be built from explicit, sourced inputs?","label":"Research question","source":"research/measurement.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The diffraction release computes 56,656 reciprocal points, 4,766 numerically suppressed points, and 5,962 powder shells. An independent NIST SRM640g geometry check reproduces eleven tabulated computed angles to within 0.000435607°. Two different point arrangements have exactly identical intensity for every real q within the equal-scatterer model.","label":"Reported findings","source":"research/measurement.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"Seven new unit groups verify all 92 phase-coordinate records, known neighbor polyhedra, oriented hull volumes and Euler topology, compatibility with the previous nearest-site environments, hydrogen normalization/orthogonality, normal-incidence color preservation and graphite's planar-shell boundary. The model is elastic, coherent, kinematic scattering from identical points. It omits element-dependent atomic form factors, thermal displacement, absorption, multiple scattering, texture, background and instrument response. Consequently the displayed weights are geometry-only interference weights, not calibrated detector counts or material-color predictions. A real diffraction measurement can require physics that the point model omits.","label":"Checks and conditions","source":"research/measurement.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which calibrated independent observation can check the point-scatterer geometry and material-response approximations?","label":"The next question","source":"research/measurement.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"elements","figures":[{"url":"archive/8288069653e6-diffraction_validation.png","caption":"diffraction_validation.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Element Projection Lab/diffraction_validation.png","sha256":"8288069653e6561517da018f327519d924ffc1dea850279065accbd3af2afb8c"}],"figure":{"url":"archive/8288069653e6-diffraction_validation.png","caption":"diffraction_validation.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Element Projection Lab/diffraction_validation.png","sha256":"8288069653e6561517da018f327519d924ffc1dea850279065accbd3af2afb8c"}},"matter":{"id":"matter","title":"Matter Harmony & observer banks","area":"Matter & chemistry","version":"1.5.0","status":"Synthetic & published-data comparisons","question":"Which molecular, spectral, and observation coordinates are needed to distinguish physical behaviour?","build":["Same-formula isomer comparisons, projected 5D motion, water vibration/relaxation, sun–water–eye views, and acoustic droplet observables.","Observer-rank, exposure, phase, and generator-gauge controls; hydrogen transitions and isotope-shift holdouts.","A growing claim ledger retains both supported bounded statements and explicit representation collisions."],"results":["The supplied-matrix classifier recovers four generator families in 512/512 randomized cases, with maximum frequency error 1.11e−15.","A two-frequency linear 5D observer cannot reproduce four distinct Balmer features; exposure changes visibility, not frequency support.","The frozen isotope operator predicts −201.996425 Hz on the separate 2S–8S target, moving the central prediction slightly farther from its measurement.","Its holdout contrast is only 0.019484 combined standard deviations; the record preserves unresolved ambiguity."],"boundary":"Synthetic higher-dimensional coordinates are mathematical states. The isotope check uses historical published inputs; it supplies neither a new measurement nor confirmation of an extra physical dimension.","origin":"The observer question extends to molecules, spectra, exposure, and examples where different hidden states share an observation.","contribution":"A hidden state can be classified while its physical interpretation remains ambiguous. Observer banks and holdouts distinguish representation success from a new physical measurement.","recordDates":["2026-09-20"],"dateLabel":"Saved 20 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/measurement.html"},{"label":"Matter_Harmony_Claim_Ledger.md","url":"archive/4286df93f3ee-Matter_Harmony_Claim_Ledger.md"},{"label":"Matter Harmony 1.5 · isotope holdout","url":"archive/matter-harmony-lab-1.5.0-matter-harmony-lab-RESULTS_1.5.md"}],"lab":null,"measurement":"512/512 classifier cases","group":"Matter & light","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which new held-out molecular or spectral observation distinguishes the proposed coordinates from competing explanations?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/03af7a213e27-At_Fr_Followup_Report.md","archive/03ea1efe29ee-Reality_Revision_1.54.md","archive/07cef9ed332f-Parallel_Lines_Check.md","archive/1dcee8467de9-Reality_Revision_1.46.md","archive/21c9ff49e14b-Reality_Revision_1.51.md","archive/3a2a485fc9f0-Reality_Revision_1.52.md","archive/4286df93f3ee-Matter_Harmony_Claim_Ledger.md","archive/435b7200338e-Element_Harmonic_Report.md","archive/565c4b7a0100-Reality_Revision_1.45.md","archive/6df375e4347b-Reality_Render_Math_Check.md","archive/7aa233486073-Reality_Revision_1.55.md","archive/7ba09023fac2-Reality_Revision_1.50.md","archive/7c616040c25f-Reality_Revision_1.58.md","archive/876994ae70a5-Reality_Revision_1.47.md","archive/92f68f02a2fa-Circular_Structure_Report.md","archive/a19a33573c53-Reality_Revision_1.53.md","archive/a3fce32241d0-Reality_Revision_1.48.md","archive/a76f54a6d077-Reality_Revision_1.44.md","archive/c74f4adf9d1f-Element_By_Element.md","archive/fa4c581af7dc-Reality_Revision_1.49.md","archive/matter-harmony-lab-1.5.0-matter-harmony-lab-README.md","archive/matter-harmony-lab-1.5.0-matter-harmony-lab-RESULTS_1.5.md"],"checks":[{"text":"An audit that imports neither production isotope module recomputes the Yukawa matrix elements by direct radial quadrature and independently replays the covariance. It reproduces the material prediction.","label":"Independent verification and next test","source":"archive/matter-harmony-lab-1.5.0-matter-harmony-lab-RESULTS_1.5.md","sectionId":"source-h-4","provenance":"Source excerpt"}],"journey":{"question":{"text":"Which molecular, spectral, and observation coordinates are needed to distinguish physical behaviour?","label":"Research question","source":"research/measurement.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The supplied-matrix classifier recovers four generator families in 512/512 randomized cases, with maximum frequency error 1.11e−15. A two-frequency linear 5D observer cannot reproduce four distinct Balmer features; exposure changes visibility, not frequency support. The frozen isotope operator predicts −201.996425 Hz on the separate 2S–8S target, moving the central prediction slightly farther from its measurement. Its holdout contrast is only 0.019484 combined standard deviations; the record preserves unresolved ambiguity.","label":"Reported findings","source":"research/measurement.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"An audit that imports neither production isotope module recomputes the Yukawa matrix elements by direct radial quadrature and independently replays the covariance. It reproduces the material prediction.","label":"Checks and conditions","source":"research/measurement.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which new held-out molecular or spectral observation distinguishes the proposed coordinates from competing explanations?","label":"The next question","source":"research/measurement.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"matter","figures":[{"url":"archive/ad9a90c30e87-harmony_observer_diagnostic.png","caption":"harmony_observer_diagnostic.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Matter Harmony Lab/harmony_observer_diagnostic.png","sha256":"ad9a90c30e8733c12c3e70b20cd96a3e37841200b0e48579325a84916a4b4097"}],"figure":{"url":"archive/ad9a90c30e87-harmony_observer_diagnostic.png","caption":"harmony_observer_diagnostic.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Matter Harmony Lab/harmony_observer_diagnostic.png","sha256":"ad9a90c30e8733c12c3e70b20cd96a3e37841200b0e48579325a84916a4b4097"}},"gauge":{"id":"gauge","title":"Fixed Grid String & coupled gauge–matter","area":"Dynamics","version":"0.22.0","status":"Conditional mathematics & numerical audits","question":"Can the field and matter respond to one another while the declared conservation laws remain checkable?","build":["A progression from oscillator and hydrogen foundations to prescribed gauge fields, a self-consistent 1D ring, and a 2D U(1) plaquette model.","Three-grid checks, manufactured forcing, longer unforced trajectories, and smooth-versus-cusp counterexamples.","Dispersion, sampled-continuum, mirror-shadow, optical-tail, and paired-reference identifiability audits."],"results":["15 October update: Fixed Grid 0.25.0 is an explicitly new reconstruction that passes 167 tests. The original damaged 0.24 archive has not been restored, and five older files remain lost.","The 2D plaquette release records 142 passing tests and an independent final-state agreement within 1.76e−13.","Removing matter-current feedback breaks Gauss and energy accounting; removing magnetic feedback can break energy while retaining Gauss.","The corrected evolving three-grid example gives finite comparison ratios 3.8156–4.1557 for its short-time smooth case.","The current optical-reference counterexample separates what is measured from what can be assigned to material response."],"boundary":"Finite synthetic gauge models and convergence examples retain their scope. They do not establish a fundamental lattice, general continuum convergence, or QED.","origin":"Interaction moves inside the evolution rule. Field and matter feedback are tested through conservation and independent numerical audits.","contribution":"Coupled matter and field dynamics make interaction part of the state evolution. Conservation and feedback controls test the equations instead of relying on the rendered image.","recordDates":["2026-09-26"],"dateLabel":"Saved 26 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/state-of-the-theory.html"},{"label":"Fixed Grid String Lab 0.22.0 · README (saved 26 Sep)","url":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md"},{"label":"fixed-grid-string-lab.zip","url":"archive/f247ee0ef717-fixed-grid-string-lab.zip"}],"lab":null,"measurement":"142 checks · independent numerical audit","group":"Dynamics","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which refinement study can establish convergence beyond the currently declared finite synthetic examples?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/021dc11952bb-FOUNDATION_DERIVATION.md","archive/03e1b6b1c0c4-FOUNDATION_CONTRACT.md","archive/0a81254b1bd1-DIMENSIONAL_SLICE_DERIVATION.md","archive/1c5e7fdacf87-RESULTS_0.3.md","archive/24c14a8b651c-Fixed_Grid_String_Claim_Ledger.md","archive/441b2e8db915-RESULTS_0.2.md","archive/44b733bfc8d2-SOURCES_DIMENSIONAL_SLICES.md","archive/5d2c11aea25f-RESULTS_0.1.md","archive/8a175a69be60-SOURCES_DIPOLE.md","archive/a7a6cee5a51d-DIPOLE_DERIVATION.md","archive/f76a02c88aec-RESULTS_0.7.md","archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md"],"checks":[{"text":"Run python reference_calibration.py, python independent_reference_calibration_audit.py, and python -m unittest discover -p 'test_*.py' -q; inspect RESULTS_0.22.md. Under an exactly shared detector and optical-path kernel, the sample/reference Laplace-transform ratio identifies the material kernel. A sample-only path mismatch multiplies into the same ratio, and an exact counterexample replaces the entire 0.8 ns material delay with an observationally identical 0.8 ns excess-path delay. This is conditional mathematics plus finite synthetic checking, not a measured afterglow or evidence of an extra dimension.","label":"Version 0.22.0 — paired-reference calibration boundary","source":"archive/fixed-grid-string-lab-fixed-grid-string-lab-README.md","sectionId":"source-h-1","provenance":"Source excerpt"}],"journey":{"question":{"text":"Can the field and matter respond to one another while the declared conservation laws remain checkable?","label":"Research question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"15 October update: Fixed Grid 0.25.0 is an explicitly new reconstruction that passes 167 tests. The original damaged 0.24 archive has not been restored, and five older files remain lost. The 2D plaquette release records 142 passing tests and an independent final-state agreement within 1.76e−13. Removing matter-current feedback breaks Gauss and energy accounting; removing magnetic feedback can break energy while retaining Gauss. The corrected evolving three-grid example gives finite comparison ratios 3.8156–4.1557 for its short-time smooth case. The current optical-reference counterexample separates what is measured from what can be assigned to material response.","label":"Reported findings","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"Run python reference_calibration.py, python independent_reference_calibration_audit.py, and python -m unittest discover -p 'test_*.py' -q; inspect RESULTS_0.22.md. Under an exactly shared detector and optical-path kernel, the sample/reference Laplace-transform ratio identifies the material kernel. A sample-only path mismatch multiplies into the same ratio, and an exact counterexample replaces the entire 0.8 ns material delay with an observationally identical 0.8 ns excess-path delay. This is conditional mathematics plus finite synthetic checking, not a measured afterglow or evidence of an extra dimension.","label":"Checks and conditions","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which refinement study can establish convergence beyond the currently declared finite synthetic examples?","label":"The next question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"gauge","figures":[]},"optics":{"id":"optics","title":"Spectral renderer & Maxwell solver","area":"Light & rendering","version":"Studio 0.3","status":"Discrete physics demonstration","question":"How does a physical spectral state become an observer response and then a displayed image?","build":["A three-layer spectral engine: physical spectrum, CIE 1931 observer response, and display output.","Direct-light spectral ray tracing, coherent equal-wavelength interference, objects and shadows.","A live 224 × 144 TMz/TEz Yee-grid solver and a separate six-vector-component 72 × 96 × 24 Maxwell run."],"results":["The earlier spectral validation records 23/23 tests, 471 CIE samples, and matrix reconstruction below 2e−14 relative error.","The Maxwell build records 27 checks plus slit/polarization browser-engine checks.","At 1,100 2D steps, closed/single/double-slit detector sums are 0 / 0.0465 / 0.1405 in relative units.","The saved 620-step 3D result reaches a nonzero detector with several interference lobes."],"boundary":"The absorbing boundary is a lossy sponge, not PML. Discrete-grid checks establish the demonstration; continuous convergence and calibrated experimental agreement are separate targets.","origin":"The sun–water–eye work separates physical spectrum, observer response, and display. The Maxwell lab evolves fields before reading a detector.","contribution":"The visible image is the last map in a field-to-detector pipeline. The spectral renderer and Maxwell grids keep the propagating state and the observer response separate.","recordDates":["2026-09-26","2026-09-27"],"dateLabel":"Saved 26–27 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/aharonov-bohm.html"},{"label":"MAXWELL_VALIDATION.md","url":"archive/c300050706ec-MAXWELL_VALIDATION.md"},{"label":"SPECTRAL_VALIDATION.md","url":"archive/ed0171b0bc6a-SPECTRAL_VALIDATION.md"},{"label":"Rotor_Spectral_Studio_v0.3.zip","url":"archive/239b698fe6ef-Rotor_Spectral_Studio_v0.3.zip"}],"lab":"maxwell","measurement":"Six field components · 620 3D steps","group":"Matter & light","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":5,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which calibrated experimental comparison and grid-refinement study can check the optical model beyond its discrete demonstration?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/c300050706ec-MAXWELL_VALIDATION.md","archive/ed0171b0bc6a-SPECTRAL_VALIDATION.md"],"checks":[{"text":"- python -m unittest discover -s tests -v: 27 checks, including the 3D Courant limit, source-free magnetic divergence, periodic plane-wave temporal recurrence, field past a 3D aperture, and standalone PNG equality. - node tools/check_maxwell.cjs: opaque screen has zero downstream detector energy; a single slit transmits; double-slit total detector intensity exceeds single-slit; the central interference lobe exceeds an adjacent trough; both polarizations are finite and transmit. - node tools/check_optics.cjs: existing ray optics checks still pass. - node --check web/maxwell.js, plus full standalone script syntax check.","label":"Validation","source":"archive/c300050706ec-MAXWELL_VALIDATION.md","sectionId":"source-h-4","provenance":"Source excerpt"},{"text":"The reproducible demonstration in run_spectral_demo.py creates a 250–2500 nm spectrum containing UV, visible, and IR power. Its current fixture contains 39.9833% power inside the CIE table band and 60.0167% outside it. The visible projection is normalized XYZ [1.05608, 1.00000, 0.85441] and display-mapped sRGB [1.00000, 0.80277, 0.74808].","label":"Automated verification","source":"archive/ed0171b0bc6a-SPECTRAL_VALIDATION.md","sectionId":"source-h-8","provenance":"Source excerpt"}],"journey":{"question":{"text":"How does a physical spectral state become an observer response and then a displayed image?","label":"Research question","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The earlier spectral validation records 23/23 tests, 471 CIE samples, and matrix reconstruction below 2e−14 relative error. The Maxwell build records 27 checks plus slit/polarization browser-engine checks. At 1,100 2D steps, closed/single/double-slit detector sums are 0 / 0.0465 / 0.1405 in relative units. The saved 620-step 3D result reaches a nonzero detector with several interference lobes.","label":"Reported findings","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"- python -m unittest discover -s tests -v: 27 checks, including the 3D Courant limit, source-free magnetic divergence, periodic plane-wave temporal recurrence, field past a 3D aperture, and standalone PNG equality. - node tools/check_maxwell.cjs: opaque screen has zero downstream detector energy; a single slit transmits; double-slit total detector intensity exceeds single-slit; the central interference lobe exceeds an adjacent trough; both polarizations are finite and transmit. - node tools/check_optics.cjs: existing ray optics checks still pass. - node --check web/maxwell.js, plus full standalone script syntax check. The reproducible demonstration in run_spectral_demo.py creates a 250–2500 nm spectrum containing UV, visible, and IR power. Its current fixture contains 39.9833% power inside the CIE table band and 60.0167% outside it. The visible projection is normalized XYZ [1.05608, 1.00000, 0.85441] and display-mapped sRGB [1.00000, 0.80277, 0.74808].","label":"Checks and conditions","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which calibrated experimental comparison and grid-refinement study can check the optical model beyond its discrete demonstration?","label":"The next question","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"optics","figures":[{"url":"archive/51e79cefb5c4-maxwell3d_diffraction.png","caption":"maxwell3d_diffraction.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/maxwell3d_diffraction.png","sha256":"51e79cefb5c4ea8686bea37b5118dee142e231f658fa16f62d6a7f57f0999ca3"}],"figure":{"url":"archive/51e79cefb5c4-maxwell3d_diffraction.png","caption":"maxwell3d_diffraction.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/maxwell3d_diffraction.png","sha256":"51e79cefb5c4ea8686bea37b5118dee142e231f658fa16f62d6a7f57f0999ca3"}},"filaments":{"id":"filaments","title":"String & Hair mechanics","area":"Dynamics","version":"3D lab + RRLS v27","status":"Interactive mechanical model","question":"How do delayed excitation, stretch, twist, contact, and end forces shape attached strands?","build":["An orbitable 3D strand lab with linked fixed-rest-length segments, travelling anchor waves, paired motors, damping, bending, and contact.","Endpoint reach/rest-length readouts, paths, neighbouring histories, and contact displays.","The RRLS dimensional work also formalizes modular recurrence, event skipping, curvature/torsion, and analytic captured-strand mechanics."],"results":["The exact integer collision solver is compared with tick enumeration on 1,080 cases; rational and signed-start variants each record 500 cases.","A collision schedule can be computed by gcd reduction and generalized CRT without generating intermediate ticks.","The later source audit corrects period scaling, a stale capture time, an overdamped branch, and a cancellation-prone formula."],"boundary":"The browser model is discrete and uses arbitrary units. Contact penalties and open-ended braids are not a proof of continuously enforced no-crossing or permanent knots.","origin":"The rope-and-hair idea becomes boundary-driven motion, finite propagation speed, delayed response, and sampled contact.","contribution":"A boundary excitation, propagation speed, and collision history give the programme a concrete forward model for time, phase, and delayed response.","recordDates":["2026-09-06","2026-09-27"],"dateLabel":"Saved 6–27 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/aharonov-bohm.html"},{"label":"RRLS_v27_DIMENSIONAL_FUTURE_REPORT.md","url":"archive/4d0f85755df4-RRLS_v27_DIMENSIONAL_FUTURE_REPORT.md"},{"label":"RRLS_v27_SOURCE_AUDIT.md","url":"archive/8cae97ff1389-RRLS_v27_SOURCE_AUDIT.md"},{"label":"string-hair-3d-lab.html","url":"archive/92fee4c0df6c-string-hair-3d-lab.html"}],"lab":"string","measurement":"Travelling waves · collision schedules","group":"Dynamics","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":3,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which invariant and refinement checks can establish no-crossing behavior beyond the current penalty-based discrete model?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/4d0f85755df4-RRLS_v27_DIMENSIONAL_FUTURE_REPORT.md","archive/8cae97ff1389-RRLS_v27_SOURCE_AUDIT.md"],"checks":[{"text":"6 September 2026 · Theory of Reality revision 1.15","label":"RRLS v0.27 source audit and v0.27.1 repair","source":"archive/8cae97ff1389-RRLS_v27_SOURCE_AUDIT.md","sectionId":"source-h-1","provenance":"Source excerpt"}],"journey":{"question":{"text":"How do delayed excitation, stretch, twist, contact, and end forces shape attached strands?","label":"Research question","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The exact integer collision solver is compared with tick enumeration on 1,080 cases; rational and signed-start variants each record 500 cases. A collision schedule can be computed by gcd reduction and generalized CRT without generating intermediate ticks. The later source audit corrects period scaling, a stale capture time, an overdamped branch, and a cancellation-prone formula.","label":"Reported findings","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"6 September 2026 · Theory of Reality revision 1.15","label":"Checks and conditions","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which invariant and refinement checks can establish no-crossing behavior beyond the current penalty-based discrete model?","label":"The next question","source":"research/aharonov-bohm.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"filaments","figures":[]},"fluids":{"id":"fluids","title":"Water, dye, light & fields","area":"Light & rendering","version":"3D + time lab","status":"Interactive transport model","question":"Which visible structures come from fluid motion, diffusion, and prescribed electromagnetic forces?","build":["A 20³ staggered 3D incompressible grid and an 80 × 120 2D section with pressure projection.","Conservative slope-limited dye transport, viscosity, Boussinesq density force, quasi-static J×B, and a diamagnetic gradient force.","A 3D observer, field readouts, spacetime history, and impact-scale Reynolds/Weber/Ohnesorge/Schmidt calculations."],"results":["The model retains D = 4.0e−10 m²/s as a Rhodamine 6G diffusion proxy.","At its displayed scale, molecular diffusion alone travels about 0.09 mm in ten seconds; visible curling mainly comes from moving water.","Field/history panels make the (ct,x,y,z) event and six independent field-tensor components explicit."],"boundary":"The free surface is flat; impact retention and the initial ring are uncalibrated closures. It does not solve induced magnetic fields, molecular H₂O, or unresolved turbulence.","origin":"Water separates the medium, a transported signal, and its visible image. The dye grid makes conservation inspectable.","contribution":"The dye lab separates the motion of the medium, transport of a signal, and the fields acting on it. That separation matters when an observer sees only the final pattern.","recordDates":["2026-09-27"],"dateLabel":"Saved 27 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/state-of-the-theory.html"},{"label":"water-dye-light-lab.html","url":"archive/aa952be50c08-water-dye-light-lab.html"}],"lab":"water","measurement":"20³ flow grid · conservative transport","group":"Dynamics","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":3,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which measured closure and refinement checks can replace the currently uncalibrated impact and free-surface assumptions?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":[],"checks":[],"journey":{"question":{"text":"Which visible structures come from fluid motion, diffusion, and prescribed electromagnetic forces?","label":"Research question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The model retains D = 4.0e−10 m²/s as a Rhodamine 6G diffusion proxy. At its displayed scale, molecular diffusion alone travels about 0.09 mm in ten seconds; visible curling mainly comes from moving water. Field/history panels make the (ct,x,y,z) event and six independent field-tensor components explicit.","label":"Reported findings","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The linked sources retain the methods and original record. This editorial brief does not add an independent validation.","label":"Checks and conditions","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Editorial reading guide"},"nextQuestion":{"text":"Which measured closure and refinement checks can replace the currently uncalibrated impact and free-surface assumptions?","label":"The next question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"fluids","figures":[{"url":"archive/65d5d23255d9-sun_water_eye_snapshot.png","caption":"sun_water_eye_snapshot.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Matter Harmony Lab/sun_water_eye_snapshot.png","sha256":"65d5d23255d962d841cefee584bdbaea26edf2aba2caadb26972e18b76cb6396"}],"figure":{"url":"archive/65d5d23255d9-sun_water_eye_snapshot.png","caption":"sun_water_eye_snapshot.png","provenance":"Saved project figure; see original source for its conditions","originalPath":"/The Theory of Reality/Matter Harmony Lab/sun_water_eye_snapshot.png","sha256":"65d5d23255d962d841cefee584bdbaea26edf2aba2caadb26972e18b76cb6396"}},"chess":{"id":"chess","title":"Dimensional Chess: C1 through C8","area":"Computation","version":"C1–C8 + R1","status":"Exact finite & bounded proofs","question":"Which symmetries and future-preserving abstractions actually reduce the cost of a proof?","build":["An exact KRK graph solver, symmetry quotient, retrograde fixed point, independent certificate checker, and deliberate semantic-tamper test.","Full-rule state lifting, horizon-safe projection, tension and exchange-dependency fields, and movement-frequency move ordering.","Initial-position bounded forced-mate predicates with independent lexical checks."],"results":["C1 solves all 399,112 legal states in its declared KRK universe, reducing them to 50,015 symmetry classes; the maximum forced mate is 32 plies.","All 400,120 symmetry-transition comparisons and the independent Bellman/policy audit pass.","C8 reduces the nine-ply White proof from 575.877 to 375.703 seconds (34.76%); including its 31.087-second training cost, the reduction is 29.36%.","Both C7 and C8 return the same no-forced-mate-within-nine-plies predicate."],"boundary":"The KRK result solves its explicitly defined universe without FIDE history clocks. The initial full-chess game value is not solved; C8 changes ordering, not the game theorem.","origin":"The relation-and-representation programme gains a finite ground truth: solved endgame states and bounded certificates, alongside tests that resist full-chess shortcuts.","contribution":"A closed game universe supplies an exact reference. Later ordering improvements can be measured against the same bounded proof predicate, so speed and theorem remain distinct.","recordDates":["2026-09-15"],"dateLabel":"Saved 15 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/state-of-the-theory.html"},{"label":"Dimensional_Chess_Experiment.md","url":"archive/6875140b9128-Dimensional_Chess_Experiment.md"},{"label":"Dimensional_Chess_Movement_Frequency_C8.md","url":"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md"},{"label":"Dimensional_Chess_Horizon_Projection_C7.md","url":"archive/bc77a3eb88d2-Dimensional_Chess_Horizon_Projection_C7.md"}],"lab":null,"measurement":"399,112 legal KRK states solved","group":"Inference","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":6,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which larger rules-complete universe can receive an independently replayable proof while retaining history and draw conditions?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/192640670d05-Dimensional_Chess_Constraint_Wave_C4.md","archive/3fe7cf744ab8-Full_Chess_Dimensional_Lift_C2.md","archive/6875140b9128-Dimensional_Chess_Experiment.md","archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md","archive/88c2103b5c5b-Dimensional_Chess_Tension_Field_C5.md","archive/9b58e8d87cb0-Dimensional_Chess_Exchange_Dependency_C6.md","archive/b7e0db547cd6-Dimensional_Chess_Initial_Position_Run_R1.md","archive/bc77a3eb88d2-Dimensional_Chess_Horizon_Projection_C7.md","archive/d06ca187fd05-Full_Chess_State_Probe_C3.md"],"checks":[{"text":"verify_dimensional_chess.py imports no production function. It independently reconstructs: 1. all 399,112 raw legal positions; 2. all 50,015 symmetry orbits; 3. every legal transition and checkmate/stalemate condition; 4. all 400,120 symmetry-closure comparisons; 5. every win/loss/draw Bellman equation; 6. every shortest-mate and longest-defense distance; 7. every stored optimal policy edge; 8. all 32 concrete moves in the longest principal variation; 9. the certificate and principal-variation digests.","label":"6. Independent proof audit","source":"archive/6875140b9128-Dimensional_Chess_Experiment.md","sectionId":"source-h-8","provenance":"Source excerpt"},{"text":"The C8 result agrees with the separately implemented and independently verified C7 certificate that neither side can force mate within nine plies. A structural audit samples 960 deterministically reachable states and checks seven ordering schemes over 168,882 legal-move instances. Every ordered list is exactly a permutation of the corresponding legal list. Of the state/scheme cases, 6,720 actually change order, establishing that the test is not a lexical no-op. Audit status: PASS.","label":"Audit","source":"archive/709ba3d90a0c-Dimensional_Chess_Movement_Frequency_C8.md","sectionId":"source-h-7","provenance":"Source excerpt"},{"text":"The verifier imports no C7 solver code. It independently reconstructs the candidate prefix, defender draw actions, and AND/OR recurrence using the audited legal-state engine. It reproduces every reported result and all node, edge, cache, horizon, and terminal counts at depths seven and nine.","label":"Independent verification","source":"archive/bc77a3eb88d2-Dimensional_Chess_Horizon_Projection_C7.md","sectionId":"source-h-8","provenance":"Source excerpt"}],"journey":{"question":{"text":"Which symmetries and future-preserving abstractions actually reduce the cost of a proof?","label":"Research question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"C1 solves all 399,112 legal states in its declared KRK universe, reducing them to 50,015 symmetry classes; the maximum forced mate is 32 plies. All 400,120 symmetry-transition comparisons and the independent Bellman/policy audit pass. C8 reduces the nine-ply White proof from 575.877 to 375.703 seconds (34.76%); including its 31.087-second training cost, the reduction is 29.36%. Both C7 and C8 return the same no-forced-mate-within-nine-plies predicate.","label":"Reported findings","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"verify_dimensional_chess.py imports no production function. It independently reconstructs: 1. all 399,112 raw legal positions; 2. all 50,015 symmetry orbits; 3. every legal transition and checkmate/stalemate condition; 4. all 400,120 symmetry-closure comparisons; 5. every win/loss/draw Bellman equation; 6. every shortest-mate and longest-defense distance; 7. every stored optimal policy edge; 8. all 32 concrete moves in the longest principal variation; 9. the certificate and principal-variation digests. The C8 result agrees with the separately implemented and independently verified C7 certificate that neither side can force mate within nine plies. A structural audit samples 960 deterministically reachable states and checks seven ordering schemes over 168,882 legal-move instances. Every ordered list is exactly a permutation of the corresponding legal list. Of the state/scheme cases, 6,720 actually change order, establishing that the test is not a lexical no-op. Audit status: PASS. The verifier imports no C7 solver code. It independently reconstructs the candidate prefix, defender draw actions, and AND/OR recurrence using the audited legal-state engine. It reproduces every reported result and all node, edge, cache, horizon, and terminal counts at depths seven and nine.","label":"Checks and conditions","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which larger rules-complete universe can receive an independently replayable proof while retaining history and draw conditions?","label":"The next question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"chess","figures":[]},"shapes":{"id":"shapes","title":"Geometric products & inverse operators","area":"Geometry","version":"24-shape atlas","status":"Finite geometry & exact checks","question":"What happens when planar regions are multiplied, transformed, projected, and inverted?","build":["A declared Cartesian-product operation on 24 planar shapes, with a projected 4D boundary viewer.","576 ordered products, 300 unordered pairs, a full pair-analysis table, and convex-product volume checks.","Separate matrix rotor, spectral consistency, parallel-line, and shift/inverse audits retain what each transformation preserves."],"results":["The atlas checks 256 convex polygon pairs; maximum relative 4D volume error is 1.5543e−15.","A 2D×2D Cartesian product has four independent coordinates; the 3D display is its chosen projection.","The spectral matrix engine reconstructs the full benchmark matrices below 2e−14 relative error."],"boundary":"“Multiplication of shapes” depends on the stated operation. Cartesian products, Minkowski sums, sweeps, and pointwise multiplication cannot be interchanged.","origin":"The coordinate question becomes explicit geometry. Two planar regions form a 4D Cartesian product; the displayed object is a chosen projection.","contribution":"A projected image depends on its coordinate map. The product atlas makes that distinction explicit before the same question is asked of atoms or hidden model states.","recordDates":["2026-09-05","2026-09-26"],"dateLabel":"Saved 5–26 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Shape Products Atlas · README","url":"archive/shape-products-atlas-shape-products-README.md"},{"label":"shape-products-atlas.zip","url":"archive/e759ab681f2a-shape-products-atlas.zip"},{"label":"SPECTRAL_VALIDATION.md","url":"archive/ed0171b0bc6a-SPECTRAL_VALIDATION.md"}],"lab":"shapes","measurement":"24 shapes · 576 ordered products","group":"Foundation","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":2,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which inverse reconstruction remains identifiable once the product operation and observation map are fixed?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/ed0171b0bc6a-SPECTRAL_VALIDATION.md","archive/shape-products-atlas-shape-products-README.md"],"checks":[{"text":"The reproducible demonstration in run_spectral_demo.py creates a 250–2500 nm spectrum containing UV, visible, and IR power. Its current fixture contains 39.9833% power inside the CIE table band and 60.0167% outside it. The visible projection is normalized XYZ [1.05608, 1.00000, 0.85441] and display-mapped sRGB [1.00000, 0.80277, 0.74808].","label":"Automated verification","source":"archive/ed0171b0bc6a-SPECTRAL_VALIDATION.md","sectionId":"source-h-8","provenance":"Source excerpt"}],"journey":{"question":{"text":"What happens when planar regions are multiplied, transformed, projected, and inverted?","label":"Research question","source":"archive/shape-products-atlas-shape-products-README.md","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The atlas checks 256 convex polygon pairs; maximum relative 4D volume error is 1.5543e−15. A 2D×2D Cartesian product has four independent coordinates; the 3D display is its chosen projection. The spectral matrix engine reconstructs the full benchmark matrices below 2e−14 relative error.","label":"Reported findings","source":"archive/shape-products-atlas-shape-products-README.md","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The reproducible demonstration in run_spectral_demo.py creates a 250–2500 nm spectrum containing UV, visible, and IR power. Its current fixture contains 39.9833% power inside the CIE table band and 60.0167% outside it. The visible projection is normalized XYZ [1.05608, 1.00000, 0.85441] and display-mapped sRGB [1.00000, 0.80277, 0.74808].","label":"Checks and conditions","source":"archive/shape-products-atlas-shape-products-README.md","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Which inverse reconstruction remains identifiable once the product operation and observation map are fixed?","label":"The next question","source":"archive/shape-products-atlas-shape-products-README.md","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"shapes","figures":[]},"prng-markets":{"id":"prng-markets","title":"PRNG tomography & market interpreters","area":"AI & inference","version":"PRNG v4 · market v5–16","status":"Generator tests & historical holdouts","question":"Which apparent randomness is recoverable inside a declared model family, and which predictions transfer to unseen data?","build":["Finite-field affine/quadratic recurrence inference, LFSR/linear-complexity recovery, and prefix-to-untouched-suffix tests.","Market-state, path, residual, multiscale, amplitude-first, and confidence-subspace interpreters.","The v16 market check freezes v15 settings across six non-overlapping 1,000-hour forward blocks with prior-only training."],"results":["The v15 candle-range model records a 29.884% relative MAE gain against its stated baseline; amplitude conditioning leaves direction accuracy unchanged.","v16 scores 6,000 historical test hours at 52.367% aggregate direction accuracy, with a reported moving-block 95% interval of 51.0–53.533%.","The highest-confidence subsets do not transfer reliably: q90 and q95 exceed 50% in only two of six blocks."],"boundary":"PRNG recovery is conditional on a restricted generator class. Historical prediction scores do not establish a live trading edge or unrestricted prediction of random sources.","origin":"Prediction is confronted with untouched generator sequences and historical holdouts. The connection to RRLS is testing a learned relation beyond its fit.","contribution":"Generator recovery and market prediction test what a learned relation retains outside its fitting data. Restricted classes and held-out blocks define the reach of the claim.","recordDates":[],"dateLabel":"Undated release · PRNG v4 · market v5–16","dateKind":"Undated saved release","sources":[{"label":"PRNG Tomography v4 · theory","url":"archive/dimensional_prng_tomography_v4-THEORY.md"},{"label":"Amplitude-first v15 · results","url":"archive/amplitude_first_market_interpreter_v15-results.json"},{"label":"Predictability v16 · results","url":"archive/predictability_subspace_interpreter_v16-results.json"}],"lab":null,"measurement":"6,000 historical holdout hours","group":"Inference","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":7,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which frozen, out-of-time test retains predictive skill after the generator family, tuning budget and evaluation protocol are fixed?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/0e49c4b376ca-METHOD.md","archive/370642ea780a-THEORY.md","archive/95b0a3b2973e-RRLS_v08_EXPERIMENT_REPORT.md","archive/dimensional_prng_tomography_v4-THEORY.md"],"checks":[],"journey":{"question":{"text":"Which apparent randomness is recoverable inside a declared model family, and which predictions transfer to unseen data?","label":"Research question","source":"archive/dimensional_prng_tomography_v4-THEORY.md","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The v15 candle-range model records a 29.884% relative MAE gain against its stated baseline; amplitude conditioning leaves direction accuracy unchanged. v16 scores 6,000 historical test hours at 52.367% aggregate direction accuracy, with a reported moving-block 95% interval of 51.0–53.533%. The highest-confidence subsets do not transfer reliably: q90 and q95 exceed 50% in only two of six blocks.","label":"Reported findings","source":"archive/dimensional_prng_tomography_v4-THEORY.md","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"v16 scores 6,000 historical test hours at 52.367% aggregate direction accuracy, with a reported moving-block 95% interval of 51.0–53.533%.","label":"Checks and conditions","source":"archive/dimensional_prng_tomography_v4-THEORY.md","sectionId":"source-record","provenance":"Reported checks from the existing project research summary"},"nextQuestion":{"text":"Which frozen, out-of-time test retains predictive skill after the generator family, tuning budget and evaluation protocol are fixed?","label":"The next question","source":"archive/dimensional_prng_tomography_v4-THEORY.md","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"prng-markets","figures":[]},"semantic":{"id":"semantic","title":"Grounded Wave Semantic Network & NumPy LLM work","area":"AI & inference","version":"GWSN 0.1 · model work","status":"Proposal + reported model results","question":"Can explicit semantic structure be encoded as waves, transformed under constraints, and rendered into different languages?","build":["A six-module architecture: normalizer, canonicalizer/registry, wave encoder, neural wave core, typed verifier, and language renderer.","A finite Fourier byte codec with exact recoverability and a conditional invariance theorem for certified operators.","A separate NumPy language-model workstream targeting GPT-2 small and Qwen3 32B, with tensor/logit/token equivalence discussed."],"results":["The bounded canonical serializer is injectively encoded as Fourier coefficients, with a stated exact inverse.","Identical accepted semantic states and certified identical operations yield identical accepted states under the theorem’s premises.","Anthony’s project discussions report 96/96 GPT-2 token agreement and exact comparisons covering 4,846,488 intermediate elements, alongside claimed bitwise Qwen3 reproduction."],"boundary":"GWSN 0.1 reports no implementation, training run, or benchmark. The saved archive does not contain the standalone GPT-2/Qwen implementation or weights; those reproduction results are identified here as reported.","origin":"After equality comes meaning: GWSN proposes canonical semantic states and certified operations. It remains a separate architecture proposal.","contribution":"The architecture proposes a canonical semantic state, certified transformations, and an exact representation. It asks how to carry meaning beyond output equality; implementation remains open.","recordDates":["2026-09-30"],"dateLabel":"Saved 30 Sep 2026","dateKind":"Saved source window","sources":[{"label":"Current 15 October audit and next test","url":"research/state-of-the-theory.html"},{"label":"Grounded Wave Semantic Network · theorem v0.1","url":"archive/grounded-wave-semantic-network-v0.1.md"}],"lab":null,"measurement":"Six-module proposal · finite codec","group":"Learning & meaning","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":1,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Can a complete implementation and held-out benchmark test the proposed semantic-wave architecture and its declared constraints?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/grounded-wave-semantic-network-v0.1.md"],"checks":[{"text":"For a literal physical description, the intended grounding process is to obtain observations or a declared model, construct typed properties, and enforce laws within their validity regime. The network does not derive arbitrary object properties merely by receiving a noun.","label":"Grounding examples and counterexamples","source":"archive/grounded-wave-semantic-network-v0.1.md","sectionId":"source-h-11","provenance":"Source excerpt"}],"journey":{"question":{"text":"Can explicit semantic structure be encoded as waves, transformed under constraints, and rendered into different languages?","label":"Research question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The bounded canonical serializer is injectively encoded as Fourier coefficients, with a stated exact inverse. Identical accepted semantic states and certified identical operations yield identical accepted states under the theorem’s premises. Anthony’s project discussions report 96/96 GPT-2 token agreement and exact comparisons covering 4,846,488 intermediate elements, alongside claimed bitwise Qwen3 reproduction.","label":"Reported findings","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"For a literal physical description, the intended grounding process is to obtain observations or a declared model, construct typed properties, and enforce laws within their validity regime. The network does not derive arbitrary object properties merely by receiving a noun.","label":"Checks and conditions","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Can a complete implementation and held-out benchmark test the proposed semantic-wave architecture and its declared constraints?","label":"The next question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"semantic","figures":[]},"gpt2":{"id":"gpt2","title":"GPT-2: quantisation & the LayerNorm gauge","area":"Published model recovery","version":"Revised 28 Sep 2026","status":"Published preprint","question":"When the same observable output hides different weights, what extra constraint identifies the stored model?","build":["A published NumPy method separates gauge-free maps, LayerNorm-fed maps, and embedding tables.","Internal activation pairs feed least-squares recovery; float32 lattice constraints and the tied readout address distinct gauge obstructions.","The public gauge-break repository contains the method, runnable code, and run records."],"results":["The preprint reports all 124,439,808 GPT-2 small parameters recovered bit for bit, with an assembled SHA-256 matching the public checkpoint.","Its eight-column enumeration tests 107,214,677 candidates, finding eight survivors and 6,152/6,152 matching coordinates.","Two runs on x86-64 Windows and ARM64 Linux take different precision paths and recover identical bits.","The shuffled-activation controls report zero bit matches for the stated maps."],"boundary":"A published, unreviewed preprint using internal activation instrumentation. Public-checkpoint byte equality leaves the copying objection open; a hidden target or independent reproduction is the next distinguishing test. The lattice uniqueness statistic is conditional on the stated rounding null.","origin":"The hidden-model question is revisited with internal activation access and float32 constraints. This is a different observation contract from an output-only oracle.","contribution":"The published preprint places the observer boundary at LayerNorm: equal outputs hide a continuous family in real arithmetic, while stored precision and additional observations constrain recovery.","recordDates":[],"dateLabel":"Revised 28 Sep 2026","dateKind":"Dated project report","sources":[{"url":"https://www.d0re.com/paper","label":"Published preprint · method, controls & scope"},{"url":"https://github.com/sendmefather/gauge-break","label":"gauge-break · public source"},{"url":"https://github.com/sendmefather/gauge-break/tree/main/records","label":"Published run records"}],"lab":null,"measurement":"124,439,808 parameters · published report","group":"Inference","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":7,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Can a hidden target or independent reproduction distinguish genuine recovery from access to a public checkpoint?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":[],"checks":[],"journey":{"question":{"text":"When the same observable output hides different weights, what extra constraint identifies the stored model?","label":"Research question","source":"https://www.d0re.com/paper","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The preprint reports all 124,439,808 GPT-2 small parameters recovered bit for bit, with an assembled SHA-256 matching the public checkpoint. Its eight-column enumeration tests 107,214,677 candidates, finding eight survivors and 6,152/6,152 matching coordinates. Two runs on x86-64 Windows and ARM64 Linux take different precision paths and recover identical bits. The shuffled-activation controls report zero bit matches for the stated maps.","label":"Reported findings","source":"https://www.d0re.com/paper","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The preprint reports all 124,439,808 GPT-2 small parameters recovered bit for bit, with an assembled SHA-256 matching the public checkpoint. Its eight-column enumeration tests 107,214,677 candidates, finding eight survivors and 6,152/6,152 matching coordinates. The shuffled-activation controls report zero bit matches for the stated maps.","label":"Checks and conditions","source":"https://www.d0re.com/paper","sectionId":"source-record","provenance":"Reported checks from the existing project research summary"},"nextQuestion":{"text":"Can a hidden target or independent reproduction distinguish genuine recovery from access to a public checkpoint?","label":"The next question","source":"https://www.d0re.com/paper","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"gpt2","figures":[]},"d0fs":{"id":"d0fs","title":"d0fs: versioned agent memory","area":"Engineering","version":"27–28 Sep 2026","status":"Local hooks in daily use","question":"How can an agent resume work with the earlier state, its supporting evidence, and its changes still visible?","build":["Versioned file and task records, an event log, and configured context hooks for coding agents.","An optional 14-tool MCP server: eight memory/version tools, five task tools, and one session-pairing tool.","Related private projects include prism, which grades memory support, and d0hub, which retains overwritten Git versions and requires receipts for history changes."],"results":["The public project page records 23/23 matching local/service hook cases in an isolated parity test.","Three quiet-host runs on a copy of the real memory volume cover eight sessions at one tool call per second each: zero errors and zero calls over the two-second budget.","A 17-check path-safety suite refuses the tested symlink and hard-link edits and preserves permissions."],"boundary":"Daily local hooks; the shared service remains in test. Some shell writes are observed after they happen. The separate audit ledger is test code without an external witness, and the source and installer remain private. Engineering status retains the dated September source snapshot. This October research edition adds no new operational validation of this product.","origin":"The research habit of keeping the state and its evidence becomes versioned agent memory. This is an engineering application of a shared principle.","contribution":"Versioned memory carries the earlier state and supporting record into the next agent session. Its connection to the theory is the shared principle of preserving observable evidence.","recordDates":[],"dateLabel":"27–28 Sep 2026","dateKind":"Dated project report","sources":[{"url":"https://www.d0re.com/d0fs","label":"d0fs · working model & development tests"}],"lab":null,"measurement":"23/23 hook parity cases","group":"Working systems","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":8,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Can an independent witness verify the memory audit trail across failures and writes made outside the configured hooks?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":[],"checks":[],"journey":{"question":{"text":"How can an agent resume work with the earlier state, its supporting evidence, and its changes still visible?","label":"Research question","source":"https://www.d0re.com/d0fs","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The public project page records 23/23 matching local/service hook cases in an isolated parity test. Three quiet-host runs on a copy of the real memory volume cover eight sessions at one tool call per second each: zero errors and zero calls over the two-second budget. A 17-check path-safety suite refuses the tested symlink and hard-link edits and preserves permissions.","label":"Reported findings","source":"https://www.d0re.com/d0fs","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The public project page records 23/23 matching local/service hook cases in an isolated parity test. A 17-check path-safety suite refuses the tested symlink and hard-link edits and preserves permissions.","label":"Checks and conditions","source":"https://www.d0re.com/d0fs","sectionId":"source-record","provenance":"Reported checks from the existing project research summary"},"nextQuestion":{"text":"Can an independent witness verify the memory audit trail across failures and writes made outside the configured hooks?","label":"The next question","source":"https://www.d0re.com/d0fs","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"d0fs","figures":[]},"d0os":{"id":"d0os","title":"d0 OS: a traceable working environment","area":"Engineering","version":"26–27 Sep 2026","status":"Desktop in daily use","question":"How can the machine running the experiments keep its own state and identity inspectable?","build":["An independently developed NixOS/GNOME desktop with the d0 interface, signed boot, and hourly local file snapshots.","Updates can apply without reboot when the kernel is unchanged; kernel changes use a supervised reboot.","The Home edition, Windows file routing, and App Installer are in test. D0 for Windows remains a design."],"results":["The public page records enforcing Secure Boot and signed current boot images on Anthony’s laptop from 26 September 2026.","The Home installer boots under UEFI, installs offline, and reaches first-run setup in the stated 27 September VM test.","29 Windows extensions across 23 file types have handlers in the tested routing. Selected Windows applications opened in real-download tests."],"boundary":"One daily-use laptop and declared VM tests. Hourly snapshots share the same disk. There is no public release or evidence of general hardware or Windows compatibility. Engineering status retains the dated September source snapshot. This October research edition adds no new operational validation of this product.","origin":"Memory and the Console enter the operating environment. Identity, signed boot, local snapshots, and recovery become working system concerns.","contribution":"An inspectable environment puts identity, state change, and recovery into use on the machine running the work. This is an engineering connection to the programme’s principles.","recordDates":[],"dateLabel":"26–27 Sep 2026","dateKind":"Dated project report","sources":[{"url":"https://www.d0re.com/d0os/2026-09","label":"d0 OS · desktop, editions & compatibility"}],"lab":null,"measurement":"Enforcing signed boot · daily desktop","group":"Working systems","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":9,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which additional physical hardware and application tests can extend the current laptop and VM compatibility evidence?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":[],"checks":[],"journey":{"question":{"text":"How can the machine running the experiments keep its own state and identity inspectable?","label":"Research question","source":"https://www.d0re.com/d0os/2026-09","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The public page records enforcing Secure Boot and signed current boot images on Anthony’s laptop from 26 September 2026. The Home installer boots under UEFI, installs offline, and reaches first-run setup in the stated 27 September VM test. 29 Windows extensions across 23 file types have handlers in the tested routing. Selected Windows applications opened in real-download tests.","label":"Reported findings","source":"https://www.d0re.com/d0os/2026-09","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The Home installer boots under UEFI, installs offline, and reaches first-run setup in the stated 27 September VM test. 29 Windows extensions across 23 file types have handlers in the tested routing. Selected Windows applications opened in real-download tests.","label":"Checks and conditions","source":"https://www.d0re.com/d0os/2026-09","sectionId":"source-record","provenance":"Reported checks from the existing project research summary"},"nextQuestion":{"text":"Which additional physical hardware and application tests can extend the current laptop and VM compatibility evidence?","label":"The next question","source":"https://www.d0re.com/d0os/2026-09","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"d0os","figures":[]},"console":{"id":"console","title":"D0 Console: the agent workspace","area":"Engineering","version":"27 Sep 2026","status":"Core in daily use","question":"How can sessions, tasks, and decisions remain connected when an agent’s work is resumed?","build":["A desktop workspace for reopening AI coding sessions, grouping agents, and managing tasks and decisions.","d0fs supplies the neighbouring memory layer; an optional GitHub connection is working in test."],"results":["The 27 September 2026 d0re home page recorded 61 + 28 passing checks in the history and resume suites.","The core Console runs in daily internal use; GitHub integration tests used a local repository and a simulated API."],"boundary":"Internal daily use and declared test fixtures. No real GitHub account was connected in those integration tests; this is not a customer release. Engineering status retains the dated September source snapshot. This October research edition adds no new operational validation of this product.","origin":"d0fs supplies a neighbouring memory layer; the Console makes sessions, tasks, and decisions navigable in a daily workspace.","contribution":"Tasks, sessions, and decisions become a navigable record. The workspace gives the evidence-retention question a daily engineering setting beside d0fs.","recordDates":[],"dateLabel":"27 Sep 2026","dateKind":"Dated project report","sources":[{"url":"https://www.d0re.com/d0os/2026-09#console","label":"D0 Console · workspace & test scope"}],"lab":null,"measurement":"61 + 28 history/resume checks","group":"Working systems","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":9,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Can real account integration and interrupted-session tests retain the behavior reported by the current local and simulated fixtures?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":[],"checks":[],"journey":{"question":{"text":"How can sessions, tasks, and decisions remain connected when an agent’s work is resumed?","label":"Research question","source":"https://www.d0re.com/d0os/2026-09#console","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The 27 September 2026 d0re home page recorded 61 + 28 passing checks in the history and resume suites. The core Console runs in daily internal use; GitHub integration tests used a local repository and a simulated API.","label":"Reported findings","source":"https://www.d0re.com/d0os/2026-09#console","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The 27 September 2026 d0re home page recorded 61 + 28 passing checks in the history and resume suites. The core Console runs in daily internal use; GitHub integration tests used a local repository and a simulated API.","label":"Checks and conditions","source":"https://www.d0re.com/d0os/2026-09#console","sectionId":"source-record","provenance":"Reported checks from the existing project research summary"},"nextQuestion":{"text":"Can real account integration and interrupted-session tests retain the behavior reported by the current local and simulated fixtures?","label":"The next question","source":"https://www.d0re.com/d0os/2026-09#console","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"console","figures":[]},"remote":{"id":"remote","title":"D0 Remote Desktop: observer latency","area":"Engineering","version":"27 Sep 2026","status":"In daily use","question":"When state is observed across a connection, how much delay is introduced and whose machine is being observed?","build":["Saved and discovered computers in one client, with TLS and remembered certificate identities.","Changed identities require the server’s authorization. A session password is obtained for one connection and not written to disk."],"results":["The published bench records about 51 ms key-press-to-screen latency at 1920 × 1080 on a 6-vCPU server without a GPU.","The same moving-content test reports 47 screen updates per second at 1920 × 1080 and 61 at 1600 × 900 and below; an idle screen sends nothing.","30/30 identity and connection UI checks pass in the stated VM test."],"boundary":"A dated development bench under its stated conditions, not a universal network or display latency. The wider server is still alpha. Engineering status retains the dated September source snapshot. This October research edition adds no new operational validation of this product.","origin":"The desktop/server family gains a remote observer. Endpoint identity and key-to-screen delay become measurable engineering questions.","contribution":"Remote access is an engineering observer with a measurable transport delay and a checked endpoint identity. Its bench gives the observer question a practical, declared instrument.","recordDates":[],"dateLabel":"27 Sep 2026","dateKind":"Dated project report","sources":[{"url":"https://www.d0re.com/d0os/2026-09#remote","label":"Remote Desktop · latency, identity & test conditions"}],"lab":null,"measurement":"≈51 ms in the dated 1080p bench","group":"Working systems","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":3,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"How do key-to-screen latency and endpoint identity checks change under broader network, hardware and display conditions?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":[],"checks":[],"journey":{"question":{"text":"When state is observed across a connection, how much delay is introduced and whose machine is being observed?","label":"Research question","source":"https://www.d0re.com/d0os/2026-09#remote","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The published bench records about 51 ms key-press-to-screen latency at 1920 × 1080 on a 6-vCPU server without a GPU. The same moving-content test reports 47 screen updates per second at 1920 × 1080 and 61 at 1600 × 900 and below; an idle screen sends nothing. 30/30 identity and connection UI checks pass in the stated VM test.","label":"Reported findings","source":"https://www.d0re.com/d0os/2026-09#remote","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"The same moving-content test reports 47 screen updates per second at 1920 × 1080 and 61 at 1600 × 900 and below; an idle screen sends nothing. 30/30 identity and connection UI checks pass in the stated VM test.","label":"Checks and conditions","source":"https://www.d0re.com/d0os/2026-09#remote","sectionId":"source-record","provenance":"Reported checks from the existing project research summary"},"nextQuestion":{"text":"How do key-to-screen latency and endpoint identity checks change under broader network, hardware and display conditions?","label":"The next question","source":"https://www.d0re.com/d0os/2026-09#remote","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"remote","figures":[]},"server":{"id":"server","title":"d0 OS Server: operational evidence","area":"Engineering","version":"27 Sep 2026","status":"Alpha on a test server","question":"How can accounts, device state, and service health be observed and acted on with an inspectable record?","build":["D0 Server Manager coordinates accounts, enrolled devices, software inventory, certificates, and health checks.","The health monitor checks the test server each minute, with alert states that can wait, fire, and clear."],"results":["The 27 September 2026 d0re home page recorded 46 health-monitor rules, counted from source.","Account sign-in operates on the alpha server; the private certificate authority and monitoring remain in test."],"boundary":"One alpha test server. The private CA requires trusting its root and does not issue public web certificates. No production or customer deployment is claimed. Engineering status retains the dated September source snapshot. This October research edition adds no new operational validation of this product.","origin":"The d0 OS family extends into an alpha server: accounts, inventory, certificates, and observed health have explicit operational scope.","contribution":"Inventory, identity, and health readings turn changing machine states into operational evidence. The stated alpha scope fixes which environment those readings describe.","recordDates":[],"dateLabel":"27 Sep 2026","dateKind":"Dated project report","sources":[{"url":"https://www.d0re.com/d0os/2026-09#server","label":"d0 OS Server · accounts, devices & health"}],"lab":null,"measurement":"46 health rules · alpha server","group":"Working systems","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":9,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Which independent operational tests can extend the evidence beyond the present alpha test server?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":[],"checks":[],"journey":{"question":{"text":"How can accounts, device state, and service health be observed and acted on with an inspectable record?","label":"Research question","source":"https://www.d0re.com/d0os/2026-09#server","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"The 27 September 2026 d0re home page recorded 46 health-monitor rules, counted from source. Account sign-in operates on the alpha server; the private certificate authority and monitoring remain in test.","label":"Reported findings","source":"https://www.d0re.com/d0os/2026-09#server","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"Account sign-in operates on the alpha server; the private certificate authority and monitoring remain in test.","label":"Checks and conditions","source":"https://www.d0re.com/d0os/2026-09#server","sectionId":"source-record","provenance":"Reported checks from the existing project research summary"},"nextQuestion":{"text":"Which independent operational tests can extend the evidence beyond the present alpha test server?","label":"The next question","source":"https://www.d0re.com/d0os/2026-09#server","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"server","figures":[]},"octave":{"id":"octave","title":"POWM / Octave: eight learning observers","area":"Learning & meaning","version":"Design 30 Sep · benchmark saved 1 Oct 2026","status":"Trained recurrent prototype","question":"Can communicating temporal observers learn prediction while keeping ambiguity and the cost of learning visible?","build":["Eight recurrent observer identities, learned routing, fast/slow state, communication and workspace feedback.","A NumPy training school compares equal data/update budgets with a separately sized dense baseline.","Causal masking, gradient checks, streaming continuity and checkpoint continuation retain the inference contract."],"results":["Held-out Level 2 A+B bit accuracy: 92.70% recurrent versus 84.16% dense; complete forecasts: 9.90% versus 4.23%.","Dense performs better on trained-band bit forecasts, and on exact Level 1 forecasts in its Level 1-only branch.","Level 2 changes held-out Level 1 bit accuracy by +1.66 percentage points on average; exact transfer is inconsistent across three seeds.","All six broader-school recurrent final checkpoints score 0/8 exact basic-pulse forecasts; basic-pattern coverage still needs work.","Compute: the recurrent experiment took 800.82 seconds and the dense baseline 2.51 seconds on the same NumPy runtime, including final evaluation; this is not a pure training-throughput comparison."],"boundary":"Preliminary fixed-budget NumPy experiment. Data/update budgets are matched, compute and parameter counts are not. Eight-observer superiority, frontier capability, physical-phase alignment and reliable exact transfer remain unestablished.","origin":"The wave/observer programme motivates eight communicating temporal slots, fast and slow state, prediction, and memory. The number eight is an experimental hypothesis; the benchmark tests a small recurrent prototype, not the scaled world-model proposal.","contribution":"Turns an observer architecture into a trainable prototype and a fixed-budget school with held-out periods, masked sensors and complete-forecast scoring.","recordDates":["2026-09-30","2026-10-01"],"dateLabel":"30 Sep – 1 Oct 2026","dateKind":"Design date / saved benchmark","sources":[{"label":"Current 15 October audit and next test","url":"research/state-of-the-theory.html"},{"label":"Octave · full design review","url":"journey/sources/octave-design-review.txt"},{"label":"Octave · school benchmark and limits","url":"journey/sources/octave-school-benchmark.txt"}],"lab":null,"measurement":"53,200 parameters · three training seeds","group":"Learning & meaning","kind":"Editorial research brief","author":"Anthony Michael Collado","illustrationIndex":10,"illustrationLabel":"Explanatory illustration · not a reported measurement","nextQuestion":"Do matched observer-count and compute ablations support eight observers, reliable exact transfer and basic-pattern mastery?","nextQuestionBasis":"Editorial question based on the stated project limits","documents":["archive/c69c23892b03-Harmonic_Alpha_Results.md","journey/sources/octave-design-review.txt","journey/sources/octave-school-benchmark.txt"],"checks":[{"text":"Final exams did not select checkpoints, alter teaching or drive training. Train bands, held-out bands, noise protocol and reproduction commands are documented in README.txt. This is a preliminary fixed-budget experiment, not a mastery or frontier-performance certificate. More updates could change the comparison. Same data/update budget does not mean same compute: architectures, learning rates and gradient clipping differ. Eight-observer superiority requires matched observer-count ablations. Complete L2 forecasts require all 64 A+B bits correct, whereas complete L1 forecasts require 32 A bits. Log loss and Brier scores appear in raw results. No uncertainty calibration is claimed. Historical recurrence/copy reference uses strong integer-lag structure and separately trained weights.","label":"Final exam protocol and interpretation limits","source":"journey/sources/octave-school-benchmark.txt","sectionId":"source-record","provenance":"Source excerpt"}],"journey":{"question":{"text":"Can communicating temporal observers learn prediction while keeping ambiguity and the cost of learning visible?","label":"Research question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"answer":{"text":"Held-out Level 2 A+B bit accuracy: 92.70% recurrent versus 84.16% dense; complete forecasts: 9.90% versus 4.23%. Dense performs better on trained-band bit forecasts, and on exact Level 1 forecasts in its Level 1-only branch. Level 2 changes held-out Level 1 bit accuracy by +1.66 percentage points on average; exact transfer is inconsistent across three seeds. All six broader-school recurrent final checkpoints score 0/8 exact basic-pulse forecasts; basic-pattern coverage still needs work. Compute: the recurrent experiment took 800.82 seconds and the dense baseline 2.51 seconds on the same NumPy runtime, including final evaluation; this is not a pure training-throughput comparison.","label":"Reported findings","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Existing project research summary"},"checks":{"text":"Final exams did not select checkpoints, alter teaching or drive training. Train bands, held-out bands, noise protocol and reproduction commands are documented in README.txt. This is a preliminary fixed-budget experiment, not a mastery or frontier-performance certificate. More updates could change the comparison. Same data/update budget does not mean same compute: architectures, learning rates and gradient clipping differ. Eight-observer superiority requires matched observer-count ablations. Complete L2 forecasts require all 64 A+B bits correct, whereas complete L1 forecasts require 32 A bits. Log loss and Brier scores appear in raw results. No uncertainty calibration is claimed. Historical recurrence/copy reference uses strong integer-lag structure and separately trained weights.","label":"Checks and conditions","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Check excerpts from the named original sources"},"nextQuestion":{"text":"Do matched observer-count and compute ablations support eight observers, reliable exact transfer and basic-pattern mastery?","label":"The next question","source":"research/state-of-the-theory.html","sectionId":"source-record","provenance":"Editorial question based on the stated project limits"}},"headings":[],"projectId":"octave","figures":[]}},"audit":{"documentCount":160,"projectBriefCount":23,"kinds":{"Research note":23,"Mathematical note":18,"Benchmark data":1,"Research report":56,"Research manuscript":25,"Technical documentation":12,"Claim ledger":4,"Evidence audit":13,"Verification log":5,"Source note":2,"Archive documentation":1},"unassigned":["archive/6040e80f4b3d-verification_output.txt"],"documentsWithSourceFigures":7,"sourceFigureReferences":29,"uniqueSourceFigures":22,"unresolvedImageReferences":[],"sourceIntegrity":"Every document SHA-256 was calculated from the unchanged hosted source bytes.","framingBoundary":"Editorial navigation and project context are distinct from original source passages. No peer review, new measurement or validation is implied."}}