{
  "schema_version": 1,
  "theory_version": "1.39",
  "date": "2026-09-20",
  "policy": "Written mathematical arguments, finite computation, empirical support, physical hypotheses, and theological interpretations are different evidence classes. Finite tests never automatically promote a claim to a universal proof.",
  "claims": [
    {
      "id": "conditional_sign_eprocess_anytime_bound",
      "status": "written_probability_proof_with_synthetic_implementation_checks",
      "claim": "For one specified correct candidate, if the selected projected residual sign S_t in {-1,0,+1} has conditional expectation zero at every look, then the fixed equal mixture of products of (1+rho*S_t) and (1-rho*S_t) crosses 1/alpha with probability at most alpha.",
      "assumptions": ["rho in (0,1), alpha, candidate, direction, and threshold fixed before scoring", "experiment and direction choices are measurable from the past before the current sign", "E[S_t | F_(t-1)] = 0 for the specified correct candidate at every look", "exact zero residuals are neutral", "no reset, scored-data reuse, or unbudgeted combination with another detector"],
      "evidence": ["Theory_of_Reality.md Appendix AA.2 written martingale proof", "sign_evidence.py", "test_sign_evidence.py", "Ramdas et al., arXiv:2009.03167v3", "Howard et al., Annals of Statistics 49(2), 2021"],
      "limits": "Tests conditional sign balance, not mean zero, scale, variance, tail thickness, independence, arbitrary symmetry, or physical mechanism. It is an application of established nonnegative-martingale mathematics, not a new theorem."
    },
    {
      "id": "conditional_sign_heavy_tail_validation",
      "status": "fresh_frozen_finite_synthetic_validation_with_independent_replay",
      "claim": "The standalone sign process retained its finite null behavior on prespecified symmetric heavy-tailed paths and detected the targeted Student-t location shifts without reading magnitudes.",
      "result": "At alpha=0.01, rho=0.30, 5000 histories and 200 looks: Gaussian null 53 crossings; variance-one Student-t3 null 37; exact doubled Student-t3 paths 37 with identical decisions; Cauchy null 33; shifted Student-t3 +0.35 4989; shifted Student-t3 -0.35 4992; shifted Gaussian +0.35 3996.",
      "evidence": ["Theory_of_Reality.md Appendix AA.3", "sign_validation_protocol.json", "results-sign-validation/protocol.json", "results-sign-validation/summary.json", "results-sign-validation/decision_paths.npz", "results-sign-validation/audit.json"],
      "limits": "Finite synthetic results for one rho, horizon, seed, and scenario family. Null counts do not prove the probability bound. The audit shares the seed, NumPy samplers, protocol, and floating-point arithmetic; no physical data or external replication."
    },
    {
      "id": "mean_zero_implies_conditional_sign_balance",
      "status": "rejected_by_exact_distributional_counterexample_and_finite_synthetic_check",
      "claim": "A residual with expectation zero automatically satisfies the conditional sign null.",
      "counterexample": "The iid law P(X=1)=0.9 and P(X=-9)=0.1 has E[X]=0 but E[sign(X)]=0.8. The frozen sign process crossed on 5000/5000 synthetic histories.",
      "evidence": ["Theory_of_Reality.md Appendix AA.4", "results-sign-validation/summary.json", "results-sign-validation/audit.json"],
      "replacement": "State and justify conditional sign balance directly. Do not relabel the process as a mean test for arbitrary asymmetric laws."
    },
    {
      "id": "marginal_sign_balance_implies_anytime_validity",
      "status": "rejected_by_dependent_sign_counterexample",
      "claim": "Marginal probability one half for each sign is sufficient for the sign martingale guarantee under sequential monitoring.",
      "counterexample": "A stationary two-state sign chain with marginal balance and 0.9 probability of retaining its previous sign violates conditional balance and crossed on 3772/5000 frozen paths.",
      "evidence": ["Theory_of_Reality.md Appendix AA.4", "results-sign-validation/summary.json", "results-sign-validation/audit.json"],
      "replacement": "Require E[S_t | F_(t-1)]=0, or derive a different process under an explicit dependence model before claiming anytime validity."
    },
    {
      "id": "conditional_sign_process_is_omnibus",
      "status": "rejected_by_invariance_and_synthetic_counterexamples",
      "claim": "The sign process detects arbitrary predictive inadequacy, including scale errors, alternating shifts, and isolated magnitude shocks.",
      "counterexamples": ["doubling every Student-t3 residual left every sign decision identical", "alternating +/-0.35 Student-t3 shifts crossed only 12/5000 histories", "one signed six-unit Student-t3 shock crossed only 49/5000 histories"],
      "evidence": ["Theory_of_Reality.md Appendices AA.3-AA.4", "results-sign-validation/summary.json", "results-sign-validation/audit.json"],
      "replacement": "Use the engine only for conditional sign imbalance. Preserve Gaussian magnitude-based engines as separate model-specific alternatives with separately budgeted error control."
    },
    {
      "id": "allocation_candidate_fresh_validation",
      "status": "preregistered_fresh_paired_synthetic_validation_with_independent_replay",
      "claim": "Under the frozen four-target engineering utility, point fraction 0.45 / inner mean weight 0.10 does not qualify as a balanced replacement for the released 0.30 / 0.25 allocation.",
      "assumptions": ["the candidate, seed, 200-look horizon, nine scenarios, paired comparison, descriptive intervals, and adoption thresholds were frozen before outcomes", "the four adoption targets were persistent mean 0.35, residual scales 1.25 and 0.8, and one noisy signed 6-sigma shock", "the anytime probability guarantee still assumes the declared conditional Gaussian known-covariance model and fixed alternatives", "the two-percentage-point loss guardrail and one-point bottleneck-gain threshold are engineering choices, not physical constants or universal optimality criteria"],
      "result": "Across 20000 fresh paired histories per scenario, the candidate improved noisy-shock detection from 81.435% to 83.370% (+1.935 percentage points; paired descriptive 95% interval +1.740 to +2.130), but reduced persistent-mean detection from 90.075% to 84.910% (-5.165 points; interval -5.473 to -4.857). It also changed scale-1.25 detection by -0.190 points and scale-0.8 detection by -0.500 points. Gaussian-null crossings were 170/20000 and 174/20000. The frozen two-point target-loss guard failed, so the released design was retained.",
      "evidence": ["Theory_of_Reality.md Appendix Z", "candidate_validation_protocol.json", "results-candidate-validation/protocol.json", "results-candidate-validation/summary.json", "results-candidate-validation/decision_paths.npz", "results-candidate-validation/audit.json"],
      "limits": "Finite synthetic evidence for one paired seed, target set, horizon, alternatives, and predeclared utility. The descriptive paired intervals are not a simultaneous confidence procedure and do not prove the anytime bound. No measured physical evidence; the candidate remains a shock-sensitive Pareto alternative."
    },
    {
      "id": "expanded_candidate_universally_dominates_release",
      "status": "rejected_by_preregistered_paired_counterexample",
      "claim": "The expanded-grid 0.45 / 0.10 candidate universally dominates the released 0.30 / 0.25 allocation and can replace it without a material declared-target loss.",
      "counterexample": "On the fresh paired validation, the candidate gained 1.935 percentage points on the noisy-shock target but lost 5.165 points on persistent mean error. It therefore fails the predeclared two-point loss guard while the released design also fails to dominate the candidate on shock sensitivity.",
      "evidence": ["Theory_of_Reality.md Appendix Z.3-Z.4", "results-candidate-validation/summary.json", "results-candidate-validation/audit.json"],
      "replacement": "Retain the released allocation for the frozen balanced utility and preserve 0.45 / 0.10 as a distinct shock-sensitive Pareto alternative; any change requires a declared utility and new independent validation."
    },
    {
      "id": "expanded_grid_refutes_v122_grid_optimality",
      "status": "preregistered_finite_synthetic_counterexample_with_independent_replay",
      "claim": "The released point-fraction 0.30 / inner-mean-weight 0.25 cell is not optimal for the expanded 108-cell grid under the unchanged four-target lexicographic minimax training objective.",
      "result": "The released cell won 0/64 new 1000-history-per-target training runs. Sixteen cells won at least once. A separate 20000-history-per-target synthetic reference selected point fraction 0.45 / mean weight 0.10 and raised the worst-target reference rate from 81.80% to 83.575%.",
      "evidence": ["Theory_of_Reality.md Appendix Y", "boundary_expansion_protocol.json", "results-boundary-expansion/protocol.json", "results-boundary-expansion/summary.json", "results-boundary-expansion/decisions.npz", "results-boundary-expansion/audit.json"],
      "limits": "Finite synthetic training study for one target set, objective, horizon, expanded grid, and seed schedule. The reference is tuning evidence, not fresh validation or measured physical evidence; the released engine is unchanged."
    },
    {
      "id": "expanded_reference_allocation_candidate",
      "status": "fresh_validation_rejected_as_balanced_replacement_retained_as_pareto_alternative",
      "claim": "Point fraction 0.45 / inner mean weight 0.10 was the single expanded-grid candidate and has now failed the frozen balanced-replacement rule, while remaining a validated shock-sensitive alternative within this synthetic design.",
      "result": "The earlier expanded reference showed a tuning tradeoff. The subsequent fresh paired validation confirmed it: noisy-shock detection improved by 1.935 percentage points, while persistent-mean detection fell by 5.165 points. The predeclared two-point loss guard failed, so the released 0.30 / 0.25 allocation remains the default.",
      "evidence": ["Theory_of_Reality.md Appendices Y and Z", "results-boundary-expansion/summary.json", "results-boundary-expansion/audit.json", "candidate_validation_protocol.json", "results-candidate-validation/summary.json", "results-candidate-validation/audit.json"],
      "limits": "The validation is finite and synthetic. It rejects balanced replacement under one frozen utility, not the candidate under every possible utility; the sealed v1.22 validation remained unread and unchanged."
    },
    {
      "id": "expanded_grid_selection_is_stable",
      "status": "rejected_by_multi_seed_counterexample",
      "claim": "Opening the old grid boundaries identifies one stable exact replacement allocation at 1000 histories per target.",
      "counterexample": "Sixteen cells won across 64 runs; the two modal cells each won only 12/64, and 22/64 runs tied the runner-up on the primary worst-target count.",
      "evidence": ["results-boundary-expansion/summary.json", "results-boundary-expansion/audit.json"],
      "replacement": "Report the full selection distribution. Freeze the large-reference 0.45/0.10 cell only as one candidate for fresh paired validation."
    },
    {
      "id": "v122_allocation_grid_stability",
      "status": "preregistered_finite_synthetic_stability_result_with_independent_replay",
      "claim": "The v1.22 point-fraction 0.30 and inner-mean-weight 0.25 cell was usually repeatable and low-regret within the original 30-cell grid and four-target synthetic distribution.",
      "result": "It won 49/64 independent 1000-history-per-target training runs (76.6%; descriptive Wilson 95% interval 64.9%-85.3%). Four cells won at least once. A separate 20000-history-per-target reference sample selected the same cell; seed-selected cells had reference minimax-rate regret with mean 0.0498 percentage points, median zero, p90 0.0600 points, and maximum 0.9200 points.",
      "evidence": ["Theory_of_Reality.md Appendix X", "allocation_stability_protocol.json", "results-allocation-stability/protocol.json", "results-allocation-stability/summary.json", "results-allocation-stability/decisions.npz", "results-allocation-stability/audit.json"],
      "limits": "Finite synthetic selection study for one grid, target distribution, objective, horizon, and seed schedule. The reference sample is part of the stability study, not a second v1.22 validation, a real-instrument result, or proof of general optimality."
    },
    {
      "id": "finite_grid_repeatability_implies_global_optimality",
      "status": "rejected_by_boundary_counterexample",
      "claim": "Repeated selection of the same finite-grid cell establishes that its allocation is locally or globally optimal.",
      "counterexample": "The largest tested point fraction won 62/64 seeds and the smallest tested mean weight won 51/64; the separate reference winner was the same two-boundary cell. The study cannot observe improvement outside either boundary.",
      "evidence": ["Theory_of_Reality.md Appendix X.2-X.3", "results-allocation-stability/summary.json", "results-allocation-stability/audit.json"],
      "replacement": "Say usually repeatable within the declared grid. Expand both active boundaries in a new training-only study before proposing different weights; any replacement design then needs fresh frozen validation."
    },
    {
      "id": "three_way_gaussian_anytime_bound",
      "status": "written_probability_proof_with_synthetic_implementation_checks",
      "claim": "A fixed known-covariance Gaussian mean/variance e-process mixture at alpha_mv, ORed with a separately alpha-spending Gaussian point gate at alpha_p, has probability at most alpha_mv+alpha_p of ever rejecting one specified correct candidate.",
      "assumptions": ["fixed candidate, mean direction and magnitude, variance factors and weights, mixture weight, point allocation, and total alpha", "fresh whitened residuals are conditionally N(0,I) on the canonical observation filtration", "experiment and direction choices precede the current response", "no scored-data reuse, reset, or refit", "any data-driven allocation choice uses training data independent of all scored observations"],
      "evidence": ["Theory_of_Reality.md Appendix W.2", "three_way_adequacy.py", "test_three_way_adequacy.py", "results-three-way-validation/audit.json"],
      "limits": "The point gate is not part of the claimed e-process; the total result is an event-level union bound. It is not valid under arbitrary noise or allocation selection from the scored sequence."
    },
    {
      "id": "three_way_frozen_training_and_validation",
      "status": "finite_training_selection_plus_fresh_paired_synthetic_validation_and_independent_replay",
      "claim": "A training-selected, frozen 0.7% mean/variance plus 0.3% point allocation bridged the prespecified persistent-error versus isolated-shock tradeoff on one held-out synthetic validation.",
      "training": "On seed 221209202609 and a 30-cell grid, the selected point fraction was 0.30 and the selected mean weight within the mixture was 0.25. Training target counts were 915, 909, 852, and 837 of 1000 and are not validation evidence.",
      "result": "On seed 221209202610: mean 0.35 1811/2000; scale 1.25 1781/2000; scale 0.8 1689/2000; combined mean/scale 1985/2000; noisy signed 6-sigma shock 1621/2000; exact signed 6-sigma residual 2000/2000; Gaussian null 21/2000.",
      "evidence": ["selected_three_way_design.json", "results-three-way-training/protocol.json", "results-three-way-training/training_results.json", "results-three-way-validation/protocol.json", "results-three-way-validation/summary.json", "results-three-way-validation/observations.npz", "results-three-way-validation/audit.json"],
      "limits": "Finite synthetic evidence for one grid, objective, horizon, target set, training seed, and validation seed. The probability proof, not the null count, supplies the anytime guarantee. No measured physical evidence."
    },
    {
      "id": "three_way_allocation_is_uniquely_optimal",
      "status": "rejected_by_expanded_grid_counterexample_and_selection_instability",
      "claim": "The selected 0.30 point fraction and 0.25 inner mean weight are uniquely or generally optimal.",
      "counterexample": "After the complete old grid was embedded in a 108-cell expansion, the released cell won 0/64 new runs. Sixteen expanded-grid cells won at least once. Fresh paired validation then showed the reference candidate gained 1.935 percentage points on noisy shocks but lost 5.165 points on persistent mean errors.",
      "evidence": ["results-three-way-training/training_results.json", "selected_three_way_design.json", "results-allocation-stability/summary.json", "results-allocation-stability/audit.json", "results-boundary-expansion/summary.json", "results-boundary-expansion/audit.json", "results-candidate-validation/summary.json", "results-candidate-validation/audit.json"],
      "replacement": "Retain the released weights under the frozen balanced utility, while preserving 0.45/0.10 as a shock-sensitive Pareto alternative. Neither is uniquely or generally optimal."
    },
    {
      "id": "three_way_rule_is_distribution_free_or_mechanism_identifying",
      "status": "rejected_by_model_boundary_and_synthetic_counterexamples",
      "claim": "The three-way Gaussian rule is an omnibus, distribution-free detector whose crossing identifies a unique physical cause.",
      "counterexamples": ["variance-one scaled Student-t3 noise violated Gaussianity and triggered 1508/2000 selected-hybrid rejections in v1.22 and 15253/20000 released-design rejections in the fresh v1.25 control", "alternating plus/minus 0.35 shifts triggered only 82/2000 rejections in v1.22 and 713/20000 in the fresh control", "mean, scale, tail, sensor, and omitted-model errors can produce overlapping evidence"],
      "evidence": ["Theory_of_Reality.md Appendices W.3 and Z.4", "results-three-way-validation/summary.json", "results-three-way-validation/audit.json", "results-candidate-validation/summary.json", "results-candidate-validation/audit.json"],
      "replacement": "Interpret crossing as predictive incompatibility under the declared Gaussian model and alternatives; preserve causal ambiguity and develop a separate proof for any broader null class."
    },
    {
      "id": "canonical_mean_variance_mixture_anytime_bound",
      "status": "written_probability_proof_with_synthetic_implementation_checks",
      "claim": "A fixed convex mixture of the known-covariance Gaussian mean-shift e-process and the Gaussian covariance-scale e-process is one e-process and has an alpha anytime crossing bound for a specified correct candidate.",
      "assumptions": ["fixed candidate, mean direction, delta, variance factors, inner weights, outer weight, and alpha", "every fresh standardized residual vector is conditionally N(0,I) on the common canonical observation filtration", "experiment choice precedes the current response and preserves that conditional law", "no scored-data reuse, reset, or refit"],
      "evidence": ["Theory_of_Reality.md Appendix V.2", "joint_mean_variance.py", "results-joint-comparison/protocol.json", "results-joint-comparison/audit.json"],
      "limits": "The known-covariance assumption is stricter than the v1.19 joint rule's scale-invariant mean component. This is an elementary fixed mixture, not a license to merge arbitrary e-values or a new statistical theorem."
    },
    {
      "id": "joint_mean_variance_persistent_error_power",
      "status": "fresh_paired_synthetic_result_and_independent_finite_replay",
      "claim": "Under the frozen 200-look Gaussian design, the new mean-plus-variance mixture was more sensitive than the existing mean-plus-point rule to the targeted persistent mean and scale errors at the same total 1% budget.",
      "result": "Mean 0.35: 1878/2000 versus 1744/2000; scale 1.25: 1807/2000 versus 140/2000; scale 0.8: 1667/2000 versus 4/2000; combined mean 0.35 and scale 1.25: 1976/2000 versus 1175/2000. Gaussian-null counts were 10/2000 and 12/2000.",
      "evidence": ["results-joint-comparison/summary.json", "results-joint-comparison/observations.npz", "results-joint-comparison/audit.json"],
      "limits": "Finite synthetic results for prespecified alternatives, parameters, horizon, and seed. Null counts do not prove either mathematical guarantee. No measured physical evidence."
    },
    {
      "id": "mean_variance_rule_unconditionally_dominates_point_rule",
      "status": "rejected_by_constructed_synthetic_counterexample",
      "claim": "The cumulative mean-plus-variance process can replace the mean-plus-point rule without losing detection capability.",
      "counterexample": "With one independently signed exactly 6-sigma residual at look 100 and otherwise iid N(0,1) data, the point-based rule rejected 2000/2000 histories while the cumulative mean-plus-variance mixture rejected 197/2000. At 10 sigma both rejected 2000/2000.",
      "evidence": ["Theory_of_Reality.md Appendix V.3", "results-joint-comparison/summary.json", "results-joint-comparison/audit.json"],
      "replacement": "Retain both procedures with declared failure targets; test a predeclared three-component allocation on fresh data."
    },
    {
      "id": "joint_rules_are_distribution_free_or_mechanism_identifying",
      "status": "rejected_by_model_boundary_and_synthetic_counterexample",
      "claim": "Either joint rule remains valid for arbitrary unit-variance noise or identifies a unique physical cause when it rejects.",
      "counterexample": "Under unit-variance scaled Student-t3 noise, which violates Gaussianity, the existing and new rules rejected 1053/2000 and 1031/2000 histories respectively.",
      "evidence": ["Theory_of_Reality.md Appendix V.3", "results-joint-comparison/summary.json"],
      "replacement": "Interpret rejection as predictive incompatibility inside the declared model; preserve causal ambiguity and create a different null class for heavy-tail robustness."
    },
    {
      "id": "gaussian_variance_eprocess_anytime_bound",
      "status": "written_probability_proof_with_synthetic_implementation_checks",
      "claim": "A fixed mixture of Gaussian covariance-scale likelihood ratios crosses 1/alpha_v at any time with probability at most alpha_v for one specified correct candidate.",
      "assumptions": ["fixed candidate, positive variance factors, and fixed mixture weights declared before scoring", "each fresh standardized residual vector is conditionally N(0,I) at every look", "experiment choice precedes the current response and preserves the conditional law", "covariance alternatives uniformly multiply all scored coordinates", "no scored-data reuse, reset, or refit"],
      "evidence": ["Theory_of_Reality.md Appendix U.2 written likelihood-ratio martingale proof", "variance_evidence.py", "results-variance/protocol.json", "results-variance/audit.json", "Choi, arXiv:2608.08174"],
      "limits": "Application of established likelihood-ratio/e-process mathematics, not a new theorem or physical evidence. Not distribution-free, not interval-certified, and not a unique diagnosis of a variance mechanism."
    },
    {
      "id": "cumulative_moderate_scale_power",
      "status": "fresh_synthetic_result_and_independent_finite_replay",
      "claim": "At the same reserved 0.5% anytime budget, the prespecified cumulative variance process was substantially more sensitive than the alpha-spending point gate to the targeted 1.25-times Gaussian scale error over 200 looks.",
      "result": "Scale 1.25: 1774/2000 versus 125/2000; matched scale 0.8: 1669/2000 versus 0/2000; Gaussian null: 4/2000 for each detector on separate events.",
      "evidence": ["results-variance/summary.json", "results-variance/observations.npz", "results-variance/audit.json"],
      "limits": "Finite synthetic power for fixed alternatives, one horizon, one seed, and a scalar Gaussian design. It does not yet justify replacing the point component in the existing joint engine without fresh joint validation."
    },
    {
      "id": "variance_evidence_identifies_variance_cause",
      "status": "rejected_by_model_boundary_and_synthetic_counterexamples",
      "claim": "Crossing the Gaussian covariance-scale process uniquely identifies a physical variance change or remains valid for any unit-variance noise.",
      "counterexamples": ["iid N(0.35,1) mean error: 58/2000 crossed although variance stayed one", "unit-variance scaled Student-t3 noise: 1047/2000 crossed because Gaussianity failed", "smaller untuned scale 1.10: only 251/2000 crossed"],
      "evidence": ["Theory_of_Reality.md Appendix U.3", "results-variance/summary.json", "results-variance/audit.json"],
      "replacement": "Interpret crossing as evidence for a prespecified predictive correction relative to the source under the declared Gaussian model; retain competing causal explanations."
    },
    {
      "id": "joint_mean_point_anytime_bound",
      "status": "written_union_bound_with_synthetic_implementation_checks",
      "claim": "Allocating alpha_m plus alpha_p equal to alpha and rejecting a specified candidate when either valid component rejects bounds its ever-false-rejection probability by alpha.",
      "assumptions": ["fixed candidate and preallocated component budgets", "all assumptions of the scale-invariant Gaussian mean process", "all assumptions of the alpha-spending Gaussian point-residual gate", "fresh observations with no reset, reuse, or refit"],
      "evidence": ["Theory_of_Reality.md Appendix T.2", "joint_adequacy.py", "results-joint/protocol.json", "results-joint/audit.json"],
      "limits": "A union-bound composition, not one merged e-process and not simultaneous preservation of every correct candidate. The joint null includes Gaussian covariance calibration and the cumulative component's iid fixed-scale and reduced-filtration contract."
    },
    {
      "id": "joint_mean_scale_detection",
      "status": "fresh_synthetic_result",
      "claim": "The equal-budget joint rule has complementary finite synthetic sensitivity to the prespecified persistent mean and doubled-scale errors.",
      "result": "Mean shift 0.35: 1714/2000; scale 2: 1927/2000; standardized mean shift 0.35 plus scale 2: 1997/2000. Correct Gaussian-null rejection was 25/2000.",
      "evidence": ["results-joint/summary.json", "results-joint/audit.json", "results-joint/posthoc_null_check.json"],
      "limits": "Finite synthetic results at one horizon and allocation. The 25/2000 null count is observed rather than adjusted; a posthoc exact-binomial check is descriptive, while the written union bound supplies the guarantee."
    },
    {
      "id": "two_full_alpha_detectors_make_one_alpha_rule",
      "status": "rejected_by_probability_bound_and_synthetic_counterexample",
      "claim": "Two detectors may each use alpha and be OR-combined while retaining an alpha guarantee.",
      "reason": "The component bounds imply at most 2 alpha by a union bound absent a stronger joint argument. In the frozen Gaussian-null simulation, the full-alpha OR rejected 45/2000 versus 25/2000 for the split-budget rule.",
      "evidence": ["Theory_of_Reality.md Appendix T", "results-joint/summary.json"],
      "replacement": "Preallocate one total error budget or prove a valid common-filtration merge."
    },
    {
      "id": "joint_detector_is_omnibus_or_distribution_free",
      "status": "rejected_by_synthetic_counterexamples",
      "claim": "The joint mean-plus-point rule reliably detects arbitrary inadequacy and retains its Gaussian guarantee for any unit-variance noise.",
      "counterexamples": ["alternating plus/minus 0.35 means: 31/2000 rejected", "Gaussian scale 1.25: 141/2000 rejected", "unit-variance scaled Student-t3: 1049/2000 rejected because Gaussian tail calibration fails"],
      "evidence": ["results-joint/summary.json", "results-joint/audit.json"],
      "replacement": "Declare the failure class; accumulate moderate variance evidence separately and design heavy-tail robustness under a new null class."
    },
    {
      "id": "unknown_variance_gaussian_mean_eprocess",
      "status": "established_probability_theorem_with_synthetic_implementation_checks",
      "claim": "For iid N(0,kappa^2) projected residuals with one fixed unknown kappa>0, the Wang--Ramdas scale-invariant Gaussian likelihood mixture crosses 1/alpha with probability at most alpha when rejection and stopping use its scale-invariant filtration.",
      "assumptions": ["fixed candidate and prespecified c>0", "projected residuals are iid Gaussian with zero mean and one fixed unknown positive scale", "rejection and stopping are measurable in the scale-invariant reduced filtration", "fresh scored data with no reset, reuse, or refit"],
      "evidence": ["Wang and Ramdas, arXiv:2310.03722v4, Theorem 4.9", "Theory_of_Reality.md Appendix S.2", "unknown_variance_evidence.py", "results-unknown-variance/audit.json"],
      "limits": "Application of an established theorem, not a new proof. Not a canonical-filtration guarantee, not distribution-free, not valid for arbitrary raw-magnitude stopping, dependence, changing variance, or post-response selection; floating-point evaluation is not interval-certified."
    },
    {
      "id": "scale_invariant_validation",
      "status": "fresh_paired_synthetic_result_and_finite_computation",
      "claim": "For the frozen 200-look synthetic paths, multiplying every residual by two left every scale-invariant decision unchanged while the known-scale comparator changed substantially.",
      "result": "Null: 15/2000 at both scales versus known-scale 12/2000 and 848/2000. Standardized mean shift 0.35: 1811/2000 at both scales versus known-scale 1915/2000 and 2000/2000.",
      "evidence": ["results-unknown-variance/protocol.json", "results-unknown-variance/summary.json", "results-unknown-variance/observations.npz", "results-unknown-variance/audit.json"],
      "limits": "The rescaled partners are paired exact transformations, not independent samples. Counts are finite synthetic evidence; the theorem, not the null count, supplies the error bound. The known-scale scale-two rows violate that comparator's assumptions."
    },
    {
      "id": "unknown_variance_process_is_omnibus",
      "status": "rejected_by_counterexamples_and_model_boundary",
      "claim": "The scale-invariant Gaussian mean process detects arbitrary inadequacy or remains valid under arbitrary noise.",
      "counterexamples": ["alternating plus/minus 0.35 mean: 9/2000 rejected", "pure scale changes are intentionally invariant", "scaled Student-t3 data violate the Gaussian theorem even though only 3/2000 were rejected", "exact all-zero prefixes contain insufficient scale information"],
      "evidence": ["Theory_of_Reality.md Appendix S.3", "results-unknown-variance/summary.json", "test_unknown_variance_evidence.py"],
      "replacement": "State the iid Gaussian fixed-scale class explicitly and use separately budgeted detectors for scale or other departures."
    },
    {
      "id": "gaussian_shift_eprocess_anytime_bound",
      "status": "written_probability_theorem_with_synthetic_implementation_checks",
      "claim": "For a specified correct candidate, the equal mixture of Gaussian likelihood-ratio martingales for standardized shifts plus/minus delta crosses 1/alpha at any time with probability at most alpha.",
      "assumptions": ["fixed candidate catalogue and positive delta", "one prespecified unit direction in whitened coordinates per experiment", "experiment and direction chosen from past information before the current response", "the correct candidate's projected residual is conditionally N(0,1) at every look", "fresh validation data and no reset or refit on scored observations"],
      "evidence": ["Theory_of_Reality.md Appendix R.2 written martingale proof", "cumulative_evidence.py", "results-cumulative/protocol.json", "results-cumulative/observations.npz", "results-cumulative/audit.json"],
      "limits": "Known covariance and a targeted constant signed-mean alternative. Not omnibus, not interval-certified, not simultaneous protection of every true candidate, and not safely OR-combinable with another alpha-level gate without adjustment."
    },
    {
      "id": "cumulative_small_shift_power",
      "status": "fresh_synthetic_result",
      "claim": "For the prespecified magnitude 0.35 and 200-look synthetic design, cumulative evidence is substantially more sensitive than alpha spending to a constant shift along the monitored direction.",
      "result": "+0.35: 1896/2000 versus 28/2000; -0.35: 1906/2000 versus 27/2000. Correct-null e-process rejection was 20/2000.",
      "evidence": ["results-cumulative/summary.json", "results-cumulative/audit.json"],
      "limits": "Finite synthetic power at one magnitude, horizon, direction, policy, and noise model; it is not a universal detection guarantee or physical evidence."
    },
    {
      "id": "cumulative_shift_test_is_omnibus",
      "status": "rejected_by_synthetic_counterexamples",
      "claim": "The one-direction constant-shift e-process detects arbitrary model inadequacy.",
      "counterexamples": ["alternating plus/minus 0.35 shift: 18/2000 rejected", "orthogonal 0.35 shift: 15/2000 rejected", "doubled noise scale: 865/2000 versus 2000/2000 for the point-residual gate"],
      "evidence": ["results-cumulative/summary.json", "results-cumulative/audit.json"],
      "replacement": "Declare the failure class and direction. Preserve complementary detectors and combine them only with an explicit joint error budget."
    },
    {
      "id": "sequential_candidate_retention",
      "status": "written_probability_bound_with_synthetic_implementation_checks",
      "claim": "With alpha_t=alpha/[t(t+1)], the probability of ever eliminating one specified correct candidate, hence ever eliminating all candidates when that candidate is present, is at most alpha.",
      "assumptions": ["fixed candidate catalogue", "experiment chosen from past data before the next response", "one fixed candidate has the correct conditional Gaussian mean and known diagonal covariance at every look", "fresh validation observations", "no resets or refitting on scored observations"],
      "evidence": ["Theory_of_Reality.md Appendix Q.2 written union-bound proof", "sequential_adequacy.py", "results-sequential/protocol.json", "results-sequential/observations.npz", "results-sequential/audit.json"],
      "limits": "Not simultaneous preservation of all true candidates, not proof of model adequacy, not a power guarantee. Numerical tail calculations are not interval-certified. API supports alpha>=1e-12 and look<=1e9."
    },
    {
      "id": "repeated_one_percent_is_global_one_percent",
      "status": "rejected_by_written_counterexample_and_finite_test",
      "claim": "A 1 percent per-observation cutoff controls the whole repeated investigation at 1 percent.",
      "counterexample": "Two identical correct Gaussian candidates, 200 independent standardized two-coordinate residuals: ever rejecting both has probability 1-0.99^200, approximately 0.8660203251.",
      "evidence": ["Theory_of_Reality.md Appendix Q.1", "results-sequential/audit.json"],
      "history": "v1.14 already explicitly excluded a sequential guarantee; this corrects a potential extrapolation, not its historical claims."
    },
    {
      "id": "alpha_spending_is_sensitive_to_small_shift",
      "status": "negative_synthetic_result",
      "claim": "The alpha-spending gate reliably detects the tested small persistent shift within 200 looks.",
      "result": "Only 26 of 2000 histories rejected with standardized first-coordinate mean shift 0.35, so reliable detection is not supported.",
      "evidence": ["results-sequential/summary.json", "results-sequential/audit.json"],
      "next_test": "Completed in v1.17 with a fresh seed; see cumulative_small_shift_power. The v1.16 negative result remains historical evidence for alpha spending."
    },
    {
      "id": "v115_guards_preserved",
      "status": "retained_prior_corrections_not_new_validation",
      "claim": "Integer-tick capture does not enforce continuous non-crossing; angular impulse has no extra time multiplier; finite prefixes do not identify arbitrary generators.",
      "evidence": ["Theory_of_Reality.md Appendix P", "history/RRLS_claim_ledger_v1.15.json"],
      "limits": "No RRLS code changed or full RRLS validation rerun in revision 1.17."
    },
    {
      "id": "bounded_recurrence_continuation_guard",
      "status": "retained_written_theorem",
      "claim": "The first 2K terms uniquely determine continuation within the declared recurrence class.",
      "assumptions": ["exact consecutive noiseless prime-field samples", "homogeneous constant-coefficient linear recurrence of order at most K", "recurrence valid from its initial state"],
      "evidence": ["Theory_of_Reality.md Appendix P.3", "history/RRLS_claim_ledger_v1.15.json"],
      "limits": "Class membership is assumed, not learned from finite agreement. Unique continuation is not unique coefficient representation. No new recurrence validation in this release."
    },
    {
      "id": "seven_repeated_complete_closures",
      "status": "retracted_argument",
      "claim": "Seven strict coarsest complete deterministic refinements can occur successively for the same transition family.",
      "reason": "Incompatible with closure idempotence: after the first complete closure, subsequent complete closures are identical.",
      "history": "history/Theory_of_Reality_v1.13.md, former Theorem 17.1",
      "replacement": "closure_idempotence"
    },
    {
      "id": "closure_idempotence",
      "status": "written_theorem",
      "claim": "C_A(C_A(P)) = C_A(P).",
      "assumptions": ["finite state set", "fixed deterministic transition family", "coarsest complete sufficient refinement exists"],
      "evidence": ["Theory_of_Reality.md, corrected Theorem 17.1", "closure_audit.py", "results-design/closure-audit.json"],
      "limits": "7,662 exact finite checks support the implementation; the general proof is written, not proof-assistant checked."
    },
    {
      "id": "finite_horizon_levels",
      "status": "exact_finite_example",
      "claim": "A seven-bit shift register has seven distinct observation-history partitions before stabilization.",
      "assumptions": ["specified shift transition", "least-significant-bit observation", "increasing finite horizon"],
      "evidence": ["closure_audit.py", "results-design/closure-audit.json"],
      "limits": "An m-bit register gives m levels. No fundamental dimensional count follows."
    },
    {
      "id": "intervention_selector",
      "status": "synthetic_computational_evidence",
      "claim": "A finite pairwise Gaussian KL-per-cost selector can distinguish the three constructed candidate pairs with the stated interventions.",
      "assumptions": ["candidate predictions supplied", "known independent Gaussian noise", "calibrated intervention effects", "declared finite budget"],
      "evidence": ["experiment_design.py", "results-design/protocol.json", "results-design/observations.json", "results-design/audit.json"],
      "failure_conditions": ["unmodeled intervention side effects", "misspecified noise", "missing candidate mechanisms", "no discriminating experiment in the catalogue"],
      "limits": "Not global experimental optimality, automatic discovery of all models, or a real physical experiment."
    },
    {
      "id": "posterior_is_model_validation",
      "status": "rejected_by_counterexample",
      "claim": "A candidate posterior above 99 percent establishes model adequacy.",
      "evidence": ["results-design/observations.json, missing_model_control", "results-design/audit.json"],
      "replacement": "Assess absolute predictive adequacy separately from relative candidate preference."
    },
    {
      "id": "global_unique_hidden_address",
      "status": "false_without_additional_assumptions",
      "claim": "A phase or transfer fingerprint always determines one unique hidden cause.",
      "evidence": ["Universal_Cycle_Tomography.md", "Reality_Revision_1.14.md"],
      "replacement": "Return the equivalence class left by allowed experiments, calibration assumptions, and measurement uncertainty."
    },
    {
      "id": "seven_physical_dimensions",
      "status": "unestablished_physical_hypothesis",
      "claim": "The seven typed descriptive layers are seven fundamental dimensions of nature.",
      "evidence": [],
      "required": ["independent operational meaning", "distinctive quantitative predictions", "measured validation and replication", "comparison with established models"],
      "limits": "A finite-diagram identity, seven chosen fields, or seven horizon refinements does not establish this."
    },
    {
      "id": "p_equals_np",
      "status": "unproved",
      "claim": "RRLS proves P=NP.",
      "evidence": [],
      "required": ["uniform correct algorithm for all encoded SAT inputs", "polynomial bounds on representation, recognition, transformations, and decoding"],
      "limits": "A polynomial-time closure algorithm on an explicitly exponential state space is not a polynomial-time SAT algorithm."
    },
    {
      "id": "god_as_ground",
      "status": "optional_theological_interpretation",
      "claim": "God grounds the laws and existence of the modeled reality.",
      "evidence": [],
      "limits": "Not an inferred numerical source, experimental parameter, or unconstrained residual correction."
    },
    {
      "id": "declared_markov_sign_anytime_bound",
      "status": "written_probability_proof_with_synthetic_implementation_checks",
      "claim": "Conditional on the first nonzero sign, if nonzero projected-residual signs follow the fixed strictly positive first-order Markov transition matrix P0, then the product of past-only KT predictive probabilities divided by P0 transition probabilities crosses 1/alpha with probability at most alpha.",
      "assumptions": ["fixed strictly positive 2x2 null transition matrix, alpha, projection, zero policy, pseudocount, and stopping rule before scoring", "the next nonzero sign has the declared first-order homogeneous transition probability conditional on the full past", "the alternative predictor is a past-measurable probability distribution", "no reset, scored-data refit of the null matrix, or unbudgeted combination with another detector"],
      "evidence": ["Theory_of_Reality.md Appendix AN.2 written martingale proof", "markov_sign_evidence.py", "test_markov_sign_evidence.py", "Fields, Javidi, and Shekhar, arXiv:2501.13187 (2025)"],
      "limits": "The first sign is conditioned on. Skipped zeros change the time index and require the Markov law to hold for the nonzero-sign sequence. The result is not distribution-free and is an application of established predictive-likelihood martingale mathematics."
    },
    {
      "id": "declared_markov_sign_validation",
      "status": "fresh_frozen_finite_synthetic_result",
      "claim": "In the frozen 400-look study, the KT Markov-sign process was calibrated under the declared 0.90-persistence null and detected the targeted transition alternatives.",
      "result": "Declared stationary null: 39/5000 crossings; sign-inverted paired null: the identical 39/5000 decisions; fixed-positive-initial null: 36/5000; persistence 0.97: 4629/5000; persistence 0.75: 4999/5000; iid balanced persistence 0.50: 5000/5000.",
      "evidence": ["markov_sign_validation_protocol.json", "results-markov-sign-validation/summary.json", "results-markov-sign-validation/decision_paths.npz", "results-markov-sign-validation/audit.json"],
      "limits": "Finite synthetic computation only. The proof, not observed null counts, supplies the anytime bound. Alternative counts establish neither universal consistency nor physical evidence. The independent replay shares the frozen seed, NumPy generator, and floating-point arithmetic."
    },
    {
      "id": "iid_sign_process_valid_under_marginally_balanced_markov_dependence",
      "status": "rejected_by_counterexample",
      "claim": "The v1.26 iid conditional-sign process retains its 1% guarantee when signs are only marginally balanced but repeat with probability 0.90.",
      "counterexample": "On fresh declared p_stay=0.90 Markov-null paths, the old iid-sign comparator crossed on 4134/5000 histories.",
      "evidence": ["Theory_of_Reality.md Appendix AN.3", "results-markov-sign-validation/summary.json", "results-markov-sign-validation/audit.json"],
      "replacement": "Use the old sign process only under conditional sign balance, or use the new Markov process only when its fixed transition law is justified. Marginal balance alone validates neither shortcut."
    },
    {
      "id": "markov_sign_process_is_distribution_free",
      "status": "rejected_by_model_boundary",
      "claim": "The new Markov-sign process is valid for estimated, changing, higher-order, or arbitrary dependent signs.",
      "reason": "The martingale cancellation uses the exact fixed conditional transition probability in the denominator at every scored transition.",
      "replacement": "Declare the transition model before scoring. The next test must derive a uniformly valid composite-null process for a prespecified persistence interval and challenge its boundary cases."
    }
  ]
}