# Element Projection Lab claim ledger

| ID | Claim | Status | Assumptions / evidence | Boundary |
|---|---|---|---|---|
| E-001 | The atlas contains one neutral-element record for every atomic number 1--118. | Checked finite computation | Unique sequence, symbols, and grid cells; production and independent audits. | Element identity is reference input, not a new discovery. |
| E-002 | The rotationally averaged one-electron density is spherical. | Established by written mathematics | Normalized SO(3) average in Equation BK.1. | Does not say every oriented open-shell state is spherical. |
| E-003 | A uniformly occupied closed subshell is spherical. | Established by written mathematics and checked computation | Spherical-harmonic addition theorem; l=0--3 independently sampled. | Applies to the complete subshell sum, not an arbitrarily selected orbital. |
| E-004 | An oriented s/p/d/f orbital-density basis can contain even angular ranks from 0 through 2l. | Established within declared basis | Angular-momentum product rule; catalog checked for all records. | Basis orientation is chosen and is not one rigid atom surface. |
| E-005 | The saved configurations contain exactly Z electrons and obey subshell capacities. | Checked finite computation | All 118 configurations independently reparsed. | Configurations are compiled inputs; 109--118 are predicted. |
| E-006 | Slater-screened hydrogenic r50, r90, and peak radii are accurate measured atom sizes. | Not supported | They are normalized low-cost radial proxies. | Requires comparison with ab initio or measured density observables. |
| E-007 | The atlas is a complete many-electron quantum solution. | Rejected | No correlation, relativistic, spin--orbit, nuclear, field, bonding, or band operator is implemented. | Each missing channel requires a declared state/evolution/observer and fresh validation. |
| E-008 | Different orbital lobes prove different physical dimensions. | Not supported | Rotated px and pz bases give different pictures within ordinary 3D quantum mechanics. | An extra dimension needs a coupling and a distinguishing prediction. |
| E-009 | Isolated-atom 3D signatures alone determine molecular phase or metallic conductivity. | Rejected as an inference | Those observables depend on interactions, structure, and many-body bands. | Extend to molecules/solids and validate separately. |
| E-010 | Any unexplained discrepancy identifies God or another unique cause. | Not supported | Many model omissions and alternative causes remain. | Preserve physical and theological ambiguity. |
| E-011 | Bulk gold and silver color is determined by the isolated-atom atlas image. | Rejected as an inference | The atlas contains no lattice Hamiltonian, bands, occupations, optical matrix elements, or dielectric response. | Atomic orbitals can seed a solid-state model but do not by themselves predict bulk color. |
| E-012 | The Johnson--Christy measured n,k values plus the Fresnel equation reproduce the wavelength selectivity associated with gold and silver color. | Checked measured-input forward calculation | Room-temperature measured optical constants; normal incidence from air; 1 nm linear interpolation only within the compiled range. | Reproduces reflectance from measured inputs; does not predict n,k from first principles. |
| E-013 | Gold suppresses blue reflection much more strongly than silver while both are highly reflective in red. | Checked finite computation from measured inputs | At 450.9 nm: Au 0.408220, Ag 0.980347; at 659.5 nm: Au 0.962585, Ag 0.990566. | Applies to the cited thin-film dataset and ideal normal-incidence surface; morphology, contamination, temperature, and angle can change observations. |
| E-014 | Similar atomic configurations or shared fcc structure force identical color. | Refuted by measured counterexample | Au and Ag are both group-11 noble metals with filled d shells plus one s electron and ordinary fcc bulk structure, yet their measured visible reflectances differ strongly. | A predictive theory needs energy bands, relativistic terms, occupations, transition matrix elements, and damping. |
| E-015 | Relativity is irrelevant to gold's visible response. | Inconsistent with established band calculations | Relativistic and nonrelativistic gold bands differ by shifts/splittings comparable to approximately 1 eV gaps; later many-body calculations refine the 5d--6sp gap. | This release cites those calculations but does not independently solve the relativistic many-electron solid. |
| E-016 | A remaining spectral mismatch would uniquely establish a fourth/fifth dimension or theological cause. | Not supported | Surface state, film thickness, temperature, defects, electron correlation, spin--orbit coupling, phonons, and model form remain alternatives. | Extra-dimensional models require a derived coupling and a frozen distinguishing spectrum. |
| E-017 | A free-electron-only response is sufficient to predict gold's visible reflectance. | Refuted within the frozen model comparison | Eleven wavelengths fit each model; on five untouched wavelengths, gold reflectance MAE is 0.154691 for Drude and 0.019718 for Drude plus one Lorentz oscillator. | The comparison is conditional on these two phenomenological classes and this measured thin-film table. |
| E-018 | Adding one interband oscillator improves untouched reflectance predictions for both metals. | Checked finite train/holdout computation | Gold MAE reduction 87.253%; silver 60.125%; five fixed holdouts per metal. | Only five holdout wavelengths per metal; the same dataset supplies train and test points, so this is not an independent-laboratory replication. |
| E-019 | The oscillator toggle directly measures relativistic physics. | Rejected as an interpretation | Drude and Lorentz terms are effective response channels; neither fit solves a relativistic band Hamiltonian. | A relativity claim requires explicit relativistic and nonrelativistic Hamiltonians with otherwise matched assumptions. |
| E-020 | The one-oscillator response is a complete microscopic theory. | Refuted by diagnostics | Gold Drude damping and silver background permittivity hit declared lower bounds. | Boundary hits signal model strain or non-identifiability; multiple oscillators, band structure, matrix elements, and sample effects remain. |
| E-021 | Better held-out reflectance uniquely supports a fourth/fifth dimension. | Not supported | An ordinary 3D causal oscillator model already supplies the improvement, and many conventional microscopic refinements remain. | A higher-dimensional term needs a quantitative coupling and fresh out-of-sample gain over matched conventional baselines. |
| E-022 | The 0.3.0 response coefficients and protocol are frozen for external validation. | Checked artifact and executable contract | Freeze ID EPL-AU-AG-COLOR-2026-09-20-v1; exact hexadecimal floats; source/result/prediction hashes; refitting, bound changes, and model selection disabled. | A future revision may define a new model under a new identity, but it cannot overwrite the frozen benchmark and still claim the same test. |
| E-023 | The frozen evaluator can silently retrain on a new dataset. | Refuted by implementation | The evaluator imports no optimizer, exposes no fit function, and verifies the original artifacts before scoring. | This is a software guard, not a proof that no external actor can edit files; edits instead invalidate the recorded digest. |
| E-024 | Freezing converts the 0.3.0 finite result into independent physical evidence. | Rejected | The coefficients still came from one Johnson--Christy table and the current holdout shares its experimental systematics. | Independent evidence begins only when the unchanged frozen evaluator is applied to a separate measurement series. |
| E-025 | A 3D animation of the declared five-coordinate skew-linear motion is physical evidence for a fifth spatial dimension. | Refuted for this model | Every continuous linear 3-vector output is exactly a constant plus at most two ordinary sine/cosine pairs. Production and independent implementations agree to roundoff. | A latent-coordinate representation is not a spatial ontology; nonlinear or interacting models are separate hypotheses. |
| E-026 | A higher output Hankel rank counts physical spatial dimensions. | Rejected as an inference | Hankel rank can identify minimal dynamical state order only within declared realization assumptions. Ordinary 3+1D systems can have arbitrarily many internal modes. | Spatial dimension requires a model-specific coupling and a distinguishing physical observable. |
| E-027 | Two peaks can confirm the simple compact-circle Kaluza--Klein mass relation. | Refuted by parameter count and construction | Any labelled pair with 0 <= m0 < m1 fixes m0 and 1/R exactly; the first mass constraint is the n=2 mode. | Later masses, widths, spins, couplings, branching ratios, and cross-channel relations must be frozen predictions. |
| E-028 | The current projected-harmonic engine passes a physical-dimension evidence gate. | Rejected | It has a measurable visualization and a conventional baseline, but no fixed dimensional coupling, distinguishing constraint, reserved measured validation, measured excess, or experimental replication. | The visualization is retained; its interpretation is narrowed. |
| E-029 | Current primary experimental searches provide positive evidence for an extra spatial dimension. | Not supported by the cited measurements | ATLAS periodic-spectrum, CMS high-mass diphoton, and Eot-Wash short-range gravity searches reported null results and model-specific limits. | Null searches constrain declared parameter regions; they do not exclude every possible extra-dimensional model. |
| E-030 | A constrained mode tower would by itself uniquely prove an extra dimension. | Not supported | Finite tower subsets may be mimicked by conventional resonances or other new physics. | Require preregistered spin, widths, coupling and channel relations, multiplicity control, systematics, and independent replication. |
| E-031 | The published ATLAS periodic-signal result passes a necessary cross-channel evidence screen for an extra physical dimension. | Rejected by measured publication summary | At the preselected `R<50%` row, signed significances are +1.5 (dielectron) and -0.2 (diphoton); the model-dependent search reports no significant deviation. | This evaluates the publication summary, not the full event-level likelihood, and does not exclude every extra-dimensional model. |
| E-032 | The largest positive ATLAS model-independent fluctuation survives the declared four-variant multiplicity correction. | Rejected by finite computation on measured inputs | The dielectron maximum is 1.5 sigma: one-sided local p=0.0668072 and Bonferroni p=0.267229. The diphoton maximum is -0.2 sigma and adjusted p=1.0. | The four variants are correlated; Bonferroni is used because it does not assume independence. No across-row combination is claimed. |
| E-033 | A local 3.1-sigma value in both channels would automatically pass the 3-sigma evidence screen after four searches. | Refuted by constructed counterexample | One-sided local p=0.000967603 becomes 0.00387041 after Bonferroni, above the frozen 0.00135 familywise threshold. | This is synthetic arithmetic illustrating multiplicity, not an ATLAS observation. |
| E-034 | One strong channel is equivalent to independent experimental replication. | Refuted by constructed counterexample and gate definition | A synthetic 6-sigma dielectron value paired with a zero-sigma diphoton value fails the cross-channel rule. | Two channels in one experiment are still not independent experimental replication; the rule is only a necessary screen. |
| E-035 | This release is a blind preregistered spectrum reanalysis. | Rejected and prohibited | The ATLAS data and null conclusion were public before the protocol; the release consumes printed summary values and does not reproduce the full likelihood. | A future evidence claim must freeze before genuinely independent data are opened and retain a full calibrated statistical model. |

Provenance: release 0.1.0 adds the all-118 compiled atlas, exact angular
distinction, Slater radial proxy, interactive observer builder, static audit
figure, eleven production tests, and a thirteen-check independent audit. It
does not alter Hydrogen Matrix Lab 0.8.0, RRLS, or earlier negative results.

Release 0.2.0 preserves every 0.1.0 artifact and adds the measured-input
gold/silver Fresnel observer. Eight production tests pass; an independent
implementation replays 802 dense values with maximum absolute discrepancy
5.55e-16 and performs eleven additional point/order checks. No RRLS or
Hydrogen Matrix source is changed.

Release 0.3.0 preserves all earlier artifacts and adds the frozen 11/5
train/holdout response experiment. Nine new production tests pass. A separate
scalar implementation imports no production band module, replays 64 model
predictions, performs 218 checks, and reproduces aggregate metrics with maximum
absolute discrepancy 2.16e-16. The finite result supports an interband response
channel; it is not a microscopic band solution, relativity toggle, new measured
evidence, higher-dimensional proof, or theological identification.

Release 0.4.0 preserves the 0.3.0 coefficients and results byte-for-byte and
adds the immutable external-validation contract. Eight freeze tests pass. An
independent audit verifies the manifest and four artifact hashes, decodes every
parameter from its hexadecimal representation, and replays all 64 predictions
with maximum absolute discrepancy 4.44e-16. No physical model result, RRLS
source, Hydrogen Matrix source, or earlier negative result is changed.

Release 0.5.0 preserves all earlier optical artifacts and adds an exact
observational-equivalence theorem, executable dimension-evidence gate, simple
compact-circle tower boundary, nine production tests, and an independent
299,919-component scalar audit. The release records current primary
experimental null results without reclassifying them as this project's data.
No RRLS, Hydrogen Matrix, frozen optical coefficient, or earlier result is
changed.

Release 0.6.0 preserves all earlier artifacts and adds a frozen retrospective
audit of the exact ATLAS Table 2 significance matrix and published
model-dependent conclusion. Eight new production tests pass; a separate
standard-library implementation verifies the protocol digest and twelve
publication-gate checks. The measured summary fails the necessary
cross-channel and familywise screens. The release does not reproduce the
ATLAS likelihood, claim blind preregistration, reject all extra dimensions, or
alter RRLS, Hydrogen Matrix, optical coefficients, or earlier results.