# Hydrogen Matrix Lab claim ledger

| ID | Claim | Status | Assumptions / evidence | Boundary |
|---|---|---|---|---|
| H-001 | `rho(r) = exp(-2r/a0)/(pi a0^3)` is the ideal hydrogen `1s` position density. | Established within model | Written Schrödinger solution; fixed point proton, no external field, non-relativistic Coulomb Hamiltonian. | Not the exact full description of a real atom. |
| H-002 | The released `129^3` matrix numerically represents that density. | Checked finite computation | Integrated mass 1.000038674597; moments independently recomputed; tests passed. | Discretization and finite-box errors remain. |
| H-003 | The released OBJ encloses 90% of represented matrix probability at radius 2.660474582 `a0`. | Checked finite computation | Radius obtained from sorted voxel probability; mesh derived from that radius. | The envelope is a visualization convention, not a physical shell. |
| H-004 | The `1s` state produces a spherical static probability shape. | Established within model | Density depends only on `r`; three computed second moments agree. | Does not imply a localized electron is motionless at a definite point. |
| H-005 | The lab has revealed new physical evidence about reality. | Not supported | No experiment or measured hydrogen data was used. | Do not promote this implementation check into an ontological claim. |
| H-006 | A residual or unexplained visual feature identifies God or another unique cause. | Not supported | No identifying experiment exists here. | Preserve physical and theological ambiguity. |
| H-007 | A pure hydrogen energy eigenstate has time-independent position density. | Established within model | The global factor `exp(-iEt/hbar)` cancels in `|psi|^2`. | The complex phase still evolves; “static density” is not “nothing moves.” |
| H-008 | An equal coherent `1s + 2p_z` superposition produces a changing 3D density with a 405.287959 as ideal-model cycle. | Established within model and checked computation | Written cross term; 2022 CODATA Rydberg energy; `24 x 49^3` finite matrix; independent audit. | Fixed point proton, non-relativistic Coulomb model; not a measured atom. |
| H-009 | The released `2p_z` basis has an exact `z=0` node, odd `z` parity, and numerical orthogonality to `1s`. | Checked finite computation | Nodal and parity errors zero; overlap `-1.0842e-18`; analytic normalization independently integrated. | Finite-grid normalization error remains. |
| H-010 | The two synthetic 3-spheres remain tangent at the 4D origin throughout the declared rotation. | Written geometric result and finite checks | Centers are `+Ru(t)` and `-Ru(t)` with unit `u(t)`; 33 sampled phases checked. | This is a geometric construction, not established atomic structure. |
| H-011 | Projected waves from the touching-rotor construction produce a nonnegative, periodic 3D intensity sequence. | Checked synthetic computation | `24 x 35^3` matrices; minimum zero; cycle error `3.11e-15`. | Source-envelope projection is approximate and parameters are not learned from hydrogen. |
| H-012 | The touching-rotor generator is physically equivalent to hydrogen. | Not supported | No Hamiltonian derivation, spectral equivalence, or held-out fit has been shown. | Must remain a competing hypothesis until a discriminating test succeeds. |
| H-013 | The release-0.2 ideal Coulomb clock matches the NIST hydrogen Lyman-alpha doublet exactly. | Rejected | NIST lists 121.566824 and 121.567364 nm; the ideal fixed-proton model gives 121.502273411 nm, `-0.0532468%` from their listed-intensity-weighted centroid. | Spectroscopy tests energy/time scales, not a unique spatial ontology. |
| H-014 | The `121.567004 nm` centroid is a measured 3D hydrogen density. | Rejected category error | It is an intensity-weighted combination of two NIST spectral wavelengths. | It calibrates the animation clock only; voxel shapes remain modeled. |
| H-015 | A tangent-3-sphere projected-envelope model fit on eight phases predicts the sixteen unseen quantum-reference phases better than frozen baselines. | Rejected by frozen synthetic holdout | Rotor Hellinger `0.172620`; time-mean `0.022197`; radial `0.072179`. Independent replay agrees. | This rejects the exact parameterized family, not every possible higher-dimensional mechanism. |
| H-016 | The fitted rotor reproduces the reference axial motion and opposite-phase structure. | Rejected by frozen synthetic holdout | Held-out centroid correlation `-0.086074`; nodal leakage `0.057650`; mirror TV `0.053451`; all fail preregistered gates. | Full-cycle periodicity still passes and tangency remains true. |
| H-017 | Hydrogen nodal structure has no measured experimental support. | Rejected broadly | Stodolna et al. (2013) directly observed nodal structure for hydrogen Stark states using photoionization microscopy. | That experiment is an externally driven excited-state preparation, not interchangeable with the lab's field-free `1s + 2p_z` voxels. |
| H-018 | Release 0.3 provides measured time-resolved 3D density for a hydrogen atom. | Not supported | No matching 3D voxel measurement was ingested. | The release combines spectral calibration with ideal-model and synthetic-model matrices. |
| H-019 | Temperature supplies two opposite phase/rotation directions for hydrogen. | Rejected for the declared model | For `rho_beta = exp(-beta H)/Z`, `[rho_beta,H]=0`; finite computation at 300 K, 10,000 K, and -10,000 K leaves the two-level thermal density stationary. The coherent control reverses phase slope only under time reversal. | Negative temperature in the bounded truncation reverses population ordering, not time or the Hamiltonian; the full unbounded atomic spectrum does not admit this canonical negative-temperature equilibrium. |
| H-020 | Absolute zero and a finite maximum Kelvin are opposing endpoints. | Rejected | In positive-temperature canonical coordinates, `beta` runs from positive infinity toward zero as `T` rises from `0+` toward positive infinity; there is no finite maximum Kelvin in this model. | Special negative-temperature states require an upper-bounded energy spectrum and are hotter than positive temperatures, not colder than zero. |
| H-021 | Extra omitted rotors are the only explanation for the failed single-rotor fit. | Rejected as an exclusive inference | Missing variables are one possible explanation among wrong geometry, dynamics, projection, observable map, calibration, or optimization. | A model family must state which variables exist and what fresh result would reject them. |
| H-022 | Up to four same-geometry phase-shifted rotor components rescue the spatial model. | Rejected by bounded frozen holdout | Four components change held-out squared Hellinger error from `0.172620216` to `0.172032715` (0.3403% relative), remain worse than the `0.022196552` time-mean baseline, and fail motion, node, and mirror gates. | This does not reject every richer string, rotor, or higher-dimensional mechanism; it rejects this prespecified extension only. |
| H-023 | Taking longer to melt a frozen sample establishes opposite microscopic rotation. | Not supported | Heating time includes sensible heat, latent heat, heat-transfer rate, geometry, pressure, and material state. | The macroscopic delay alone does not identify a microscopic direction variable. |
| H-024 | The release-0.3 fixed-proton hydrogen model omitted electromagnetism. | Rejected | Its Hamiltonian contains the Coulomb potential `-e^2/(4*pi*epsilon_0*r)`, the nonrelativistic electromagnetic interaction. | It omits important two-body, relativistic, radiative, spin, finite-size, and environmental corrections. |
| H-025 | Standard electromagnetic corrections explain most of the old Lyman-alpha discrepancy. | Supported within the declared ladder | Reduced mass removes 97.7729% of the H0 centroid absolute error. The reduced-mass point-Dirac model removes 99.3796%, predicts two lines, and leaves a `-3.30342 ppm` centroid residual. Independent Decimal audit agrees. | H2 is not full bound-state QED: complete recoil, Lamb/self-energy/vacuum polarization, proton size, hyperfine, linewidth, and external-field terms remain omitted. |
| H-026 | The remaining spectroscopy residual identifies forces produced by a fourth spatial plane. | Not supported | No extra coordinate, action, coupling, gauge symmetry, operator, or distinct fitted prediction has been specified. Known standard terms remain omitted. | A future model must derive `H_candidate = H_standard + lambda O_4`, freeze its parameters, and beat the complete declared standard baseline on fresh observables. |
| H-027 | The hydrogen engine had omitted the Schrödinger equation. | Rejected | Releases 0.1--0.5 already used Coulomb Schrödinger eigenstates and their coherent phase evolution. | The omitted bridge was an explicit probability-current/continuity calculation and observable operator, not Schrödinger evolution itself. |
| H-028 | The release-0.6 `1s + 2p_z` probability current obeys `partial_t rho + div(j)=0`. | Established within model and checked finite computation | Written eigenvalue-equation proof gives exact cancellation. The production analytic residual is zero. An independent 129^3 fourth-order finite-difference audit gives relative L2 `0.0128041` outside the declared `r<0.5 a0` Coulomb-cusp region and preserves the `0.116031` full-interior diagnostic. | Fixed-proton, nonrelativistic, spinless, field-free (`A=0`) Coulomb model; current is not a localized electron path. |
| H-029 | The exact `1s`--`2p_z` dipole matrix element is `256/(243 sqrt(2)) a0`, producing an oscillating equal-packet dipole. | Established within model and checked computation | Independent radial quadrature and the production grid agree; grid relative error `3.70e-6`. The ideal E1 rate is `6.26831503e8 s^-1` and lifetime `1.59532505 ns`. | Ideal electric-dipole result, not a precision-QED lifetime or new measurement. |
| H-030 | Every energy-gap/density harmonic must appear in emitted electric-dipole light. | Rejected by analytic counterexample | `1s + 2s` changes local density but `<1s|z|2s>=0`; in an equal `1s + 2p_z + 3s` packet all three density gaps occur but only two have nonzero `z` matrix elements. | A different multipole, two-photon process, external field, or measurement operator can expose other harmonics; “E1 silent” does not mean “physically nonexistent.” |
| H-031 | Release 0.6 establishes a fourth/fifth spatial dimension or a hidden electron orbit. | Not supported | All new equations are standard three-spatial-dimensional nonrelativistic quantum mechanics; no extra coordinate or coupling was introduced. | Probability-current arrows are a representation of conserved probability flow, not measured trajectories or higher-dimensional strings. |
| H-032 | The golden ratio occurs exactly in ratios of ideal hydrogen Coulomb transition gaps. | Rejected by written proof | `E_n=-1/(2n^2)` Hartree is rational for every positive integer `n`; every nonzero gap and every ratio of two gaps is rational, while `phi=(1+sqrt(5))/2` is irrational. | Relativistic, radiative, external-field, molecular, and many-body spectra are different model classes; the proof is for the ideal Coulomb bound spectrum. |
| H-033 | A close decimal match to `phi` in a large spectral search establishes a golden law. | Rejected | The frozen `n<=40` scan checks 303,809 distinct gap-pair comparisons. Its closest ratio is `7491169/4629825 = 1.618024223...`, about `9.76537e-6` below `phi`, but it remains an ordinary rational number. | Multiple comparisons make near matches expected; admission requires a prior symbolic mechanism and fresh prediction. |
| H-034 | The exact golden angle can be one step of a finite fixed angular grid and recur exactly. | Rejected by written proof | A finite grid step is `k/N`, rational; the golden-turn fraction `1/phi^2=(3-sqrt(5))/2` is irrational. Fibonacci fractions such as `987/2584` approximate it but create periodic substitutes. | An infinite-precision or algebraic-state engine can store the irrational rotation, but then it is not a finite `N`-state angular grid. |
| H-035 | Fibonacci growth, declared icosahedral coordinates, and the `E8` mass identity are exact manifestations of `phi`. | Established within their declared mathematics | The Fibonacci companion polynomial is `x^2-x-1`; standard icosahedral coordinates contain `(0, +/-1, +/-phi)`; `2 cos(pi/5)=phi`. Production and independent checks pass. | The icosahedral and golden-angle cases contain chosen geometry. External `E8` evidence does not validate hydrogen or hidden dimensions. |
| H-036 | Release 0.7 proves that `phi` is a universal hidden-dimensional constant of the Theory of Reality. | Not supported | The audit classifies exact, imposed, approximate, and externally measured occurrences and finds no exact `phi` in the ideal hydrogen gap ratios or a finite grid step. | A physical claim needs a derived operator or generator, units, coupling, and a frozen distinguishing prediction. |
| H-037 | One declared coherent hydrogen state can be compiled into density, probability flow, charge/current, dipole, far-field coherent light, and operator-filtered spectral channels. | Established within the declared model and checked finite computation | Written observation operators; `48 x 65 x 65` synchronized slices; eight frozen checks; independent replay. | The state is ideal, fixed-proton, non-relativistic, spinless, and prepared rather than the stationary ground state. |
| H-038 | The release-0.8 far field is transverse, obeys `|B|=|E|/c`, has a dipole `sin^2(theta)` power pattern, and integrates to the Larmor dipole power. | Established within the semiclassical far-zone approximation and checked computation | Vector identities plus 721-point angular quadrature; transversality relative error `1.34e-16`; power-integral relative error `4.53e-12`. | Electric-dipole and radiation-zone approximation; no near field or self-consistent backreaction. |
| H-039 | The classical field radiated by the expectation dipole is the complete photon output of the coherent atom. | Rejected by written conditional mathematics | For the equal `1s + 2p_z` state, cycle-average classical coherent power is `2.562023753e-10 W`; the initial quantum E1 energy-loss rate of its half-excited population is `5.124047506e-10 W`. Their ratio is exactly `1/2`. | The missing half does not identify a hidden dimension; quantized-field vacuum fluctuations and incoherent emission are absent from the classical projection. |
| H-040 | Release 0.8 calculates and displays every physical property of hydrogen or reality. | Rejected | The executable registry marks spontaneous photon statistics and spin/magnetic moment as blocked and higher-dimensional cause as non-identified. | Completeness requires explicit state variables, evolution, couplings, observer operators, and passed conservation/validation gates for each added channel. |

Provenance: release 0.1.0 files remain preserved. Release 0.2.0 adds `hydrogen_4d_wave.py`, `four_d_touching_rotors.py`, their tests, `independent_wave_check.py`, `outputs/wave_summary.json`, `outputs/independent_wave_check.json`, and `outputs/touching_rotor_summary.json`. Release 0.3.0 adds the frozen NIST-clock calibration, train/holdout rotor test, independent replay, and comparison matrices without overwriting earlier negative or positive results. Release 0.4.0 adds the frozen bounded latent-component extension and temperature/phase-direction test; the 0.3 outputs and rejection remain unchanged. Release 0.5.0 adds the frozen H0/H1/H2 electromagnetic correction ladder and independent Decimal audit; no rotor, spatial-density, RRLS, or earlier validation output is changed. Release 0.6.0 adds the field-free probability-current engine, observable harmonic catalog, exact parity counterexamples, rendering, and an independent finite-difference/quadrature audit. Release 0.7.0 adds the frozen golden-ratio protocol, exact algebraic classifier, exhaustive bounded hydrogen scan, fixed-grid proof boundary, visualization, and independent replay. Release 0.8.0 adds the forward observable compiler, synchronized charge/current and radiation matrices, an explicit channel-coverage registry, exact classical/quantum emission boundary, visualization, and independent replay; no prior output, negative result, or core Hamiltonian is changed.