# Claim ledger — Matter Harmony Lab 1.5.0

| ID | Claim | Type | Assumptions | Status |
|---|---|---|---|---|
| MH-001 | A formula-only deterministic regressor has worst absolute error at least 13.3 K on the frozen pentane boiling data. | Written proof + measured inputs | One prediction for all C5H12 isomers; NIST averages accepted | Supported |
| MH-002 | Endpoint calibration on carbon-skeleton Wiener index predicts held-out isopentane at 295.9 K versus 301.1 K, a 5.2 K error. | Finite computation + measured inputs | Frozen endpoint rule; three-isomer scope | Supported |
| MH-003 | The held-out prediction is on the condensed side of the boiling boundary at 293.15 K; measured fusion data identify the observed equilibrium phase as liquid at about one atmosphere. | Finite computation + measured inputs | Pure substance, equilibrium, about 1 atm | Supported, conditional |
| MH-004 | Wiener index orders the three boiling points but does not order their fusion points. | Finite comparison + measured inputs | Three frozen isomers only | Supported counterexample |
| MH-005 | A shared period-5/fcc/d10 signature cannot identify Ag/Pd 300 K resistivity; the measured ratio is 6.470. | Representation collision + reference data | Matula recommended total resistivity values | Supported counterexample |
| MH-006 | Molecular geometry is relevant to properties. | Empirical inference | Confounding is limited by the same-formula isomer comparison | Supported in this bounded comparison |
| MH-007 | A hidden-dimensional interference geometry explains these properties. | Physical hypothesis | Requires derived dynamics, shared parameters, and fresh predictions | Untested |
| MH-008 | One scalar “harmony” predicts arbitrary phases or conductivity. | Universal hypothesis | None adequate | Rejected by fusion and Ag/Pd counterexamples |
| MH-009 | A C5/C6 ordinary least-squares topology model using carbon count, Wiener index, and first Zagreb index reduces C7 boiling MAE from 8.554 K to 4.500 K versus carbon count alone. | Finite computation + compiled reference data | Frozen split; all nine C7 isomers excluded from fitting; NIST selected values | Supported on this holdout |
| MH-010 | The same topology coordinates improve C7 fusion prediction. | Finite computation + compiled reference data | Same split and unmodified model form | Rejected: MAE worsens from 27.574 K to 135.934 K |
| MH-011 | A topology descriptor validated for one property can be reused as a general material harmony coordinate. | Generalization hypothesis | Cross-property mechanism invariance | Rejected by MH-010 |
| MH-012 | The C7 result is prospective blind validation. | Provenance claim | Targets hidden from all prior human/model contact | Not claimed; it is a frozen-fit retrospective reference-data test |
| MH-013 | The fusion failure uniquely identifies missing higher-dimensional strings, rotations, or interference. | Ontological claim | A unique residual-to-mechanism map | Unsupported; ordinary omitted packing/conformation variables and model misspecification remain alternatives |
| MH-014 | A skew-symmetric 5×5 generator produces norm-preserving latent motion whose position and velocity have explicit 3D projections. | Written mathematics + finite computation | Declared row-state convention, fixed projector, real skew generator | Supported as a mathematical construction |
| MH-015 | The 17 reference boiling/fusion values can be represented by two latent frequency coordinates and decoded to machine precision. | Finite computation + reference inputs | Linear min/max encoder chosen using the same target table | Supported but tautological; not predictive evidence |
| MH-016 | Exact temperature-to-frequency reconstruction identifies physical 4D/5D rotations. | Physical identification claim | The inverse map is unique and independently constrained | Rejected: shuffled targets reconstruct equally exactly |
| MH-017 | An arbitrary hidden-plane angular speed is recoverable from a 3D projection when that plane is uncoupled from the visible coordinates. | Identifiability claim | Fixed projector \(P=[I_3\;0]\) | Rejected constructively: every such speed gives the identical projection |
| MH-018 | A fixed-tick trajectory uniquely determines a continuous plane-rotation frequency. | Identifiability claim | Samples occur only at integer multiples of one tick | Rejected: \(\omega+2\pi k/\Delta\) is an exact alias family |
| MH-019 | The displayed n-heptane motion is a measured molecular trajectory or quantum probability density. | Provenance claim | Time-resolved experimental positions and a validated observation operator | Not claimed; it is a graph-based synthetic candidate |
| MH-020 | Static scalar property tables alone can uniquely reconstruct hidden-dimensional molecular motion. | General inverse-problem claim | Injective forward observation map | Rejected by MH-016 through MH-018 |
| MH-021 | A 64-molecule periodic tetrahedral scaffold constructed from 997.047 kg/m3 and 18.0153 g/mol has a 12.429442 Å box, degree four, 128 links, and 2.691053 Å nearest O-O spacing. | Finite construction + reference inputs | Ordered diamond scaffold; 298.15 K density accepted | Supported by construction; not a liquid-structure prediction |
| MH-022 | The water-network generator `G=[0 C;-C^T 0]` preserves the dimensionless state norm. | Written mathematics + finite computation | Real fixed coupling C; exact linear evolution | Supported; drift 2.220e-16 in the executed trajectory |
| MH-023 | The renderer preserves 0.9572 Å O-H bonds and a 104.52 degree H-O-H angle while projecting the visible network state. | Finite computation + reference geometry | Rigid three-site model; no intramolecular vibration | Supported in 36,864 audited coordinate scalars |
| MH-024 | An arbitrary hidden rotation without visible coupling generates observable 3D water motion. | Identifiability claim | Fixed projector onto the visible block | Rejected constructively: executed projection error is exactly zero |
| MH-025 | The Water Harmonics movie is a measured liquid-water trajectory or validates a physical fifth dimension. | Provenance/physical claim | Time-resolved measurements and a uniquely constrained observation operator | Not claimed; the scaffold, coupling, pulse, colors, tick, and scale are constructed |
| MH-026 | Matching the reference density and molecular geometry counts as an out-of-sample prediction. | Validation claim | Those values were not used to construct the output | Rejected: both are direct inputs |
| MH-027 | Release 0.4.0 simulates electric, magnetic, hydrodynamic, or quantum water behavior. | Historical scope claim | Validated force/field laws and relevant observables | Rejected; those mechanisms are absent from 0.4.0. Release 0.5.0 adds only a bounded linear dielectric baseline. |
| MH-028 | The declared -0.834e/+0.417e/+0.417e rigid charge geometry is neutral and has a 2.346971 D molecular dipole. | Written electrostatics + finite computation | TIP3P-like charges and rigid 0.9572 angstrom / 104.52 degree geometry | Supported as a model property; not a fresh measurement |
| MH-029 | A single-Debye response driven at its 18.56 GHz relaxation frequency has gain 1/sqrt(2) and 45 degree lag. | Written mathematics + calibrated reference input | Linear steady state, one relaxation, 25 degree C frequency accepted | Supported; RK4 error 3.529e-10 |
| MH-030 | Two distinct 64-molecule unit-dipole histories can produce the identical full vector-mean oscilloscope trace. | Written construction + finite computation | Observation is A=(1/N)[I3 ... I3]; paired transverse cancellation | Supported; trace difference exactly zero in stored orientations |
| MH-031 | A perfect polarization trace uniquely identifies the molecular orientation movie. | Identifiability claim | Observation map injective on the admissible state class | Rejected by MH-030; explicit-charge trace difference is 4.441e-16 while microstates stay separated |
| MH-032 | The 18.56 GHz agreement is an out-of-sample prediction of hidden-dimensional water theory. | Validation claim | Frequency not used to set the model | Rejected; it is a calibration input from reference data |
| MH-033 | The Water Origami Oscilloscope is liquid-water molecular dynamics or evidence for a physical fifth dimension. | Provenance/physical claim | Validated interactions, ensemble, and unique observation operator | Not claimed; microscopic folds are constructed controls |
| MH-034 | Sampling on one fixed time grid uniquely determines the continuous driving frequency. | Identifiability claim | Aliases excluded by independent bandwidth information | Rejected; f+k/delta-t is an exact sampled alias family |
| MH-035 | The IAPWS room-temperature refractive index decreases from 1.345110691 at 380 nm to 1.328482654 at 780 nm in the executed visible range. | Reference formulation + finite computation | IAPWS R9-97; 298.15 K; 997.047 kg/m3 | Supported as a reference-input calculation, not a prediction of the theory |
| MH-036 | The declared ray interface obeys vector Snell refraction and unpolarized Fresnel energy partition. | Written classical optics + finite computation | Geometric optics; locally smooth interface; air-to-water incidence | Supported by exact tests and independent replay |
| MH-037 | A fixed distant source and the declared moving surface generate a time-varying underwater spectral caustic. | Finite synthetic computation | Frozen surface, ray grid, spectral bins, depth, and exposure | Supported for this constructed scene; no measured water movie was used |
| MH-038 | A CIE-standard color observer is one-to-one on visible spectra and can therefore measure every optical property. | Identifiability claim | Observer output restricted to XYZ | Rejected: distinct nonnegative spectra differ by 0.709286 in relative spectral norm while XYZ differs by at most 1.421e-14 |
| MH-039 | The 60 fps Sun-water animation is a hologram. | Provenance/optics claim | Optical phase and coherent wavefront must be reconstructed | Rejected: the engine transports spectral irradiance and discards phase |
| MH-040 | Motion faster than visible flicker is sufficient to create a physically solid or complete three-dimensional object. | Perceptual/physical claim | Temporal fusion would have to restore lost depth, spectrum, and phase | Unsupported; display continuity is not wavefront reconstruction |
| MH-041 | The rendered rays are measured individual photon trajectories. | Quantum provenance claim | Single-photon preparation/detection and a valid quantum measurement model | Rejected; rays are classical expected-energy samples |
| MH-042 | Intensity alone identifies absolute optical phase. | Identifiability claim | Direct intensity observation only | Rejected exactly: quarter-cycle-shifted unit fields have equal intensity |
| MH-043 | The fixed Sun must rotate to generate the moving underwater pattern. | Mechanism claim | Moving interface allowed | Rejected for the executed construction: the source is fixed and surface motion alone moves the caustic |
| MH-044 | The rendered caustic establishes a physical fourth/fifth-dimensional generator or universal grid/tick. | Ontological claim | Unique higher-dimensional prediction beating ordinary optics on fresh data | Unsupported; ordinary classical optics generates the result and fixed-time aliases remain |
| MH-045 | Human vision has one universal frames-per-second cutoff that guarantees smoothness for every stimulus. | Perceptual claim | Luminance, contrast, spatial structure, eye movement, and observer would have to be irrelevant | Rejected; primary experiments report stimulus-dependent thresholds and artifacts above 500 Hz for structured displays |
| MH-046 | The declared 0.800 mm bubble at 4 mm depth has an ideal Minnaert frequency of 4110.9205 Hz. | Written classical acoustics + finite computation | One spherical bubble; ideal gas response; small amplitude; surface tension, thermal, viscous, and wall corrections omitted | Supported inside the declared model; stored 60 ms FFT peak is 4116.67 Hz |
| MH-047 | The declared 0.025 m radial ripple carrier obeys the finite-depth capillary–gravity dispersion relation. | Written surface-wave mathematics + finite computation | Linear small-amplitude packet on 0.080 m water depth | Supported for the synthetic packet; it is not a solved drop-impact cavity |
| MH-048 | The pressure candidate reaches a microphone 0.750 m away after 2.16682 ms and scales as inverse distance. | Written compact-source acoustics + finite computation | Homogeneous air at 346.13 m/s; far-field compact source; no walls or atmospheric attenuation | Supported in the executable and independent replay |
| MH-049 | Release 0.7.0 reproduces the exact sound of an unspecified real water drop. | Provenance/validation claim | Bubble formation, coupling, damping, environment, and calibrated measurements would have to be supplied | Rejected; those values are declared and playback is peak-normalized |
| MH-050 | One observed bubble tone uniquely determines bubble radius. | Identifiability claim | Pressure, density, and corrections independently known | Rejected constructively: doubling radius and quadrupling pressure preserves the ideal Minnaert frequency |
| MH-051 | Failure of the acoustic candidate uniquely identifies a missing string, rotation, or extra dimension. | Ontological claim | Ordinary fluid, bubble, propagation, boundary, and sensor errors excluded | Unsupported; the bounded engine omits nonlinear entrainment, two-phase flow, multiple bubbles, room response, and hearing |
| MH-052 | The release-0.7 value 4110.9205 Hz is the unique small-amplitude prediction for its declared 0.800 mm bubble. | Model-scope claim | Vapor pressure, surface tension, thermal response, damping, and boundary corrections irrelevant | Rejected; the added stiffness relation gives 4048.9557 Hz at fixed \(\kappa=1.4\), 1.5073% lower, while preserving the old value as ideal Minnaert mathematics |
| MH-053 | With vapor pressure and surface tension included, the old 4110.9205 Hz target implies radius 0.6659558--0.7879498 mm as \(\kappa\) ranges from 1 to 1.4. | Written conditional mathematics + finite computation | Spherical small-amplitude bubble; 298.15 K reference properties; fixed 4 mm depth; endpoint \(\kappa\) bracket | Supported inside the declared sensitivity model; not a measured confidence interval |
| MH-054 | A complete damped pressure waveform uniquely identifies radius, effective polytropic exponent, and fractional volume amplitude. | Identifiability claim | Compact-source observation map injective in those variables | Rejected constructively: 401 distinct states preserve frequency and oscillating-volume scale; endpoint traces differ by at most \(3.667\times10^{-16}\) Pa |
| MH-055 | The local inverse from frequency, oscillating-volume scale, and decay to radius, \(\kappa\), fractional amplitude, and decay is full rank. | Written linearization + finite computation | Declared log-parameterization and small-amplitude model | Rejected: the 3-by-4 Jacobian has rank three and nullity one |
| MH-056 | The interval \(1\le\kappa\le1.4\) is a measured thermal law for this real drop. | Provenance claim | Direct thermodynamic or acoustic calibration | Not claimed; it is a bounded sensitivity bracket motivated by primary thermal-bubble analysis |
| MH-057 | The waveform-equivalence residual identifies a hidden dimension or missing string. | Ontological claim | All ordinary thermodynamic, interfacial, damping, boundary, coupling, and sensor alternatives excluded | Unsupported; the exact collision is produced entirely by ordinary variables within the declared classical model |
| MH-058 | An isolated H2O fundamental-mode vector uniquely identifies whether a bulk sample is solid, liquid, or gas. | Identifiability claim | Phase is a deterministic function only of the isolated vector (1595, 3657, 3756 cm^-1) | Rejected exactly: the same vector is paired with solid, liquid, and gas controls; best descriptor-only accuracy is 1/3 on the balanced set |
| MH-059 | A collective velocity spectrum can contain both diffusive gas-like and solid-like vibrational contributions. | Primary-method provenance + finite construction | Declared two-component 2PT-like basis; fixed finite window | Supported as a model family; not a claim that a liquid is a macroscopic gas/solid mixture |
| MH-060 | With fixed bases satisfying F_s(0)=0 and F_g(0)>0, the declared fraction is f_g=F(0)/F_g(0). | Written conditional mathematics + finite computation | Gas basis and collision rate fixed; exact noiseless zero-frequency value | Supported; 101 fractions recovered with maximum error 1.11e-16 |
| MH-061 | The collective diagnostic supplies three universal natural phase thresholds. | Universality claim | Spectral coordinate alone fixes equilibrium phase for all substances and state points | Rejected for this release: low-frequency mass varies continuously from 0.000009 to 0.459944; no threshold is inferred |
| MH-062 | The three constructed reference spectra are distinct on the frozen grid. | Finite synthetic computation | Declared basis shapes and normalization | Supported: squared Hellinger distances are 0.307797, 0.751221, and 0.183233 |
| MH-063 | The reference spectra are measured condensed-phase water or argon data. | Provenance claim | Direct spectroscopy or molecular-dynamics trajectories supplied | Rejected; only published modes/state parameters and one published f_g anchor are retained; line shapes are constructed |
| MH-064 | Failure of a vibrational phase diagnostic uniquely identifies a missing higher-dimensional variable. | Ontological claim | Thermodynamic state, density, free energy, force law, sampling, and phase labels independently validated | Unsupported; ordinary ensemble variables and model form remain live alternatives |
| MH-065 | Every fixed real skew-symmetric 5-by-5 generator has at most two nonzero rotation frequencies and one zero direction, and its 3D linear projection is a constant plus at most two sine/cosine pairs. | Written linear algebra + finite computation | Fixed real skew generator; linear passive projection | Supported; all reference and randomized matrices satisfy the annihilating equation to numerical tolerance |
| MH-066 | One instantaneous 3D projection uniquely identifies a five-coordinate state. | Identifiability claim | Observer is P=[I3 0] | Rejected exactly: the instantaneous observation kernel has dimension two |
| MH-067 | The rank of the instantaneous visible-hidden coupling block determines time-observability. | Structural-identification claim | Fixed generator and observer | Rejected constructively: two rank-one cases have observability ranks four and five because hidden-hidden mixing changes information flow |
| MH-068 | Full state observability for a known generator implies that one autonomous output history identifies the generator or latent dimension. | System-identification claim | Generator unknown; only one initial condition observed | Rejected: the equal-frequency example has known-generator observability rank five but one-history Hankel rank three |
| MH-069 | The matrix-aware bounded spectral classifier recovers the four frozen generator families. | Finite synthetic computation | Generator matrix supplied; skew-linear noiseless class; denominator at most 16 for bounded rational search | Supported on 512/512 randomized cases; maximum frequency error 1.11e-15 |
| MH-070 | The orientation of the two hidden coordinate axes is identifiable from the default 3D observer. | Identifiability claim | Hidden-basis O(2) transformations permitted with matched state and generator | Rejected: 101 gauge transforms change the generator by as much as 4.0736 while all 6,464 gauge-time outputs agree within 5.17e-14 |
| MH-071 | Finite exposure merely samples the same recoverable harmonic content. | Observer-model claim | Centered boxcar exposure | Rejected: one mode-period exposure lowers the sqrt(2) reference rank from five to three; a 3:2 common-period exposure lowers rank to one |
| MH-072 | The passive projection/exposure operator physically collapses or alters the latent state. | Measurement-back-action claim | Current classical observer equations only | Rejected by scope: the observer changes reported data and has no back-action term |
| MH-073 | A five-dimensional Hankel-compatible output proves five physical dimensions. | Ontological claim | Arbitrary nonlinear, time-varying, and higher/lower-dimensional realizations excluded | Unsupported; the rank is conditional on the finite linear realization class and is not a unique ontology |
| MH-074 | Failure to find a small rational frequency ratio proves that an observed ratio is irrational. | Arithmetic-identification claim | Finite-precision frequencies; denominator search capped at 16 | Rejected; the engine reports only “no small rational match,” while sqrt(2) is irrational solely because that reference was constructed exactly |
| MH-075 | A residual after this observer taxonomy uniquely identifies a fifth-dimensional particle or theological cause. | Ontological claim | Ordinary nonlinear dynamics, time variation, noise, calibration, and observer misspecification excluded | Unsupported; no residual is assigned to an extra dimension or to God |
| MH-076 | A fixed real 5-by-5 skew generator with a linear observation can contain at most two distinct positive temporal frequencies. | Written linear algebra | Fixed real skew generator; linear passive observation | Supported by the real skew normal form; finite exposure only attenuates these modes |
| MH-077 | The four frozen visible H I Balmer features can all be the linear temporal spectrum of the current five-coordinate observer. | Reference-data gate + written mathematics | The four NIST features are resolved; one fixed linear generator and observer | Rejected: four distinct features exceed the two-positive-frequency capacity |
| MH-078 | Two free harmony frequencies constitute a prediction of two Balmer wavelengths. | Calibration/provenance claim | Frequencies selected after seeing the spectrum | Rejected: any selected pair can be fit exactly, so this is calibration rather than prediction |
| MH-079 | The tested 3:2 family explains the Balmer spectrum because it matches two features within 1%. | Model-identification claim | One calibrated scale; four-feature target; 1% tolerance | Rejected: it matches only two of four after calibration and is not uniquely selected |
| MH-080 | Finite exposure can generate the missing Balmer features. | Observer-model claim | Linear centered exposure | Rejected: multiplication by sinc changes amplitudes but not frequency support |
| MH-081 | Failure of the linear spectrum gate proves that no higher-dimensional model can explain hydrogen. | Generalization claim | All nonlinear, transition-based, interacting, time-varying, and larger-state classes excluded | Rejected by scope; only the present fixed linear observer is ruled out as complete |
| MH-082 | The two missing features identify physical fifth-dimensional strings or a theological cause. | Ontological claim | Unique residual-to-cause map | Unsupported; ordinary quantum state transitions and other model classes remain live alternatives |
| MH-083 | A fixed real skew-symmetric generator in dimension d has at most floor(d/2) distinct positive rotation frequencies. | Written linear algebra | Fixed finite-dimensional real skew generator | Supported by orthogonal 2-by-2 rotation-block normal form |
| MH-084 | One three-output instantaneous observer identifies an arbitrary d-dimensional state for d greater than three. | Identifiability claim | No additional time samples or model restrictions | Rejected: rank(P) is at most three and nullity is at least d-3 |
| MH-085 | A simultaneous calibrated observer bank identifies every latent state exactly iff its vertically stacked matrix has rank d. | Written linear algebra | Same state observed at the same tick; observer matrices known; noiseless values | Supported by injectivity and least-squares inversion |
| MH-086 | The frozen coordinate observer banks reconstruct the synthetic state in dimensions 4, 5, 6, and 8. | Finite synthetic computation | Exact known matrices and simultaneous noiseless observations | Supported to numerical precision; this is not physical tomography |
| MH-087 | Adding more 3D observers adds intrinsic frequencies to the hidden generator. | Spectral claim | Fixed generator A; passive linear observers | Rejected: observers change amplitudes and visibility, not the eigenfrequencies of A |
| MH-088 | Eight latent dimensions explain hydrogen because floor(8/2)=4 matches four visible Balmer features. | Model-identification claim | Feature count treated as a full spectral prediction | Rejected: the count predicts no wavelength, intensity, selection rule, or transition relation |
| MH-089 | The displayed 4D/5D vectors are measured physical strings. | Provenance claim | Time-resolved higher-dimensional measurements supplied | Not claimed; the trajectories and observer matrices are constructed |
| MH-090 | Multiple uncalibrated or asynchronous observers can be stacked as though they measured one common state. | Measurement claim | Shared coordinates, calibration, and simultaneity absent | Rejected by scope; the rank theorem requires known P_j and one common state |
| MH-091 | A `Delta2 + Delta4` transition law calibrated on H-alpha and H-beta improves held-out H-gamma/H-delta prediction over the one-parameter Rydberg form. | Finite computation + compiled reference data | Frozen split; Peck--Reeder standard-air conversion; representative NIST features | Rejected: held-out RMSE rises from 6.030008 to 6.948567 ppm |
| MH-092 | The two-parameter candidate exactly interpolates both calibration features. | Finite computation | Two free coefficients; H-alpha/H-beta only | Supported to numerical precision; this is calibration, not prediction |
| MH-093 | The held-out comparison is an artifact of the last displayed digit in the NIST air-wavelength table. | Reporting-precision sensitivity check | Displayed half-step used as an endpoint check, not a complete uncertainty model | Rejected for the directional comparison: the candidate is worse at both endpoints for both held-out features |
| MH-094 | Two exactly fitted hydrogen transitions uniquely identify the continuation law. | Identifiability claim | Unrestricted additional functions permitted | Rejected exactly: `D(Delta2-Delta2(3))(Delta2-Delta2(4))` is zero on both training lines for every D and changes later lines |
| MH-095 | A fitted `Delta4` coefficient identifies a physical extra dimension. | Ontological claim | Operator, coupling, symmetry, standard corrections, and unique residual map supplied | Unsupported; the term is phenomenological and ordinary relativistic/QED/level-structure alternatives remain |
| MH-096 | Failure of this `Delta4` candidate disproves every higher-dimensional hydrogen theory. | Generalization claim | All derived higher-dimensional operators covered by this one term | Rejected by scope; only the frozen phenomenological candidate is rejected |
| MH-097 | The updated ordinary-physics expression evaluated with `rd=2.12763(78) fm` predicts the direct H-D 1S-2S isotope shift within the combined uncertainty. | Published theory + measured inputs + finite computation | Lensky et al. Eq. 58; contact LEC fixed to zero; quoted uncertainties combined in quadrature | Supported conditionally: +1.436632 kHz error, +0.309753 sigma |
| MH-098 | A nonrelativistic reduced-mass calculation is sufficient at kilohertz precision for the H-D 1S-2S isotope shift. | Model-adequacy claim | Relativistic, recoil, QED, finite-size, polarizability, and two-photon terms omitted | Rejected: it misses by +12695.900398 kHz; the modern ladder reduces absolute error by factor 8837.3 |
| MH-099 | The remaining central isotope-shift residual requires an additional finite-range interaction. | Model-necessity claim | Frozen three-sigma rule and quoted covariance approximation | Rejected: the residual is only 0.309753 combined sigma |
| MH-100 | One 1S-2S isotope-shift residual uniquely identifies both the range and coupling of `delta V/h=g exp(-r/lambda)/r`. | Identifiability claim | Both parameters free and only one scalar calibration supplied | Rejected exactly: every positive range with nonzero sensitivity has a fitted coupling |
| MH-101 | The 61 tested range/coupling pairs fit the same central residual but disagree on prospective state dependence. | Written construction + finite computation | Hydrogenic nS expectation values; 1 fm--10 nm range grid | Supported: endpoint 1S-3S corrections differ by 121.784 Hz and unrecalibrated H shifts by 3.519441 MHz |
| MH-102 | The tested Yukawa-like central operator is derived from a physical fifth-dimensional action. | Provenance claim | Higher-dimensional fields, compactification, symmetries, couplings, and reduction supplied | Rejected by scope; it is a phenomenological proxy |
| MH-103 | Any residual left by the isotope gate identifies a physical dimension, string particle, or theological cause. | Ontological claim | Unique residual-to-cause map and ordinary alternatives excluded | Unsupported; the standard prediction covers the datum and the proxy parameters remain non-identifiable |
| MH-104 | Fixing the range at the electron reduced Compton wavelength and fitting only the 1S-2S residual gives a definite H-D 2S-8S correction. | Written model + finite computation | Hydrogenic nS states; central Yukawa proxy; release-1.4 calibration; no holdout refit | Supported conditionally: -201.996425 Hz |
| MH-105 | The published H and D 2S-8S values and their experimental correlation imply an isotope shift of 209691233.7(10.35) kHz. | Measured inputs + covariance computation | de Beauvoir et al. central values; CODATA 2010 correlation 0.1225 | Supported; the full comparison uses 10.367652 kHz after radius and theory covariance |
| MH-106 | The frozen operator improves the ordinary 2S-8S prediction. | Historical holdout comparison | Named range and fitted coupling fixed before scoring; same ordinary reference | Rejected: signed error changes from -0.700628 to -0.720112 combined sigma |
| MH-107 | Failure to reject the frozen operator on 2S-8S is evidence for that operator. | Evidential claim | Holdout has power to resolve the predicted contrast | Rejected: the combined uncertainty is 51.326 times the predicted effect |
| MH-108 | The 2S-8S score is a blind prospective prediction. | Provenance claim | Target values unknown before model choice | Rejected; the values have been public since 1997, so this is a historical holdout |
| MH-109 | The frozen range or its non-rejection establishes a fifth dimension, universal grid/tick, string particle, or theological cause. | Ontological claim | A derived higher-dimensional action and unique empirical identification | Unsupported; the range is a named scale and the operator is phenomenological |

No residual is assigned to God, an extra dimension, or a missing string
particle.  A residual is evidence that the declared predictor is incomplete.