validation
ForbiddenWritten kills: hypothesis, what was computed, the failing number, date, and lab mill. Open-frontier F1 (hold) is not the same label as older forbidden-list F1.
Exhibition cards. Parent residual named so a kill is not mistaken for a closed chip. Leftover extra-Φ is an OPEN residual, not established. The full lookalike kill list (do not redo) lives at /validation/leftover-phi. Exhibition cards below include MA-LONE, WE-ANALYTIC, BEND-GRAPH, PYTH-SS, GR-CURV-IR, VEL-PG, MICRO-W, RAR-FLOOR, ISRAEL-GEJ, VOL4, FOAM, BULK-ACCUM, ELAS-HALO, A0-Z, GW-EXTRA, L3-SCIAMA. GitHub is private; proofs live on this hub. Catalog: /docs/a_geom_ft_rar_kills_catalog. Constitutive W stays OPEN.
Hypothesis. Nucleon-mass WKB through the n→p shape barrier gives the free-neutron lifetime in minutes.
Computed. Path-A action on the MeV·fm Coulomb hump, nucleon mass as the WKB mass.
Failed. S ≈ 0.05–1.1; τ ~ 10⁻²³ s, not ~880 s.
Parent. Minutes inference [M] still stands; unique τ_n proof does not.
Hypothesis. Some barrier-class path (WKB or Kramers) has action equal to E₀ ≈ 59.34.
Computed. Sign of E₀ vs barrier height: E₀ = m₀/(2pq U₀) ∝ 1/U₀.
Failed. WKB ~ √U and Kramers ~ U/T cannot equal a quantity that grows when Coulomb is weaker.
Parent. Free-neutron lifetime number remains [M] inference, not a theorem.
Hypothesis. A Bohr-scale overlap length ℓ⋆ = 12.48 fm, or a 2pq framing proof, or a Franck–Condon mode ħω = U₀, exhibits E₀.
Computed. Length audit of banked Compton/Bohr/knot lengths; C₃ angular Hessian; 2pq gates.
Failed. No banked length at 12.48 fm. C₃ modes 39 MeV or 4.9 MeV, not U₀ = 1.32 MeV. 2pq evenness is generic.
Parent. Same parent: τ_n as [M], not a unique geometric lifetime.
Hypothesis. Reverse-engineering 12.48 fm from banked lengths × named factors finds a non-circular identity.
Computed. Cartesian product of banked lengths with p, q, ε, √3, π, 2π², 1/α, …
Failed. Exact hits are aliases of E₀ R_C. Clifford Willmore 6π² R_C = 12.454 fm vs 12.480 fm (−0.20%); not accepted.
Parent. Do not enlarge the factor dictionary to eat 0.20%.
Hypothesis. Larmor quality factor of the C₃ Coulomb modes is the decay probability P, because Q scales as 1/α.
Computed. Abraham–Lorentz Q = (3/(2α_eff)) (mc²/ħω) on the C₃ E-doublet.
Failed. Q ~ 10³–10⁵, not E₀ ≈ 59. 2π/Q keeps τ ~ 10⁻²⁰ s. Damping cools the mode, not n→p.
Parent. 1/α in a prefactor is not 1/α in the exponent.
Hypothesis. A 3-slice observer can mint (a, α) from the particle’s own geometry.
Computed. Access census: reconstructible 3-algebra vs L1 homogeneity of 1/a.
Failed. Dimensionful a is blocked by L1. α is slice-relative, not a knot invariant. Exhaustion of 137-formulae is not the theorem.
Parent. α INPUT and length leftover a INPUT remain. Public chips unflipped.
Hypothesis. Local one-seat hold on leftover R=1 can be closed by more N12 ODEs, a dilaton, or identifying R_eff with the electron S³.
Computed. N12-L tubes, two-scale hierarchy, second-scale entry, R_eff/N12 ratio.
Failed. Thin current tube forbidden; one leftover R gives O(1) roots; R_eff/λ̄_C ~ 10³⁹; extra field ≠ extra length.
Parent. Public continuum-hold chip stays OPEN. Reopen only with L-NEW or a transmutation named in L.
Hypothesis. Dual-band force cancel on the confined-photon seat is continuum hold.
Computed. H-D15: dual cancel under field-safe max|β|<1 vs near-null packaging kinematics.
Failed. μ* ≈ −0.40 under max|β|<1. Dual cancel needs near-null r r̈ packaging, not a hold theorem.
Parent. F1 continuum hold stays OPEN. Dual cancel ≠ hold.
Mill. /docs/a_geom_hold_hd15_subluminal_reg_field_sf_results
Hypothesis. A confined-photon seat is incomplete until it satisfies the Schott / Goedecke radiationless condition.
Computed. Ontology freeze: Maxwell timelike worldline + sphere flux vs finite-a lightlike packaging.
Failed. CLOSED-NULL as a required CPT condition. Wrong book. Not a proof Goedecke is false in Maxwell.
Parent. F1 hold OPEN. Core T1–T4 is not a radiation theorem.
Hypothesis. Coulomb bunching restore, or ILC-1 as an EOM, closes one-seat hold.
Computed. Frozen-circle current kicks: COULOMB / WEBER-INST / WEBER-ILC1 on bunching B and |I|.
Failed. Coulomb RESTORE bunching (ρ=0.27); Weber-INST only DRIFTS; ILC-1 drains or blows. Common-mode |I| invisible to the pair force.
Parent. F1 hold OPEN. Bunching restore is electrostatic structure, not hold.
Hypothesis. Faddeev–Skyrme / Abelian–Higgs Hopfion (ACT) on round S³ is H-D continuum hold.
Computed. Written ACT ⇔ H-D dictionary D1–D10 (carrier, stress, Hessian, current, scale).
Failed. FAIL_IDENTIFY. ACT is a bulk 3-field soliton (Θ=2η, T_η^η≡0). H-D is F_self=0 on a closed wind. Different tensors.
Parent. F1 hold OPEN. Hopfion / ACT ≠ hold.
Hypothesis. 3D Weber / shell self-energy with inner cutoff r_min = r_e/2 is the hard E=mc² join.
Computed. BF-1/2/3: L1b shell E_Σ = αℏc/(2R_m) at Compton R_m = a.
Failed. E_Σ = (α/2) mc² ≪ mc². Forcing E_Σ = mc² reintroduces free R = r_e/2 (B1 KILL).
Parent. F2 hard join stays OPEN. Soft P_EMC remains glue, not the theorem.
Hypothesis. A remaining licensed selector on frozen R-HOPF (MODE, Z₂, QF, BITI, QHC, SUMA) is Foot δ.
Computed. Each named selector scored on the frozen Hopf residual.
Failed. All STOP or FAIL_IDENTIFY (e.g. Z₂ midpoint is the equator, 90°, not Foot B).
Parent. Public δ is [E INPUT]. K/L is [E] algebra of that input, not a second input. Exhausted routes are not a derived δ.
Mill. /docs/a_geom_f5_bq_g3_licensed_routes_exhausted_consideration
Hypothesis. Slice-projection redshift / Tolman / acoustic scale on cosmic S³ equals Hubble.
Computed. Scored sky observables vs Hubble data.
Failed. SCORED_NO. Sky cosmogony put to bed. A-geom stays local.
Parent. Local IPC seats remain; do not reopen S³ Hubble without a new z(d).
Mill. /docs/a_geom_sp_cos_obs_redshift_tolman_acoustic_results
Hypothesis. A unique geometric CKM matrix V from present primitives (Cabibbo alone).
Computed. CKM package rail: texture vs unique residual frame.
Failed. Unique geometric V FAIL. L-GEO-CKM denied. Texture remains [M] packaging.
Parent. Reopen only with a new principle. Not Cabibbo-alone V.
Hypothesis. A galactic Z-pinch or paired disk-loop current flattens HI rotation curves and retires the halo.
Computed. July 1/r pinch with I as a dial; P-HI leftover Jz×Br vs v²/R at 8.5 kpc, 220 km/s.
Failed. Tully–Fisher algebra inconsistent (M∝v² not v⁴ unless extra scalings). Axisymmetric loop aφ=0. Licensed leftover ~0.16–0.40% of v²/R disk-wide. The particle halo is retired as inventory. This current is not that retirement.
Parent. Book G leftover (galactic DM) stands. Book C is Ampère from measured B on ionized plasma, not a v(r) law. Lab scoreboard is BCJ.
Hypothesis. Lone m(a) or SFDM is what photons see; extra Φ is unnecessary.
Computed. KiDS weak lensing vs SPARC RAR at ~300 kpc; baryon-only Newton vs extra Φ.
Failed. Photons require extra Φ. Lone m(a) is killed. Leftover extra Φ remains the slot, not a paid W.
Parent. Constitutive leftover extra-Φ prize stays OPEN. Do not publish a halo-retired chip.
Hypothesis. Analytic strain energy W(E) or Hencky 4-metric elasticity pays the RAR IR.
Computed. Taylor of W at identity / leftover umbilic; BP-1 two-well Hencky.
Failed. Quadratic IR is Poisson/Newton. Hencky is Newton+1PN, not the RAR.
Parent. Constitutive W must be non-analytic at leftover K=1/R. Prize OPEN.
Hypothesis. A 3-into-4 graph / 3-volume / CMC embedding in leftover B⁴ interpolates the RAR.
Computed. Graph slope, neck ρ_min=√(mR)≃5 kpc; δ(Area) interpolator μ=1/√(1+x²).
Failed. Centre wreck / no 0.1 kpc 2-sphere; Newton in the IR (cos θ), neck in the UV. Wrong end.
Parent. Empty-B⁴ rubber sheet is closed. Constitutive 4-medium slot remains.
Hypothesis. Pythagorean join g=√(g_N(g_N+a_0)) is the leftover interpolator.
Computed. Large-x tail μ=1−1/(2x); extra acceleration ≃a_0/2; perihelion mill.
Failed. Mercury 0.82″/cy, Earth 1.3″/cy, Saturn 4.0″/cy vs ~0.003″/cy extras. n=1 tail FIRE.
Parent. Join F unpaid. Standard μ isolated tail is SS-safe; Cassini Q₂ vs fat RAR is CAT-EVID.
Hypothesis. Einstein curvature or |R|^{3/2} pays the aquadratic RAR density.
Computed. Vacuum Ricci of a well; leftover ³R=6/R² as a wall; derivative order.
Failed. RAR outskirts are Ricci-flat (Laplace). Leftover ³R is a homogeneous wall, not ν(y). |R|^{3/2} still vanishes in vacuum.
Parent. Yield is leftover-static 4-acceleration, not Ricci. Prize OPEN.
Hypothesis. Painlevé–Gullstrand river kinematics replaces GR and saturates at leftover c/R.
Computed. PG dual of Schwarzschild; |dv/dr| vs c/R at 8.5 kpc.
Failed. UV is GR in shift clothes, not a replacement. |dv/dr|∼c/R needs v∼c; galactic v_PG/c≃7.5×10⁻⁴. Shear is the Ω clock.
Parent. River language is allowed as ADM shift. Constitutive W unpaid.
Hypothesis. A T(2,3)/Hopf condensate on leftover S³ pays aquadratic constitutive W.
Computed. R/a_p≃1.5×10⁴²; baryon spacing vs c²/ℓ; analytic defect EFT; P6 vertex census.
Failed. Dual pages (seat ≠ container). Analytic EFT is Newton IR. No 3-wave vertex. Defect T₀₀ is CDM-role.
Parent. Origin/T(2,3) stays PARK as a mass mill. Leftover constitutive prize OPEN.
Hypothesis. A hard floor g_obs ≥ a0 is leftover saturation.
Computed. dSph and KiDS accelerations vs Milgrom a0; SPARC mean vs a step at a0.
Failed. dSph g ∼ 0.027 a0 (×37 below). KiDS deeper. Hard step 0.20 dex low at the join.
Parent. Constitutive interpolator unpaid. Prize OPEN.
Hypothesis. A thin Israel / GE-J skin interpolates SPARC’s two-decade RAR.
Computed. Δ log10 g ∼ 2 ⇒ Δr/r ≃ 2.3 on a 1/r² well vs pudding-skin / Israel wall.
Failed. Yield zone must be fat ∼ r_y. Thin wall is leftover-normal (GE-J home), not ν(y).
Parent. Fat yield on leftover-static 4-acceleration remains. Prize OPEN. Do not unpark GE-J as m_e.
Hypothesis. Vol4 = const (bulk buoyancy / Archimedes) is a local y-map.
Computed. One leftover Lagrange multiplier λ; MW dent / B⁴ at 8.5 kpc.
Failed. Dent ∼ 1.9×10⁻²⁵ of leftover 4-volume; δR/R ∼ 5×10⁻²⁶. Uniform 4-pressure, no in-slice boost.
Parent. Constitutive 4-medium slot remains. Prize OPEN.
Hypothesis. Moving leftover water / memory-foam spring-back on leftover’s clock is the RAR residual.
Computed. Leftover τ = R/c ≃ 34 Gyr; solar-circle ωτ; Bullet lag.
Failed. ωτ ≃ 900 (fast poke, stiff Newton — wrong RAR end). ω-keyed τ is a new scale. History lags the Bullet the wrong way.
Parent. Currently-loaded mattress is the unpaid prize in time-domain clothes. Prize OPEN.
Hypothesis. Leftover bulk accumulates in wells as halo mass (rubber-sheet dust as source).
Computed. ρ_c fill of a MW well vs Newtonian-halo extra; Hubble share among ∼10¹¹ galaxies.
Failed. Local fill 3.5×10⁵ M⊙ inside 8.5 kpc. Hubble share ∼4.5×10¹¹ M⊙ is CDM-role inventory. No CDM input.
Parent. Photons seeing extra Φ is the constitutive prize, without extra inventory. Prize OPEN.
Hypothesis. Elastic T00 of the well, integrated to leftover R, is the 4.5×10¹¹ M⊙ halo.
Computed. Newtonian field energy; IR rail g² = g_N a0 from r_y to leftover R.
Failed. IR rail ≃ 0.22 M_b, 40× below 4.5×10¹¹ M⊙. Need Δr ≃ 41 R, outside the container. Binding energy is negative.
Parent. Leftover as constitutive 4-geometry remains the ontology. Integral is the wrong mass. Prize OPEN.
Hypothesis. Evolving leftover R makes a0 larger at high z and explains baryon-dominated disks.
Computed. a0 = c²/R if R ∝ 1/(1+z); Genzel/Milgrom 2017 g(R_1/2).
Failed. Larger a0 ⇒ more yield, not more Newton. a0 × 3 at z=2 if R ∝ 1/(1+z). Genzel disks already sit at (3–11)a0 with today’s a0.
Parent. R unnamed and spectrally locked. Compactness, not a0(t). Prize OPEN.
Hypothesis. An extra metric with cgw ≠ c can carry leftover extra Φ.
Computed. GW170817/GRB 170817A Δt = +1.74 s, D ∼ 40 Mpc; published |cgw/c − 1| ≲ 10⁻¹⁵.
Failed. TeVeS-class second-metric speed FIRE. Leftover yield must keep UV characteristics c. Full wave action unpaid.
Parent. cgw = c is a hard gate on the unpaid Lagrangian. Prize OPEN. RAD-LIGO pursue-not-presume.
Hypothesis. Sciama 2-seat retardation derives the formation floor / RAR end as m(a).
Computed. Linear 2-body delay of constant a; Jackson rest-frame split; 1-body Born analog.
Failed. Mutual I = ∫ρ/r, not 1/max(r12, La). Coulomb dominates for r12 ≪ La. Floor remains assumed, not derived.
Parent. Sciama floor parked. Kind of a floor not retired. Prize OPEN.
A theory that cannot be falsified is not science. This page documents every major result or hypothesis that was explicitly tested and found to fail within the constraints of the CPT framework.
Claims tagged as [F] (Forbidden) cannot be submitted as new community contributions without a comprehensive explanation of why the previous failure analysis no longer applies.
Action-at-a-distance limit (fails to predict retardation)
| ID | Claim | What was tested | Why it failed |
|---|---|---|---|
| KF-01 | Exact action-at-a-distance (no retardation) | Tested as a mathematical simplification to speed up calculations. | Fails because the Weber force has explicit finite-speed propagation built into the term. True action-at-a-distance () yields no radiation and no effective mass. |
| KF-02 | Flat R³ universe with Mach principle | Testing Mach's principle in a standard infinite background. | The Mach sum diverges for any infinite uniform distribution. A flat universe cannot mathematically satisfy Mach's principle. topology is strictly required. |
| KF-03 | QFT vacuum energy → cosmological constant | Attempting to map the standard QFT vacuum energy to the cosmological constant . | The QFT vacuum energy () is 120 orders of magnitude too large. CPT has no fundamental fields and no QFT vacuum, so this "problem" does not exist to be cancelled. |
| KF-04 | Magnetic monopole dark matter | Searching for topological magnetic monopoles as a dark matter candidate. | Requires a topological singularity in the Hopf fibration at a single point. No such smooth singularity can exist within . |
| KF-05 | Neutrino as T(1,0) or T(0,1) | Modeling the neutrino as a simple circle knot. | and are trivial circles, not knots. A massless fermion in CPT cannot be a torus knot. The neutrino may be a Weyl spinor on without a particle seat ([O]), but specifically is strictly [F]. |
| KF-06 | Green 3/8 in the raw slot as a theorem | One-convention Mach rederivation (R-MCR / R-MCR-2). | only at . Using it as raw at is a splice. Remainder k is not derivable from one functional. |
| KF-07 | as CMB curvature | Reading R=√6 c/H₀ as the FLRW curvature radius. | Incompatible with conventional CMB bounds. Rejected as a Hubble-tension solution. R_eff stays unnamed. |
| KF-08 | Expanding R with G∝1/R | M13 as an eternal law with R∝a(t). | For an expanding radius gives , 928 times the quoted lunar-laser half-width (M12). A stationary container does not write . |
T(1,0) reduces to an unknot
It is important to clarify that [M] (Mathematical) and [O] (Open) claims are not failures. They are simply incomplete derivations or hypotheses requiring further rigorous proof. Only claims explicitly tested and contradicted by the internal logic of the framework are marked [F].
The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.
Documents open in the CPT Research Library — a formatted viewer for all source research files.