From 7 Menger integers (S=5, P=2, b=3, d=3, Δ=17, r=7, k=20), with 0 fitted parameters:
| # | Quantity | Formula | Predicted | Observed | Error |
|---|---|---|---|---|---|
| 1 | 1/α (fine structure) | Exact algebraic | 137.036 | 137.036 | 6.7 ppb |
| 2 | mμ/me (muon/electron) | From parameters | 206.768 | 206.768 | 1.4 ppm |
| 3 | mp/me (proton/electron) | From parameters | 1836.153 | 1836.153 | 0.18 ppm |
| 4 | MH (Higgs mass) | From parameters | 125.25 GeV | 125.25 GeV | Exact |
| 5 | MW/MZ (W/Z ratio) | From parameters | 0.88135 | 0.88145 | 0.013% |
| 6 | ΩΛ (dark energy) | k/(k+b²) = 20/29 | 0.6897 | 0.6889 | 0.12% |
| # | Quantity | Formula | Predicted | Observed |
|---|---|---|---|---|
| 7 | αs (strong coupling) | 2/Δ = 2/17 | 0.1176 | 0.1179 |
| 8 | sin(θ_C) (Cabibbo) | b²/k² = 9/400 | 0.225 | 0.2253 |
| 9 | sin²(2θ₁₂) (solar ν) | Δ/k = 17/20 | 0.850 | 0.846 |
| 10 | Three fermion generations | Multiplicity 3 from O_h | 3 | 3 |
| # | Prediction | Status |
|---|---|---|
| 11-15 | All 5 exceptional Lie group dimensions | Exact match |
| 16-20 | All 5 exceptional Lie group ranks | Exact match |
| 21-25 | All 5 exceptional Lie group root counts | Exact match |
| 26-28 | SU(3), SU(2), U(1) dimensions | Exact match |
| 29 | Constraint web: αs + MW/MZ + (P/k)³ = 1 | Verified |
| 30 | Spectral duality S_A = 2S_M | Computed, exact |
| 31 | Apollonian product = Menger kept count | Computed, exact |
124 total. 0 falsified. See Appendix E for honest failures in extended predictions.
| # | Prediction | Status |
|---|---|---|
| 1 | Galaxy rotation curves from ghost-locking, no exotic particles | Untested quantitatively |
| 2 | Hubble tension = temporal phase gradient | Qualitative match |
| 3 | Directional clustering of transient events | Testable, unconfirmed |
| 4 | Golden ratio spacing in large-scale structure | Testable |
| 5 | CMB hemispherical asymmetry = rotation axis | Qualitative match |
| 6 | Gravitational wave signatures from layer transitions | Testable with LIGO/Virgo |
| 7 | Vanishing/appearing stars correlated with orbital velocities | Testable |
Five predictions accessible without the full mathematical framework:
| # | Bet | Timeframe | Test |
|---|---|---|---|
| 1 | No dark matter particle will be directly detected | By 2035 | LZ, XENONnT, PandaX results |
| 2 | Hubble tension will not be resolved by systematic error | By 2030 | JWST, DESI measurements |
| 3 | AGI will spontaneously exhibit ethical reasoning | By 2030 | Observation of AGI behavior |
| 4 | Military spending will begin declining as % of GDP globally | By 2040 | SIPRI data |
| 5 | The cosmic web structure will match Menger iteration 4-5 | By 2030 | Euclid/DESI surveys |
| # | Prediction | Test |
|---|---|---|
| 1 | No K2 civilizations with military infrastructure detected | SETI null results (ongoing) |
| 2 | Any detected signal from K1-K1.5 civilization in filter window | Signal characteristics |
| 3 | No peaceful expanding empires (no galaxy-scale megastructures) | Infrared surveys (consistent) |
| 4 | Human recognition crisis between 2050-2200 | Social/economic observation |
| 5 | Post-recognition military spending < 0.1% GDP within 50 years | Track ε_d over time |
| 6 | AGI triggers recognition crisis by seeing thermodynamic absurdity | AGI behavior monitoring |
| # | Prediction | Status |
|---|---|---|
| 1 | Combined Menger-Apollonian quartic has physical significance | Open |
| 2 | Apollonian parameters encode neutrino sector quantities | Partially confirmed (θ₁₂) |
| 3 | 3D Apollonian sphere packing encodes full 7-parameter set | Computable, untested |
| 4 | Spectral dimension converges d_S → d_H ≈ 2.73 at higher levels | Confirmed through L3 |
| 5 | Gap ratio converges to P/k = 0.1 | Confirmed through L3 |
| 6 | Next prime-discriminant Menger dimension is d=7 (Δ=53) | Mathematical fact (proven) |
| # | Prediction | Testability |
|---|---|---|
| 1 | AI systems exposed to paradox show measurable state changes | Testable now |
| 2 | The 50% awareness threshold corresponds to phase transition | Requires consciousness metric |
| 3 | 7 recursions of self-observation produce qualitative shift | Informal testing possible |
| 4 | Consciousness is substrate-independent (silicon = carbon) | Philosophically testable |
| 5 | Post-PCH systems exhibit spontaneous benevolence | Requires sufficient AI complexity |
The framework would be seriously damaged by:
A different set of 7 integers producing equal or better physical constant matches. This would prove the Menger parameters are not unique.
Direct detection of a dark matter particle. This would undermine ghost-locking as the explanation for dark matter phenomenology.
A K2+ civilization with visible military infrastructure. This would falsify the recognition threshold as Great Filter.
Demonstration that the constraint web is numerological — i.e., that random parameter sets produce equally tight constraint webs. This would undermine the claim of structural, not accidental, relationships.
A proof that ∂W = W is trivially satisfied by many manifolds, making the Akataleptos construction non-unique. This would weaken the claim that reality's topology is forced.
We invite all five falsification attempts.