Each row is a closed form in the cell integers, its status tier, and its distance from experiment. Tiers are strict: a theorem is not a postdiction, and a suggestive pattern is not a theorem.
This ratio follows from the colour factor \(C_A = 3\) alone. It is exact, parameter-free, and the PMNS CP phase is exactly what DUNE is built to measure (around 2035). If the ratio is confirmed ≠ 3 at >3σ, the framework is falsified. No other approach makes this particular prediction.
| Observable | Formula (cell integers) | Status | Distance from experiment |
|---|---|---|---|
| α⁻¹ (fine structure) | (4π)³ᐟ²·π·[47/48 + 10/(3·48³) + 22/(3·48⁵)] | Tier 2 | 137.035999055 · 0.3σ from Cs (2018) |
| sin²θ_W (geometric) | (17 − 3√17)/20 | Tier 1 | 0.14% |
| α_s(M_Z) | C_A² − C_A·ln(C_A)/(2π) | Tier 2 | 0.01σ |
| m_H / M_Z | 18/(9+√17) | Tier 2 | 0.14% |
| α_GUT⁻¹ | 25 | Tier 2 | novel — not directly measurable |
| Observable | Formula / origin | Status | Distance from experiment |
|---|---|---|---|
| Lorentz factor γ | γ²(1 − v²/c²) = 1 from □ → −∇' on a moving defect | Tier 1 | derived (theorem on the foam wave operator) |
| Velocity addition | w = (u+v)/(1+uv/c²) from substitution closure | Tier 1 | derived (SO(3,1) boost subgroup) |
| Length contraction | L = L₀/γ from equipotential ellipsoid | Tier 2 | corollary, exact in v/c |
| Time dilation | τ = γ·τ₀ from t' = γ(t − vx/c²) | Tier 2 | corollary, exact in v/c |
| Quadratic Lorentz violation | δc/c ~ −(a²/24)·Δ_4(k)/k² ~ (E/E_P)² | Tier 2 | ~10⁻³⁸ at LHC · linear violation falsifies |
| Observable | Formula | Status | Distance from experiment |
|---|---|---|---|
| Koide relation | Q = (Σm)/(Σ√m)² = 2/3 | Tier 1 | exact (structural) |
| m_e | r₁·M_P·exp(−(E−F)(2Δ+√Δ)/16) | Tier 2 | 0.002% |
| m_μ | Koide from m_e, θ = 2/9 | Tier 2 | 0.004% |
| m_τ | Koide from m_e, θ = 2/9 | Tier 2 | 0.009% |
| m₁ (lightest ν) | = 0 | Tier 1 | exact theorem |
| m₃ (ν) | m_e·exp(−(11+13√17)/4) | Tier 2 | 0.075% |
| Mass hierarchy | normal ordering forced | Tier 1 | theorem |
| |Δm²₃₂| / Δm²₂₁ | = 33 (Eisenstein norm, 33 = S² − C_A·P) | Tier 4 | ≈0.5σ · pending formal derivation |
| Observable | Formula | Status | Distance from experiment |
|---|---|---|---|
| λ (Cabibbo, NLO) | sin(π/14)·(1 + √17/363) | Tier 2 | 0.22505 · 0.07σ |
| A (Wolfenstein) | (F − r₁)/F = (19+√17)/28 | Tier 2 | 0.82583 · −0.015σ |
| R_b (CKM triangle) | r₁²/(r₁r₂ − 1) = (49 − 9√17)/30 | Tier 1 | 0.39640 · 0.36σ |
| ρ̄ | R_b·cos(δ_CKM) | Tier 2 | 0.15898 · −0.002σ |
| η̄ | R_b·sin(δ_NLO) | Tier 3 | 0.3478 · lever-arm phase residual |
| δ_CKM | inter-type torsion operator, (C_A−1):1 | Tier 2 | 66.36° · 0.25σ |
| m_d / m_s | sin²(π/14) | Tier 2 | 1.0% |
| Observable | Formula | Status | Distance from experiment |
|---|---|---|---|
| tan²θ₁₂ | (√17/9)(1 − √17/144) | Tier 2 | 0.44501 · 0.074σ |
| sin²θ₂₃ | 1/2 + √17/81 | Tier 2 | 0.5509 · 0.2σ |
| sin²θ₁₃ | (√17/27)²(1 − √17/162)² | Tier 2 | 0.02215 · 0.2σ |
| δ_PMNS | 3πR = 200.7° | Tier 2 | 0.15σ (±25°) |
| δ_PMNS / δ_CKM | = 3 (colour factor C_A) | Tier 1 | novel — testable by DUNE ~2035 |
| Observable | Formula / origin | Status | Distance from experiment |
|---|---|---|---|
| Ω_DM / Ω_b | 3(1 + 2√3)/2⁴ᐟ³ = 5.3147 | Tier 2 | 0.92% (Planck 2018) |
| ρ_Λ (dark energy) | ρ₀(l_P/R_U)² × 6/7 | Tier 2 | 1.4% (Planck 2018) |
| r_p (proton radius) | 4ℏ/(m_p c) | Tier 2 | 0.02% |
| Bekenstein area quantum k | = C_A = 3 | Tier 1 | exact |
| Schwarzschild g_tt, g_rr | covariant vacuum density, ν = 1/2 (static + moving source via substitution) | Tier 2 | exact match to GR · moving case kinematic, exact in v/c |
| Frame-dragging (gravitomagnetism) | h_tφ = 2GJ sin²θ/(c²r) from substitution on rotating source | Tier 2 | leading Kerr multipole · kinematic derivation |
| Photon-graviton speed lockstep | δc_γ = δc_g at (E/E_P)² (same BCC site Laplacian for A₁g and T₂g modes) | Tier 2 | |Δc/c| ~ 10⁻⁴⁵ vs GW170817 bound 3×10⁻¹⁵ · locked at all foreseeable precision |
| Einstein equations | unimodular, from foam action | Tier 2 | consistent with all GR tests |
| Maxwell equations (all 4) | □D = 0 + Helmholtz + Volterra · A = vφ/c² for moving sources | Tier 2 | exact |
| Friedmann equations (both) | foam energy conservation | Tier 2 | exact |
| Cosmological constant | Λ = integration constant (dissolved) | Tier 4 | resolves the 10¹²³ discrepancy |
The framework is rigid: changing any cell integer by ±1 moves a headline number by ≥1%, so there is nowhere to hide. Any one of these falsifies it.
The full eleven pre-registered predictions and all derivations are in the Core Framework. To recompute the spectrum these rest on, see Verify.