Paper: S2: Complete Derivations
Supplement S2: Complete Derivations (Dimensionless): All 33 Dimensionless Predictions
Brieuc de La Fournière (2026) Full text (markdown, v3.4) | v3.3 archive on Zenodo: 10.5281/zenodo.18837071
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Abstract
Provides complete algebraic derivations for all 33 dimensionless predictions from topological invariants (b₂, b₃, dim(G₂), etc.). 18 core relations VERIFIED in Lean 4; 15 extended predictions use topological formulas. Includes expression counts showing structural redundancy.
Key Results
Deviation Distribution
| Range | Count | % |
|---|---|---|
| Exact (0%) | 4 | 22% |
| < 0.01% | 3 | 17% |
| < 0.1% | 4 | 22% |
| < 0.5% | 7 | 39% |
Expression Counts (Top Observables)
| Observable | # Expressions | Status |
|---|---|---|
| Q_Koide = 2/3 | 27 | CANONICAL |
| N_gen = 3 | 24+ | CANONICAL |
| sin²θ₁₂ᴾᴹᴺˢ = 4/13 | 21 | CANONICAL |
| sin²θ_W = 3/13 | 19 | ROBUST |
| m_H/m_t = 56/77 | 16 | ROBUST |
Gauge/Holonomy Comparison
| Config | Mean Dev. | Factor |
|---|---|---|
| E₈×E₈ | 0.26% | 1× (optimal) |
| E₇×E₈ | 8.80% | 34× worse |
| SU(3)/CY holonomy | 4.43% | 17× worse |
Section Structure
- Part 0: Derivation Philosophy: Inputs vs outputs, claims vs non-claims
- Part I: Foundations: Status classification, notation
- Part II: Foundational Theorems: N_gen=3, τ=3472/891, κ_T=1/61, det(g)=65/32
- Part III: Gauge Sector, sin²θ_W=3/13, α_s=√2/12
- Part IV: Lepton Sector: Q_Koide=2/3, m_τ/m_e=3477, m_μ/m_e=27^φ
- Part V: Quark Sector, m_s/m_d=20, m_b/m_t=1/42, CKM angles
- Part VI: Neutrino Sector, δ_CP=197°, mixing angles
- Part VII: Higgs & Cosmology, λ_H=√17/32, Ω_DE, n_s, h, σ₈
- Part VIII: Summary (18 VERIFIED + 15 extended)
- Part IX: Observable Catalog
Related
- Paper Main Framework: Main paper
- Paper S1 Foundations: Mathematical foundations
- Observable Reference: Complete observable catalog
- Lean Formalization: Machine-checked proofs