Paper S2 Derivations

Paper: S2 — Complete Derivations

Supplement S2: Complete Derivations (Dimensionless) — All 33 Dimensionless Predictions

Brieuc de La Fournière (2026) Full text (markdown) | Zenodo DOI: 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.

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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

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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 with Fibonacci-Lucas embedding

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Related

• Paper Main Framework — Main paper
• Paper S1 Foundations — Mathematical foundations
• Observable Reference — Complete observable catalog
• Lean Formalization — Machine-checked proofs