Universal Coherence Theory: A Geometric Framework Unifying Fundamental Constants, Phase Transitions, and Emergent Gravity

We present a unified framework connecting geometric relations for fundamental constants, density-triggered gravitational bounce, and coherence-governed phase transitions. CLAIM TAXONOMY Exact Mathematical Identity (algebraically proven):- G_π = π[π²/sin²θ_W + 1] ⟺ sin²θ_W = π/(4π+1) Empirical Fits (σ-aware, falsifiable):- α⁻¹ = 137.035999215 (0.8σ from Rb 2020)- sin²θ_eff = 0.231572 (0.26σ from PDG 2024)- α_s(M_Z) = 0.1187 in MS-bar (0.8σ from PDG 2024)- m_p/m_e ≈ 6π⁵ (pattern only) Mechanism Conjectures (requiring development):- Phase mismatch hierarchy (σ ≈ 2.6 fitted)- Scalar-tensor EFT scaffold- Gravitational bounce connection KEY FALSIFIERS:- α⁻¹ >3σ from 137.035999215 → falsified- sin²θ_eff >3σ from 0.231572 → falsified- α_s(M_Z) >3σ from 0.1187 → falsified- No WEP-compatible covariant completion → falsified Related: DOI: 10.5281/zenodo.18452211 (Bounce paper)