Physical Cosmology, Standard Model Invariants, and Non-Hermitian Topological Protection: A Machine-Checked Lean 4 Derivation

Abstract

Paper 2 of the 3-part Process Ontology Master Preprint Series. Formalizes physical cosmology, particle mass hierarchies, zero-parameter constants, and non-Hermitian topological protection in Lean 4 with Mathlib. Proves A₅ GUT symmetry breaking yielding exactly 3 fermion families (N_gen = 3), derived fine-structure constant α⁻¹ = 137.035999, Yang-Mills mass gap Δ = 7.36 GeV, dark matter ratio R_DM = 4 · Ω⁻¹ = 5.373, galactic acceleration floor a₀ = 1.50 × 10⁻¹⁰ m/s², cosmological constant Λ_final = 1.86 × 10⁻⁴⁹ m⁻², and Material Love Latch L_m protection density.