Formal Verification of Process Ontology and Dynamic Gauge Symmetries in Lean 4

We present the first machine-checked formalization of Process Ontology—a relational, process-first physical framework—and the derivation of its core dynamic gauge symmetries in the Lean 4 interactive theorem prover. Process Ontology shifts the fundamental physical paradigm from static, substance-based entities to recursive, non-equilibrium self-measurement processes. We formalize this process as a contractive operator on a complete metric space, proving that macroscopic physical properties emerge as stable fixed-point attractor basins (eigenforms) under a master postulate M̂(X*) = X*. We verify the mathematical necessity of the conformal golden ratio (φ) as a metric scaling invariant, and formally derive the universal plasticity slip (δ_slip = (φ⁻¹)⁴ / 168) that prevents metric crystallization. Furthermore, we formalize the Standard Model gauge group dimensions (SU(3) × SU(2) × U(1)) as volumetric tiling requirements, showing they sum to the Causal Latch dimension L₁₂ = 12. Finally, we verify the weak-field limit of the Einstein Field Equations, standard model mass scales, and the first-row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. All proofs are mechanically checked and compiled under Lean 4 with Mathlib. The complete verified library is permanently archived at DOI: 10.5281/zenodo.22116208.