The Verification Phase-Transition Theorem: A Thermodynamic Critical Price for Conservation-Attestation Markets

Abstract

Staged thematic record of the Viridis Canon (route: S2 (Monitoring / verification economics)). The Intelligence-Bound spine is unchanged (frozen at v10.0.0, record 20801185); this record links to it via isDerivedFrom the concept DOI 10.5281/zenodo.19317982. There exists a critical price below which a conservation-attestation (MRV) market cannot bootstrap. The theorem locates it as a transcritical bifurcation governed by four levers — the Landauer floor on verification cost, the Intelligence-Bound ceiling on attestation throughput, zero-knowledge compression, and verifier alignment (cos²Θ). The critical price diverges exactly at ecological tipping, so the market fails precisely where restoration is most urgent. Builds on the Thermodynamic Discounting Theorem (the Appraiser), inheriting its τ*→∞ tipping divergence. The 8 core theorems are machine-checked in Lean 4 (Aristotle, zero sorry, axioms ⊆ {propext, Classical.choice, Quot.sound}, statements verbatim and non-vacuous). Scope: the Lean proofs certify the validity of the discrete reasoning, not empirical magnitudes. Working record; paper pending; not peer-reviewed.