The Thermodynamic Corridor Theorem: Onsager Variational Flux, Lambert-W Optimum, and a Percolation Threshold for Corridor Dissipation

Staged thematic record of the Viridis Canon (route: S5 (Corridors) ). 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. The variational / optimal-pricing / percolation backbone of corridor dissipation across the Planetary Thermodynamic Market Stack. Strictly-convex dissipation yields a unique flux minimizer on any convex set (Onsager) ; the optimal corridor multiplier is the Lambert-W root µₒpt=exp (W (R) /2) ; a multiplicative cocycle forces a unique pricing kernel; and corridor summability undergoes a percolation phase transition at the critical threshold µc=1+ln2. Extends the HDFM corridor pillar (P2). The 4 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 Working record; paper pending; not peer-reviewed.