The Corridor Stewardship Theorem: Effective-Resistance Restoration Pricing and the Connectivity Shadow Price (the Weaver)

Inaugural record of the Viridis Canon — Corridors & Spatial series (S5); this record’s concept DOI anchors the S5 series. Core IB spine unchanged (frozen at v9). Proves the Corridor Stewardship Theorem (CST, ‘the Weaver’, 16th Intelligence-Bound self-application; ⚡ convergence event — the edge-dual of the Monitoring Water-Filling Theorem). Modeling a habitat-corridor network with McRae circuit theory (gene/propagule flow = current, functional isolation = effective resistance), Lean 4 (Aristotle c9df1884, 6 theorems, zero sorry, axioms ⊆ {propext, Classical.choice, Quot.sound}, all non-vacuous) certifies: the marginal-current law ∂R_eff/∂r = i² (connectivity centrality IS the restoration gradient); existence/uniqueness of a single broadcast connectivity shadow price; the closed-form water-filling optimum g* = √(κ/(λ·c·δ)); strict convexity of 1/g; the cos²Θ restoration-efficiency / misallocation meter ∈ [0,1]; and that a bridge carries the full unit current (single point of failure). Pairs as the edge-dual / twin of the Surveyor (MWT, S2). Working paper; not peer-reviewed.