The Stewardship Allocation Theorem: Conservation Budgeting as Projected Dual Mirror Descent on an Emergent Price of Stewardship

Paper (featured): a working paper deriving conservation budgeting as projected dual mirror descent on an emergent price of stewardship λ*. Total connectivity-weighted D-Score yield is maximized uniquely when every funded parcel's marginal yield per dollar equals λ*; the Observe-Respond-Adjust-Repeat loop is exactly projected dual mirror descent over the Six-Law convex set, inheriting O(√T) regret. Headline regime duality (fixed by the Intelligence Bound dI/dt ≤ P·D/(k_B T ln 2)): concave parcel yield ⇒ interior equimarginal optimum (partial enrollment); linear yield ⇒ corner optimum (full enrollment) — reconciling the 2024 Jayachandran et al. full-enrollment field result as the linear-regime corner rather than a paradox. Three falsifiable predictions; 8/8 numeric checks (fitted O(√T) exponent 0.50). Verification backbone (supporting): the paper's three central theorems are machine-checked in Lean 4 by the Aristotle (Harmonic) prover — equimarginal_of_optimal, strictConcave_unique_max, linear_regime_corner (file SAT.lean). Zero sorry; axiom audit ⊆ {propext, Classical.choice, Quot.sound}; Lean v4.28.0; Mathlib pin 8f9d9cff; Aristotle project 452756cd-9b51-4bb7-9c43-e6b7365d2457. The Lean proofs certify the validity of the reasoning, not empirical magnitudes. Working paper; not peer-reviewed. Part of the Viridis canon; concept DOI 10.5281/zenodo.19317982.