The Ecopoietic Succession-Ordering Theorem: Biosphere Assembly as Bottleneck-Path Optimization

Paper supported by machine-verified Lean 4. The Ecopoietic Succession-Ordering Theorem (ESOT) recasts terraforming/ecopoiesis and ecological restoration as bottleneck-path optimization on a facilitation graph of coupled nucleation transitions. Its results: (i) facilitation lowers downstream establishment barriers (barrier renormalization); (ii) because establishment is Kramers-exponential, least-makespan assembly is a minimax bottleneck-path problem solved by a greedy lowest-barrier sweep under monotone facilitation; (iii) a reachability wall — the minimax bottleneck equals the critical drive budget, below which the target biosphere is thermodynamically forbidden regardless of elapsed time; (iv) an exact linear-in-entropy-production barrier law that derives the observed maximum-entropy-production succession trajectory; (v) an Intelligence-Bound floor on the ordering-learning time (an irreducible ordering regret); and (vi) out-of-order forcing efficiency equal to cos²Θ. This version (1.0.0) deposits the analytic core (11 theorems) together with the dedicated combinatorial reachability core (11 theorems: reach-closure fixpoint, up-set wall, and the minimax-bottleneck critical budget as a least element). Derived from the Viridis Intelligence-Bound canon, concept DOI 10.5281/zenodo.19317982.