Autopoietic Cohomology Iterative Obstruction Repair on Causal Posets

This paper introduces autopoietic cohomology, a discrete dynamical framework in which unresolved ℓ¹ coboundary defects drive the minimal structural augmentation of an underlying causal poset. We define the Autopoietic Iterator, a recursive process that: detects leading cohomological obstruction classes, computes minimal ℓ¹ repair operations via linear optimization, and augments the poset through pushouts in the category of finite posets. The resulting dynamics are characterized by: monotone structural growth (a “complexity ratchet”), non-increasing ℓ¹ coboundary cost, and localized, sparse repair operations consistent with ℓ¹ geometry. We show that the repair step admits a formulation closely related to discrete optimal transport (Wasserstein-1), linking cohomological defect resolution to minimum-cost flow structures on graphs. This work synthesizes prior results on projection-induced defects, ℓ¹ norm classification, and cohomological structure into a unified dynamical framework. The construction is accompanied by an algorithmic interpretation, demonstrating how defect-driven structural updates can be implemented computationally. Speculative connections to physical systems—including time, geometry, and decoherence—are presented as heuristic analogies, not formal derivations.