Founder's Scar: Cohomological Lock–In and Teleology Under Drift

The first viable traversal of a niche writes a cohomology class—a boundary condition—intostate space. We call this imprint the Founder’s Scar. Thereafter, what looks like “purpose”is simply KL–minimizing drift that preserves that class as the environment moves. We make the scar operational without metaphors: define a scar class S as the equivalence class of admissible update rules that (i) preserve a Fisher–information invariant I under sheaf gluing G and renormalization R, and (ii) exhibit a non–reversible eigen–mode (a V–gate ratchet). We prove: (1) Class Existence & Uniqueness under mild gap assumptions; (2) a Teleology as KL Drift law: in slowly varying ecologies, admissible flows are thesolutions of a constrained variational problem minimizing accumulated KL subject to S; (3) a Breach Bound: the Murphy cost to change class is lower bounded by a seam integral over non–gluing residuals; and (4) a Reconstruction Lemma: the scar class is recoverable from perturbation responses (lineage tokens optional). We give instruments to estimate S from streaming behavior, falsifiers, and exemplars: gossip/persistence hunting (human), chat UX (LLMs), and convergent design (wheels, scroll).