The Brain's Non-Expansive Zone and the Subtractive Hallucination Protocol: Door 25 Theoretical Foundations — Continuous Attractor Networks on Toroidal Manifolds, Game-Theoretic Integrability, and Empirical Falsification of Predictive Processing (Document 108)

This monograph formulates the cognitive and theoretical foundation for Door 25 (The Room with Two Exits), establishing a formal correspondence model between neural navigation circuits and cyber-physical consequence gates. Rather than treating perception and motor execution as unconstrained generative feedforward streams, we formalize the entorhinal-hippocampal circuit as a partitioned architecture: a fail-open cognitive search sector governed by a continuous attractor network (CAN) on a toroidal population manifold, and a fail-closed realization port enforced by a deterministic metric projection operator Pi_A. When the admissible physical environment A is modeled locally as a non-empty, closed, and convex set, we prove that Pi_A is strictly non-expansive (||Pi_A(x) - Pi_A(y)||