Perception and Time: Causal Geometry, Non-Equilibrium Thermodynamic Entropy, and Anticipatory Phase-Space Dynamics in Sovereign Cognitive Architectures

This seminal treatise establishes the mathematical and physical foundations of temporal perception, anticipatory dynamics, and non-equilibrium thermodynamic entropy in sovereign cognitive architectures. By formalizing temporal cognition as geodesic flows on a statistical Riemannian manifold endowed with Fisher-Rao metrics, the paper proves the Inadequacy of Ergodic Invariance in human and autonomous decision systems. We introduce the Asymmetric Potential Well Hysteresis model, symplectic phase-space preservation via Hamiltonian vector fields, and pre-event anticipation under coercive duress camouflage. Includes complete mathematical proofs, thermodynamic entropy bounds, and deterministic zero-heap C99 and Python reference implementations.