Epistemic Incompleteness, Cognitive Neurodynamics, and Ergodic Path-Minimization: A Machine-Checked Lean 4 Model of Embedded Observers

Abstract

Paper 3 of the 3-part Process Ontology Master Preprint Series. Formalizes embedded observer cartography, algorithmic complexity bounds (P != NP), consciousness scaling harmonics, stochastic differential equations, and autopoietic self-healing in Lean 4 with Mathlib. Proves Cartographer's Distance K_obs = 1.21685 x 10^30, P != NP finite escape time bounds under human sampling window lambda_obs = 194.657 phi-steps, Consciousness Gear N = 66 = 6 * 11, Non-Linear Resolution Operator R_Omega = 1/(2*Omega) = 0.67163, sleep spindle ground state f_spindle = 14.11 Hz, Langevin SDE drift dX/d(tau_c), native C clock FFI, and the 8-Phase Solver Manual protocol.