Deterministic 3-SAT Resolution via Continuous Physical Dynamics in Inertial Manifold Computing and its Empirical Robustness to Finite Precision Limits

This work presents Inertial Manifold Computing (IMC), a physical framework designed to natively resolve the 3-SAT problem within continuous dynamics. According to the Cook-Levin theorem, resolving 3-SAT conceptually addresses the NP-complete complexity class; however, our focus remains strictly on the physical dynamics of 3-SAT resolution rather than discrete algebraic equivalence. Building upon the theoretical foundations of the Blum-Shub-Smale (BSS) model, we demonstrate that 3-SAT instances can be resolved in polynomial time via continuous inertial dynamics. Simulations (N=1000) and theoretical frameworks substantiate the model's physical underpinnings and empirical robustness. Furthermore, we demonstrate that finite-bit quantization error inherently acts as a stochastic resource, ensuring operational viability against analog hardware limitations without requiring infinite precision.