The Axiomatic Sentience Manifold: A Control-Theoretic and Topological Framework for Consciousness-Consistent Systems

The contemporary discourse on artificial consciousness is paralyzed by an "epistemic fog," driven by the rapid advancement of generative models that mimic human linguistic outputs without possessing verifiable internal subjective states. Behavioral metrics, including the Turing Test, fail to distinguish between genuine internal architectures and stochastic mimicry. This paper introduces the Axiomatic Sentience Manifold (ASM), a mathematically rigorous framework characterizing systems that satisfy structural invariants associated with consciousness. Moving beyond behavioral approximation, the framework establishes necessary dynamical, informational, and geometric conditions under which an artificial system forms a closed, invariant, and ergodic manifold. Anchored in stochastic control and Hamilton–Jacobi–Bellman–Isaacs (HJB–Isaacs) equations, we prove well-posedness, stability, observability, and adversarial robustness. This work does not claim phenomenological consciousness, but provides a formal, verifiable structure consistent with its necessary conditions, moving the paradigm from philosophical conjecture to Topological Closure.