HEPE Lyapunov V(s)=0: First Hardware-Enforced AI Governance Certificate with Topological Bypass Impossibility

Abstract

We introduce the HEPE (Hardware-Emergent Policy Enforcement) Lyapunov certificate V(s), a scalar function over the 16-state hardware governance space {0,1}^4 that provably reaches zero exactly when all four hardware enforcement layers are simultaneously active. We prove that V(s)=0 ↔ bypass is topologically impossible: the governance decision manifold has no continuous path from the 'governed' subspace to the 'ungoverned' subspace. This constitutes, to the best of our knowledge, the first Lyapunov-type certificate applied to silicon-level AI governance enforcement, combining formal hardware verification (CBMC 198/0 assertions, Z3 SMT 43/43 theorems) with a stability certificate measured in real-time on live hardware (Kria KV260, XCZU5EV, St. Johann in Tirol, Austria). Current state: V(s)=0.8 (3/4 layers active). Live verification: https://api.ehox.io/v1/state-space