Dual-Manifold Systems and Computational Substrate Theory: An Axiomatic Framework for Local Generation and Global Admissibility

The manuscript “Dual-Manifold Systems and Computational Substrate Theory: An Axiomatic Framework for Local Generation and Global Admissibility” presents a precise, theory‑shaped foundation for a two‑layer “generator vs verifier” view of physical law. It formalizes dual manifolds (local search dynamics on an observable manifold coupled to global admissibility on a verification manifold), defines the induced projected dynamics on measures, and connects the framework to established mathematics (killed/conditioned processes, quasi‑stationary distributions, and Feynman–Kac/SMC non‑linear semigroups). It introduces history‑level admissibility (with generic non‑Markovian effects), defines model‑independent invariants (escape rate, verification information, nonlocality radius, verification dimension), and provides a minimal toy model. A conservative “computational substrate” interpretation is sketched as a program (local update bounds → causal cone; cost density → lapse‑like time dilation), while explicitly separating description complexity from thermodynamic entropy and making clear non‑claims (no P vs NP result, no superluminal signaling, no completed derivation of GR).