Beyond the Stochastic Veil: A Thermodynamic Architecture for Structural Intelligence

This paper specifies the Beyond the Stochastic Veil (BtSV) verification-layer architecture for specification-compliance auditing of foundation-model-driven AI deployments. The architecture composes Category Theory, stochastic optimisation, hyperdimensional representation, and Information Geometry to extract and refine candidate categorical structure, which must then pass through a Homotopy Type Theory verification gate before deployment commits to it. The proof-checking asymmetry at the gate, namely that proof checking is mechanically easier than proof generation, supports a regime-bounded specification-compliance audit while the assessing overseer's cognitive capacity I_H(T) suffices to anticipate the assessed system's strategic choices on deployment task family T. The architecture's central engineering challenge is the Genesis Problem: how categorical structure is extracted from unstructured data with sufficient adequacy that downstream proof-discharge becomes meaningful. BtSV proposes a three-phase approach combining LLM-based pattern extraction with verified categorical refinement, anchored by a Two-Tier Adequacy Protocol that separates Tier-1 formal mappings (§3, §4) from Tier-2 operational falsification (§5). Three architectural commitments — Two-Tier separation, Bidirectional Traceability across Tier-1 and Tier-2, and Ground-Truth Sync between empirical falsification and Tier-1 update — define the verification layer's response shape to the Formal-Sanity-Washing risk. BtSV provides Track-A specification-compliance verification under regime-bounded calibrations, conditional on stated assumption contracts plus Tier-2 falsification protocols. It does not provide Track-B semantic-correctness guarantees about whether the specification corpus captures operator intent, and its scope condition is the pre-parity regime in which I_H(T) suffices to drive residual specification-non-compliance arbitrarily close to zero.