SAFE-Matter™ Formal Admissibility State Model Mathematical Governance Structure for Deterministic Operational Authority

This paper defines the SAFE-Matter™ Formal Admissibility State Model, the mathematical governance structure underlying deterministic operational authority within SAFE-Matter™ governed environments. The model formalises how operational admissibility is continuously evaluated, constrained, propagated, escalated, or revoked through present-state evidential conditions at the exact moment execution occurs. The paper establishes the distinction between operational capability and operational admissibility. SAFE-Matter™ does not determine whether systems merely appear functional, connected, historically certified, or operationally responsive. Instead, the framework continuously evaluates whether operational reliance remains admissible through valid present-state evidence. The model formalises the mathematical relationships governing identity integrity, temporal validity, signal authenticity, dependency-chain admissibility, configuration integrity, environmental coherence, governance legitimacy, recursive governance integrity, and deterministic enforcement transitions. The paper additionally defines temporal admissibility decay, dependency propagation behaviour, UNKNOWN-state activation, recursive governance admissibility, and binary execution-boundary conditions governing operational authority. The governing constitutional principle formalised throughout the model is: Operational Authority exists if and only if Admissibility remains continuously provable. The paper further establishes that SAFE-Matter™ does not operate as a probabilistic safety-scoring framework or predictive monitoring system. Instead, it functions as a deterministic evidential governance architecture that continuously determines whether operational reliance remains justified at the exact moment execution occurs. The model therefore transforms operational trust from historically inherited assumption into continuously recomputed evidential legitimacy governed through deterministic admissibility boundaries.