Deterministic Replay Verification of Interval Programs over a Finite Primitive Core via Quantifier-Free Integer Certificates

The Analytically Derived Interval Computation Integrity Certificates (ADIC) framework is a replay-verification framework for interval-based computations over a fixed finite primitive core. The paper does not introduce a new family of interval operators. Instead, it shows that the verifier obligations for this primitive core can be reduced to finite, instantiated, quantifier-free integer checks over a realized ledger. The framework combines a fixed-point encoding of real intervals, a strict Galois insertion, explicit Euclidean witnesses for nontrivial primitive rules, and a replayable compilation of program and specification constraints. For the fixed primitive core considered here, verifier acceptance is proved to imply the existence of a concrete trajectory and enclosure of the certified specification constraints. The verifier performs deterministic replay over the realized program and specification ledgers, with linear dependence on ledger size up to integer bit-complexity. The claim concerns the verifier core only; transfer to deployed floating-point implementations is handled separately through an explicit implementation-inclusion assumption.