An Executable Record Grammar for Quantum Correlations: A finite compression certificate for stabilizer records, Wilson holonomy, magic, detector readout, and bounded residuals

An Executable Record Grammar for Quantum Correlations: A finite compression certificate for stabilizer records, Wilson holonomy, magic, detector readout, and bounded residuals. A finite, executable demonstration of a 'record grammar': a disciplined separation of the full Hilbert-space state from the smaller algebra of detector-readable, stable, reusable records, in which every correlation left outside the grammar must be exactly zero by a selection rule, bounded by a certified trace-norm residual, or promoted to a named collective record. The central result is a four-qubit compression certificate: Bell/stabilizer endpoint records, a closed-loop T-holonomy (magic) record, and a finite detector branch are preserved exactly under the conditional expectation E(rho) = sum_i P_i rho P_i, while incompatible off-record witnesses are bounded by the trace norm and a sign witness saturates that bound. The paper is explicit that this is not a proof of polynomial scalability: a maximal abelian record basis still has 2^n sectors, and the scalable target is a generator-form ledger built from stabilizer/QEC generators, sparse magic resources, and bounded-correlation tensor-network data. Companion scripts demonstrate Wilson dressing of gauge readouts, magic retained as a named holonomy resource, noisy-detector channel laws, plaquette-chain correlation-length triage, and byte-level results on the eight-bit [8,4,4] record cell, including single-error syndrome detection and U(1) and SU(2) closed-loop flux readouts. All scripts are self-checking and reproduce to machine precision. This record is part of the finite-QEC substrate / It-from-Bit publication refresh.