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

Abstract

Of all the correlations Hilbert space allows, which actually become stable, readable, reusable records — detector clicks, conserved charges, syndrome bits, pointer states, gauge-invariant loop readouts? This note answers operationally with a finite, executable record grammar: a conditional expectation E_rec(ρ) = Σ Pᵢ ρ Pᵢ that separates the full state from the smaller algebra of detector-readable records. The worked example is a four-qubit compression certificate — two qubits carry Bell/stabilizer endpoint records, one a closed-loop T-holonomy record, one a finite detector branch bit — and self-checking scripts prove every observable in the declared record algebra is preserved exactly, while incompatible off-record witnesses are changed but bounded by ‖ρ − E_rec(ρ)‖₁ (= 0.16875 for the test state, saturated by the sign witness, so the residual is a measured certificate rather than hidden bookkeeping). Crucially the compression is not Clifford-only: T-magic is not silently projected onto the stabilizer skeleton but retained as a named holonomy resource with explicit detector/feed-forward channel laws, and multi-plaquette correlations either factorize, decay with a measured correlation length, or get promoted to a collective record. Byte-level scripts bridge the toy to the framework's [8,4,4] cell. Deliberately conditional: a compression certificate, not a proof of polynomial scalability — a maximal abelian record basis still has 2ⁿ sectors, and tractability at scale waits on an unproved "bounded correlation length ⇒ O(poly n) promoted records" termination theorem. It does not replace quantum mechanics or prove the finite-QEC framework; it shows the language of "what can be said, heard, remembered, and reset" has exact operator content.

Keywords

How to cite

Elliman, D. (2026). An Executable Record Grammar for Quantum Correlations: A finite compression certificate for stabilizer records, Wilson holonomy, magic, detector readout, and bounded residuals. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21034326

@techreport{elliman2026recordgrammarcompression,
  author      = {Elliman, David},
  title       = {An Executable Record Grammar for Quantum Correlations: A finite compression certificate for stabilizer records, Wilson holonomy, magic, detector readout, and bounded residuals},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21034326},
  url         = {https://neusym.ai/papers/record_grammar_compression}
}