Foundations and Methodology for a Finite-QEC Substrate: Code, Crystallisation, Ledgers, and Audit Protocol

Abstract

States the foundational objects and audit methodology behind the program. The physics is presented not as a continuum field theory with a hidden discretization, but as a finite register system whose ordered crystalline phase supplies the visible substrate and whose correction, strain, and boundary ledgers determine which quantities become physical observables. Since the first version the foundation has sharpened: the eight-bit cell is no longer an assumed starting object — under explicit stable-record hypotheses (binary local records, commuting CSS read/write, balanced self-duality, doubly-even closure, distance-4 erasure protection) the unique minimal cell is forced to be the self-dual doubly-even [8,4,4] code, and the bare service rate α₀ = 1/137 is derived from the symmetric record-pair alphabet (Sym²(16) = 136, plus the idle channel). It also introduces the bi-cubic crystallisation picture, the distinction between syndrome and strain readouts, the 28 = 2×14 service-clock construction, and the rules that classify every claim as locked, computed, conditional, retired, or open — with the dressed-α value now a bounded conditional Maxwell-contact candidate — a finite local subtraction 2ΣQ² − 1 = 31 giving α⁻¹ = 137.036, still awaiting the endpoint-covariance → F² normal-ordering theorem, not yet a locked QED prediction. The goal is to make the later physics papers auditable: every coefficient must name its carrier, event unit, scheduler, observable map, and reproducibility check. The methodology's own kill condition is concrete — a companion-paper coefficient that cannot exhibit this ledger is, by the standard set here, not canon.

Keywords

How to cite

Elliman, D. (2026). Foundations and Methodology for a Finite-QEC Substrate: Code, Crystallisation, Ledgers, and Audit Protocol. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21111257

@techreport{elliman2026foundations,
  author      = {Elliman, David},
  title       = {Foundations and Methodology for a Finite-QEC Substrate: Code, Crystallisation, Ledgers, and Audit Protocol},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21111257},
  url         = {https://neusym.ai/papers/foundations}
}