Anomaly cancellation from a finite error-correcting code: a Standard-Model compression result

Abstract

Gauge anomaly cancellation is one of the Standard Model's quiet consistency miracles — the quark and lepton charges must make several triangle-diagram traces vanish exactly, or the chiral gauge theory is inconsistent. This note asks whether that cancellation can be compressed into a small discrete rule rather than accepted as a coincidence of measured charges. Within the [8,4,4] finite-QEC cell, four Boolean record rules select exactly the Standard-Model Weyl content; exact-rational scripts then verify that this content cancels all six anomaly conditions, forces three colours (N_c = 3) and colour charge-weight 1/3, and stays CPT-covariant only when the charge readout Q = T₃ + Y is read colour-blindly. Anomaly-freedom is shown to be rare — roughly 0.8% of comparable Boolean contents — not automatic. At the continuum limit the result reduces to the classical Geng–Marshak / Minahan–Ramond–Warner theorem (with a right-handed neutrino, anomaly cancellation fixes the hypercharges); the new contribution is upstream — the special fermion content that theorem needs, including the ν_R, is derived from the finite cell via a (B−L) residual. Deliberately modest: a compression and explanation of known SM structure in the organising spirit of Mendeleev's table, not a new empirical prediction and not a proof of the substrate.

Keywords

How to cite

Elliman, D. (2026). Anomaly cancellation from a finite error-correcting code: a Standard-Model compression result. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.20992785

@techreport{elliman2026anomalycompression,
  author      = {Elliman, David},
  title       = {Anomaly cancellation from a finite error-correcting code: a Standard-Model compression result},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.20992785},
  url         = {https://neusym.ai/papers/anomaly_compression}
}