Matter, Gauge Structure, and Spectroscopy in the Finite-QEC Substrate

Abstract

The matter-sector companion. Collects the finite-code results that produce Standard-Model-like matter bookkeeping, the gauge-structure results that survive current audits, and the spectroscopy results that remain load-bearing after the numerical-search and retraction tests. The central message is deliberately split. The strongest results are exact finite identities: charge bookkeeping, anomaly cancellation, the separation of spatial, colour, generation, and repair-axis roles, and the recovered chiral charge-cube identity ∑Q_L³ = −2/9. The continuum and dynamical results are more mixed but have sharpened: the chiral/mirror-gapping continuum problem is now rigorously reduced to ordinary SU(3) confinement (a standard pure-gauge lattice fact rather than a framework-specific gap); the electroweak/top scale, once an unexplained second anchor, is now a ~10% radiative prediction v/M_P = α₀⁸/√λ with a forced near-critical quartic λ(M_P) = 0; the W/Z sector is a pole-precision map in which the live 2/9 is a post-EWSB LSZ endpoint quotient (the old UV Weinberg-angle 2/9 is retired to a 3/8 charge trace) and α(M_Z) is simply dressed α(0) run up to M_Z; and the neutrino texture yields a sharp near-maximal second-octant prediction θ23 ≈ 45.9°. Spectroscopy still contains several robust anchors, but mass-ratio numerology is actively demoted unless the observable map is unique. The goal is not to declare the matter sector closed, but to state which parts are exact finite arithmetic, which are reproducible computations, and which remain continuum-lift or operator-definition frontiers.

Keywords

How to cite

Elliman, D. (2026). Matter, Gauge Structure, and Spectroscopy in the Finite-QEC Substrate. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21111282

@techreport{elliman2026mattergauge,
  author      = {Elliman, David},
  title       = {Matter, Gauge Structure, and Spectroscopy in the Finite-QEC Substrate},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21111282},
  url         = {https://neusym.ai/papers/matter_gauge}
}