The Standard Model as a Certified Attribute Grammar: Feynman rules as compiler phases on an [8,4,4] record alphabet

Abstract

Reads the Standard Model as a formal language: its interaction vertices become a typed rewriting grammar over a sixteen-letter matter alphabet — the sixteen codewords of the [8,4,4] = RM(1,3) Hamming/Reed–Muller code, identified with the sixteen Weyl fermions of one generation (one 16 of SO(10)). Interactions are typed productions w → w′ + response: two neutral read channels (γ, Z), a chirality-typed flip (W±), a colour rotation (g), a left–right Yukawa bridge, a ΔL=2 Majorana portal, and the gauge/scalar self-productions; conservation laws act as a static type system, and parity violation is a typing rule rather than a dynamical add-on. Two exact-arithmetic machine certificates back it: (i) the grammar compiles exactly the SM tree-level vertex set — none missing, none spurious — with right-handed-neutrino sterility emerging as a derived typing fact (the unique letter read by neither neutral channel); and (ii) the alphabet is anomaly-free, the U(1)³, grav²·U(1), SU(2)²·U(1) and SU(3)²·U(1) sums vanishing identically over the sixteen letters. The certified claim is deliberately precise: not that the labels resemble the SM, but that the record alphabet can support a consistent chiral gauge theory and the Standard Model sits naturally inside it. The paper then locates the grammar in the Chomsky hierarchy — planar tree-level diagrams are context-free (planar Wick contractions are the Dyck language), simultaneous conservation laws are multicounter constraints, non-planar contractions realise the crossed serial dependencies by which natural language exceeds context-freeness, and loops require graph rewriting, so the tree/loop boundary of QFT coincides with the tree/graph boundary of rewriting theory; as a corollary, 't Hooft's planar large-N limit is exactly the context-free fragment, making the 1/N expansion an expansion in grammatical complexity. Structural falsifiers it stakes: no right-handed charged currents, no fourth sequential generation, no tree-level γγγ, and a Majorana-only route to leptonic CP violation.

Keywords

How to cite

Elliman, D. (2026). The Standard Model as a Certified Attribute Grammar: Feynman rules as compiler phases on an [8,4,4] record alphabet. Neuro-Symbolic Ltd technical report. https://doi.org/10.5281/zenodo.21182033

@techreport{elliman2026quantumgrammar,
  author      = {Elliman, David},
  title       = {The Standard Model as a Certified Attribute Grammar: Feynman rules as compiler phases on an [8,4,4] record alphabet},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.5281/zenodo.21182033},
  url         = {https://neusym.ai/papers/quantum_grammar}
}