Can one reading rule account for the structure of the Standard Model? A compatibility map with registered checks

The structure of the Standard Model can be written with known constructions. Gauge fields are transport matrices on lattice links (Wilson). The electroweak model has a Higgs doublet (Glashow, Weinberg, Salam). The charge pattern of one family is that of Pati–Salam and of Furey's number-operator construction. A single light lattice fermion with exact chiral symmetry comes from the Ginsparg–Wilson relation and Neuberger's overlap operator. This record asks whether one reading rule from the author's framework, Mathematical Materiality (MM), gives these pieces a common meaning. It goes from the data to MM: for each piece, the measured fact, the reading, whether they are compatible, the published construction that already does the same, and what would make the reading incompatible. Selected gauge-sector structures and the charge pattern of one family admit a common interpretation under stated additional hypotheses. The checks concern separate constructions, and their joint chiral gauge realisation remains to be established. No mathematical priority is claimed, and the checks provide no experimental discrimination from the Standard Model. Files labelled "registered predictions" were fingerprinted with SHA-256 before their corresponding calculations; subsequent rechecks are identified separately, and predictions not met are reported. The fingerprints were recorded locally and are not publicly time-stamped. (1) Charges. With the rule |Q| = N_shared/3, where N_shared = 1, 2 for colour triplets and 0, 3 for singlets and conjugate states carry opposite charges, the anomaly-free family with a right-handed neutrino admits exactly Y_Q = ±1/6. +1/6 is the Standard Model, and −1/6 is the same content relabelled. The neutrino and the neutron come out neutral. Pati–Salam and SO(10) also fix the charge assignments. (2) Colour and gluons. Three binary readings give an 8-state Fock space; the number-operator spectrum divided by three is 0, 1/3, 2/3, 1, with two conjugate su(3) triplets. A 3×3 transport on the lattice link gives, at the wavevectors tested, 16 complex transverse amplitudes of the static quadratic form (8 × 2), not verified counts of propagating polarisations, and a cubic self-interaction term. The ninth mode is absent under an added det = 1 hypothesis. (3) Electroweak bosons. A U(2) transport of two units on the link, with a Higgs doublet at its vacuum, reproduces selected bosonic identities: a massless photon, massive W and Z with ρ = 1 at tree level, and W charge ±1. These checks use ingredients of the lattice electroweak construction. θ_W and v are taken from the data; the gauge kinetic normalisation and the action on fermions are not constructed. (4) One light hand. A standard overlap operator built with the matrices and parameters of the MM 2.40 checkerboard satisfies the Ginsparg–Wilson relation to 9e-16 and has one light Dirac species, from which a Weyl sector is selected by projection. With constant U(1) fluxes on a 6⁴ lattice its calibrated index equals the topological charge for Q = 0, 1, 2, −1, also with the 2.40 parameters. The light species requires the reading level to lie between the bottom of the valley and the first ridge of the Wilson term (0 < m₀ < 2r); above the top all doublers return and the net chirality cancels. The fermion measure of a chiral gauge theory is not constructed here. Non-perturbative constructions of the electroweak model exist with stated restrictions (Kadoh–Kikukawa 2008). (5) The obstacle on the checkerboard. Every finite product of single-direction steps, periodic on the same torus and with constant coins, has winding W = 0 in U(n), so the 2.40 checkerboard has no isolated hand in the bulk. The 2.40 palindromic Dirac automaton has 64 Dirac valleys (8 per parity sector), not 16 as stated in MM 2.40. (6) Higgs sector and what is not read. Tree-level fermion couplings scaling as m_f/v and W/Z couplings as m_V²/v (photon and gluon couplings are loop-induced), one electroweak scale and the Higgs mass from self-coupling are compatible by structure. Not read: θ_W, v, the fermion masses, the CKM and PMNS mixings, θ̄. No stable SU(2) is obtained from the holonomy of the record transport. A correction is included: the pion ratio Γ(π→eν)/Γ(π→μν) is consistent with the helicity suppression of a V/A amplitude but does not select a hand; the evidence for the left-handed charged current is the muon-decay data (PDG review 57). python codice/run_all.py runs the included numerical programs and compares their outputs with the reference files; the scope, and the intentional truncation of one program, are described in README section 8. Before deposit the author's full run from scratch matched all 18 compared outputs in about 2 hours on a 4-CPU laptop (documenti/COLLAUDO_COMPLETO.txt); --short skips the three long programs and takes about 10 minutes. The author is not a professional physicist; computations were done with AI assistants (Claude and Codex), not reviewed by a human referee.