Exhaustive order-resolved coarse-graining diagnostics for finite-group lattice gauge models: a corrected Q8-Z2 comparison

A dated freeze of a finite-group lattice gauge diagnostic and its full correction trail. In May 2026 an order-resolved Mobius decomposition of blocked effective actions showed Q8 higher-body coefficients 3 to 6 orders of magnitude below Z2 at equal raw coupling, initially interpreted as a non-Abelian suppression effect. An August 2026 forensic audit reproduced the tabulated values through a separately implemented dense-NumPy contraction backend and then retired the interpretation. The scale of the apparent gap is primarily explained by comparing groups with very different single-plaquette activity at equal raw beta. Matching on A_1 reduces the higher-body differences to factors of approximately 1.3 to 15 over the tested grid; matching on A_2 brings A_3 to within 6 to 24 percent of the matched Z2 value. The record preserves the May state unaltered alongside the audit, matched-comparison tables, corrected register, source code, numerical outputs, and a SHA-256 provenance manifest distinguishing contemporaneous May artefacts from August regenerations. Group-state sums are evaluated by exhaustive deterministic contraction rather than sampling or fitting; numerical weights, contractions, logarithms, and Mobius coefficients use double-precision floating-point arithmetic.