# Separate agent source and arithmetic audit

20 October 2026. A separate agent checked the submitted family against the frozen
author-copy text and independently enumerated binary-form residue distributions.
This is AI-assisted checking, not a new paid referee-panel assessment or human grade.

The author edition permits the strip root. The initial form is
f1=x^2+2xy+2y^2; its primitive nonnegative vector (n-1,1) gives shifted value n^2.
The Descartes vector (n^2,1,(n+1)^2,0) yields the proposed form coefficients.
Forms are primitive with determinant n^4. Local equivalence changes preserve counts.

The audit independently reproduced the t=1 counts modulo 5,25,125, and checked
2- and 3-adic counts for t=1,2,3. It checked the split 5-adic form, product equation
count, 2-adic bit-flip argument, remaining odd-prime factors and Euler product.
It agreed with the formula 160(2t+1)/(9*pi^2).

Qualification: continued fractions prove membership in the literal displayed
zero-offset intervals, not every alternative subinterval selected by pigeonhole.
The native arXiv source has an older coefficient typo; the author edition corrects it.
The JAMS typesetting remains uninspected. No general repair was checked.