# User-supplied argument: frozen mathematical summary

Received 20 October 2026 from Igor Rivin. This is a curated summary of the submitted
Web GPT Pro response, not a verbatim transcript or an independently returned native
referee assessment. The Web model identity is unverified.

Proposed counterexample: fixed strip packing (0,0,1,1), initial curvature 1,
n=5^t, a=n^2, a'=4n^2; use f_a=(n^2+1)x^2-2nxy+n^2y^2 and the same form with 2n.
The response claimed sigma5=(4/5)(2t+1), sigma2=2, sigma3=32/27,
sigma_p=1-p^(-2) at all other primes, giving S=160(2t+1)/(9*pi^2),
whereas the Lemma 3.6 right-hand expression is 4.

It supplied exact counts 225,40625,4687500 at moduli 5,25,125 for t=1;
a continued-fraction argument for the displayed dyadic short intervals;
and a suggested replacement common-divisor weight tau(gcd(a,a')^2).
It inspected only the author-hosted edition, not the JAMS typesetting.

Checking disposition: the accompanying report adopts the explicit-family calculation
with an additional qualification about alternative pigeonhole-selected intervals.
The general repair bound, later-paper application and correction-history claims
are not adopted without further audit.