Two certified sum-of-radii circle packings exceeding the Packomania values listed on 29 September 2026, an exact large-N verifier for the first autocorrelation inequality, and documented negative results

We report (i) certified packings of n=120 and n=250 disjoint circles in the unit square with sums of radii 5.7773030974449 and 8.3899735328377, exceeding the values listed in the Packomania csqv table when downloaded on 29 September 2026 at 21:32 (UTC-6) (5.776999746200 and 8.389775077490; gains 3.03e-4 and 1.98e-4). Both are rigid and structurally different from the listed configurations. The table changes several times a day, so this is a time-stamped comparison, not a claim of best known. (ii) An exact-arithmetic verifier (no floating-point FFT) for the first autocorrelation inequality with up to N=38,400 step-function pieces, and a certified bound of 1.505275 (N=19,200) obtained by partial re-melting of a smooth surrogate; this is NOT a record (later published bounds are 1.50317 and 1.50287). (iii) Documented matched, tied and overtaken cases, a precision artifact (n=27) and float-score overshoot. Every number is certified by an independent verifier in exact rational and 60-digit arithmetic. AI use: the software implementation, automated testing, experiment execution and a first draft of the documentation were produced with Claude Code using Claude Sonnet 5.5 (Anthropic), under the author's direction. The author defined the goals, reviewed the results and the manuscript, and takes full responsibility for the content. Packomania tables and coordinate files are not redistributed.