T-241: Couzo's certificate at 304 of Tymchishin's Kaggle notebook packing, 2.53e-3 below T-186

S3 V3 C3 Upper bound confirmed superseded by T-242

2026-10-23 published · Couzo after Tymchishin, Levy · $n=304$$n=304$

One complete rational source certificate reports a finite upper-bound improvement at the exact side it states: $s(304)\le 42654421699169959072564987841514227093543746926117736119087439/2379353056489745832681562849107891444171481219500000000000000$ = 17.92689890339264…, 2.53e-3 below T-186, the case's house best packing when it was reported.

The certificate and its duplicate-square and outside-container controls were decided here on 24 October 2026 by both maintained exact routes. Those routes share components with the producer: the source's manifest names this repository's sqpack/verify.py, through which one route decides, as its first checker, and both routes read the certificate through the evand-cert adapter, two of whose expressions are transcribed from Daniel's checkers, from which the source's verify_bound_certificate.py derives.

The 24 October review of T-241 and T-242 decided it again on a clean-room checker of its own, by separating axes and by clipped areas with twelve controls, by a Claude agent, a system family the producer also used, and found no blocking defect, so the bound is confirmed, independently re-implemented.

It is certificates/best/n304.cert in Couzo's watched repository (https://github.com/franciscouzo/square-packing), committed on 23 October 2026 and made public by the push at 23:38:42Z that also carried the release issue 763 names, by which the record dates it. The issue does not claim this count, and no issue reports it, so it is a report from its publication (the owner, 14 October 2026). The issue-763 packet retains the file byte-identical, and this import reads it from there.

The source's certified_bounds.json records the certificate as verified, 'valid': true, 4297 pairs tested, with 'GMP exact rationals via gmpy2 2.3.2'. Those statements are the author's; no source program ran here. The source's commit that first holds the certificate and the two others of that push each end with a Co-Authored-By trailer naming Claude (M-5).

Credit Tymchishin's packing, as the source credits it: "Tymchishin (kirilltym), Kaggle "CPU Alternating Reclosure" v3; earlier construction credits in its source notices; earlier seed and construction credits retained in provenance", certified by Couzo (https://github.com/franciscouzo/square-packing), who claims no refinement of it.

The provenance that line defers to is the source's witness manifest. Its 304 entry names no seed of the packing: its lineage is the notebook's output alone, and its previous_source and previous_reference name Polkovskyi's #593 certificate, T-186's packing, as the record its catalogue held at 304 before, as those fields do at every count (the 24 October stage 4 review, M-1). So the credit is Tymchishin's packing, certified by Couzo; whether the notebook started from a recorded packing is asked of Couzo in the confirmation reply of 25 October on #763 (its question 7), which awaits his answer.

The manifest also gives Polkovskyi's certificate a construction credit, "Chaoweeraprasit (itsnaka)", where the source's own RECORD_PROVENANCE.md keeps Ostashev's packing credit for Polkovskyi's update at 304 and the record measures that certificate as Ostashev's T-175 packing re-solved (M-3). It describes the record this packing replaced, not this packing; which Couzo intends is asked in the import reply of 25 October on #763 (its question 6), which awaits his answer.

The notebook's own source notices are not published. Daniel's later certificate of the same packing (T-242) calls its finder unknown and its earliest public copy kozykappa's notebook; whether Tymchishin found it is asked of Couzo in that reply (its question 5), which awaits his answer, and a question to Daniel is drafted and unposted (think-hx0e).