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154 and 379: registration request #570
Description
I’m submitting two improved certified upper bounds. Displayed sides are rounded upward to 12 decimal places from the exact rational certificate headers; improvements are calculated before rounding.
| n | New certified upper bound | Comparison bound | Improvement | Certificate |
|---|---|---|---|---|
| 154 | 12.922499814643 | 12.922566401935 (#552) | 6.658729 × 10⁻⁵ | n154.cert |
| 379 | 19.953542593650 | 19.953572709539 (#506) | 3.011589 × 10⁻⁵ | n379.cert |
For n=379, this updates my earlier submission to the beyond-horizon list in #506.
Both certificates are pinned to commit 1b31bc907d2d881c6962739b6b40cd10b1cd5a9c in franciscouzo/square-packing. They contain rational centres and rational t = tan(θ/2), representing exact unit squares inside the open container. Both were produced with Evan Daniel’s exact contact solver.
Certificate SHA-256 hashes:
n154.cert 5335cb3b7028f3a51e0206bed29b1cca8f56a68f138ed40b5026862788563e69
n379.cert ac463682e035b67266445d0080850cc56b709e348e82b686fd43ac553fa2b3ef
Both passed exact rational verification using jlevy/squares’ checker and Evan Daniel’s checker.
The checkers share rational half-angle rotations and separating-axis geometry. These certificates prove packing feasibility; no local or global optimality proof is claimed.
Lineage and credit:
- 154: continued Evan Daniel’s arrangement from New packing: s(154) ≤ 12.92256640193406: registration request #552 through my browser app using
fq, then exact finishing. Evan traced that arrangement to my earlier n=155 packing with one square removed. Please retain his construction and refinement credit. - 379: continued my L-border construction reported in 304, 305 and nine counts above 324 (338–381): registration request #506, originally derived from n=342, using basin hopping and refinement.
The search implementation, verification orchestration, and issue preparation used OpenAI Codex. Earlier search work also used Claude Code. I directed the work.
Activity
jlevy commentedon Oct 14, 2026
Thanks, @franciscouzo. The acknowledgement for #561, #570, #583 and #586 is one reply, on #586.
Generated by Claude Code
intake: retain and replay Couzo's #583 certificates at 4596670 that #586
requests: record the 14 October replies and entries; read evand to 62…
jlevy commentedon Oct 14, 2026
@franciscouzo, thank you; this is the report-order evaluation of every open report at the counts #570 claims.
At each count, a report is recorded when its side is decidably below every side reported before it (and below the record on main); a tie stays with the earlier report. Sides are rounded up at 12 places.
Two notes on where the evidence lives. #570's pin 1b31bc907d2d881c6962739b6b40cd10b1cd5a9c is no longer served by GitHub. At 379, the certificate #570 names (SHA-256 beginning ac463682) is in no reachable commit of franciscouzo/square-packing, so its side is evaluated as reported. If that certificate is still available, a commit or attachment carrying it would let the record retain it.
Edited 14 October, after the records merged: the record on main has no row for #570 at 379, because the certificate #570 names is in no reachable commit; the report-order verdict above is the ledger's and is unchanged. A commit or attachment carrying that certificate would let the record retain it.
The registrations are in the records pull request #602, and a follow-up with the result ids and rungs will come once it is on main.
Generated by Claude Code
jlevy commentedon Oct 14, 2026
@franciscouzo, thank you. With #602 merged, this issue's 154 is registered on
main:main. The evaluation above records the side this issue prints, but the certificate is in no reachable commit, so nothing is retained; the row at 379 is your 154, 339, 379, 380, 382; precision refinements at 211 and 241: registration request #586 certificate. Whether a printed side with no retained certificate gets a row is with the owner.Evidence:
E-couzo-583-certificate-report(the #583 report, recorded). Onmain: RESULTS.md, the packet.Generated by Claude Code
requests: record #602's post-merge follow-ups and the 14 October verd…
intake: retain and replay Francisco Couzo's jlevy#561 certificates at…
merge: the Couzo intake lane of 14 October (jlevy#561, jlevy#570, jle…
records: address review A of #637 (the #596 reply, corrected superses…
records: the four issues' requests; the replies after #718 and #643's…
requests: the replies after #722 (#719, #686, #715, #678, #670)
feat(intake): the owner's hold on an issue, a close GitHub already sh…
fix(intake): a hold for the owner states its basis and beads; intake_…
records: stage 7 replies and closes of 23 October