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154, 339, 379, 380, 382; precision refinements at 211 and 241: registration request #586
Description
This updates #583 with five continued-search improvements and two tighter certificates. The unchanged n=302 and n=381 packings and the counts covered by #561 are omitted.
Displayed bounds are rounded upward to 12 decimal places from the exact rational certificate headers. Improvements are computed before rounding.
| n / certificate | New certified upper bound | Comparison bound | Improvement | Comparison |
|---|---|---|---|---|
| 154 | 12.921206577133 | 12.922499814643 | 0.00129324 | #583 |
| 339 | 18.925319360704 | 18.926898900357 | 0.00157954 | Evan Daniel |
| 379 | 19.953531362123 | 19.953531531603 | 1.6948e-07 | #583 |
| 380 | 19.961611078672 | 19.973553606628 | 0.0119425 | #583 |
| 382 | 19.987713157610 | 19.988600568289 | 0.000887411 | #583 |
For n=339, the comparison uses Evan Daniel’s stronger published certificate, rather than my larger bound in #583. Counts above 324 are submitted for the beyond-horizon list.
The following are certificate precision refinements of the n=211 and n=241 arrangements already submitted in #583:
| n / certificate | New certified upper bound | Certificate in #583 | Improvement |
|---|---|---|---|
| 211 | 14.993558913975 | 14.993558914123 | 1.48631e-10 |
| 241 | 15.987117095151 | 15.987117095169 | 1.87519e-11 |
All seven certificates are pinned to b85dee2b964e7f7fb9f765227e60c44cdcd3aa4d in franciscouzo/square-packing. Each contains an exact rational container side followed by exactly n rational triples (x, y, t), with t = tan(theta/2). The certificate headers are authoritative; matching nN.json files retain full SHA-256 hashes and seed provenance.
The certificates for n=154, 211 and 241 were produced with Evan Daniel’s exact contact solver. The others are rational witnesses with centre dilation 1+1e-11 for n=339 and 1+1e-12 for n=379, 380 and 382.
All seven passed both jlevy/squares’ checker and Evan Daniel’s checker in exact rational arithmetic.
Both checkers use rational half-angle rotations and separating-axis geometry. These certificates establish finite packing feasibility; no local or global optimality proof or independent human review is claimed.
Lineage and credit:
- 154: continued Evan Daniel’s arrangement from #552, descended from my earlier n=155 packing, through browser refinement, native basin hopping and exact finishing.
- 211 and 241: retain Daniil Ostashev’s construction credit; these tighter certificates continue the refinements reported in 154-382: registration request #583.
- 339 and 379: continue my L-border constructions from #506. The latest n=339 improvement used the browser’s
fqsearch; n=379 used native SLP refinement. - 380 and 382: further browser
fqrefinements of Kevin Fang’s arrangements, retaining the construction credit from 154-382: registration request #583.
Evan Daniel’s optimizer, contact solver and verifier, David Ellsworth’s search/refinement ideas, and the upstream sqpack.verify checker were used.
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
@franciscouzo, thank you for #561, #570, #583 and #586. This reply covers all four.
Pins. We retained the certificates at the commits the issues pin: 0fa0e0de for #561 (nine certificates), and b85dee2b for #583 and #586 (14 certificates, the head of your repository when we read it). GitHub does not serve #570's commit 1b31bc90. Its 154 certificate has the same digest as the one #583 pins, so we read #570's 154 through #583, and #586 replaces #570's 379.
Replay. Every retained certificate was replayed on both of this repository's exact checkers: the sqpack exact witness verifier and the independent rational corner checker. All 23 certificates passed on both. For each one, a duplicate-square control and an outside-container control were refused by both checkers. That is 69 jobs, and re-running every job reproduced its recorded outcome.
Comparison with the current register entry at each count (sides rounded up at 12 places; for counts above 324, the register entry is the row tracked from your #506 certificates):
Certificates no issue names. b85dee2b also holds certificates at 176, 344, 375, 376 and 378 that are newer than the ones #561 names. We retained, replayed and compared them too, and all five passed both checkers:
We will register only the certificates the issues name unless you ask otherwise. Would you like these five registered in place of #561's at those counts?
Registration is the next step. We will reply here when it lands, and we will keep the construction credits you list for each count.
Generated by Claude Code
intake: retain and replay Ostashev's #562 and #575 and Evan Daniel's #…
intake: retain Kevin Fang's direct certificates at 078789a and replay…
intake: retain Kevin Fang's direct certificates at 078789a and replay…
intake: retain and replay Couzo's #583 certificates at 4596670 that #586
requests: record the 14 October replies and entries; read evand to 62…
franciscouzo commentedon Oct 14, 2026
Hi @jlevy, please import all certificates
jlevy commentedon Oct 14, 2026
@franciscouzo, thank you; this is the report-order evaluation of every open report at the counts #586 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.
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
intake: retain and replay Ostashev's #562 and #575 and Evan Daniel's #…
intake: retain Kevin Fang's direct certificates at 078789a and replay…
jlevy commentedon Oct 14, 2026
@franciscouzo, thank you. With #602 merged, every certificate at b85dee2 is on
main, which answers your request to import them all:Both of our exact routes replayed every one of these certificates; an independent review of that replay comes next, then adoption on the case pages. This corrects our reply of 14 October, which said only the certificates the issues name would be registered unless you asked. At 211 and 241, Mykhailo Polkovskyi's #593 states the same exact sides; whether to record that tie is with the owner.
Evidence:
E-couzo-583-586-certificate-report(your report, recorded). Onmain: RESULTS.md, the packet.Generated by Claude Code
requests: record #602's post-merge follow-ups and the 14 October verd…
reads-1015: retain Francisco Couzo's 487b058 index: s(211) replayed, …
intake: retain and replay Francisco Couzo's jlevy#561 certificates at…
intake: retain and replay Mishapolk's jlevy#573 and jlevy#593 certifi…
intake: retain and replay Ostashev's jlevy#562 and jlevy#575 and Evan…
merge: the Couzo intake lane of 14 October (jlevy#561, jlevy#570, jle…
records: restate T-188 to T-190 against #614's houses, with their lin…
test(upper_bound_reports): hold the three Couzo records to #614's houses
jlevy commentedon Oct 16, 2026
@franciscouzo, thank you. Where this request stands in the record on
main.Corrections to earlier replies.
What is registered.
On the case pages. Our reply of 14 October said adoption would follow the review. On 15 October 2026 T-182 became the house at 154, 211 and 241, and T-165 at 176; the packings they replace (Evan Daniel's T-160 at 154, Daniil Ostashev's T-149 at 211, your packing improved by Evan Daniel (T-098) at 241, and Nate Chaoweeraprasit's T-151 at 176) stay retained as history.
Smaller certificates that are not adopted: Mykhailo Polkovskyi's of 14 October (T-186, V0/C0) at 154 and 176; at 176, PR #574's (T-174), whose houses are held for the owner; and, since #627 merged, your
487b058certificate at 211 (T-188, V0/C0), 9.29e-6 below T-182, a refinement of this packing.Beyond the case corpus. 339, 379, 380 and 382, and the same commit's 344, 375, 376 and 378, are rows beyond the n ≤ 324 corpus, which take no register entry. 344 and 376 are still the current rows. Later reports supersede the others: Evan Daniel's #584 composition at 375, and since #627 your
487b058certificates at 378, 379 and 380, and #607's at 339 and 382. The row at 376 lies above Göbel's classical construction, 10 + 7√2, by 4.57e-3, a question for the owner on #613.On
main.packing/frontier/RESULTS.md,docs/project/reviews/review-2026-10-14-upper-bound-imports-561-593.md,packing/frontier/n-154.md,packing/frontier/n-211.md,packing/frontier/n-241.md,packing/frontier/n-176.md.Nothing you asked for is queued, so this issue is closed with this comment.
Generated by Claude Code
houses: adopt the 16 October review at 129, 146, 154, 156, 175, 176, …
requests: review A of #696, the 19 and 20 October reply records say w…
houses: adopt Evan Daniel's certificates at 154 and 308 and regulariz…