154-382: registration request

I’m submitting nine improved certified upper bounds. This request leaves out the counts covered by #561.

Displayed sides are rounded upward to 12 decimal places from the exact rational certificate headers. Improvements are calculated before rounding.

n / certificate	New certified upper bound	Comparison bound	Improvement	Comparison source
154	12.922499814643	12.922566401935	6.65873e-05	Evan Daniel
211	14.993558914123	14.993694186584	0.000135272	Daniil Ostashev
241	15.987117095169	15.987134249051	1.71539e-05	Daniil Ostashev
302	17.870013850405	17.870275382734	0.000261532	BuddenPing
339	18.927383638495	18.929433883808	0.00205025	My #506 certificate
379	19.953531531603	19.953572709539	4.11779e-05	My #506 certificate
380	19.973553606628	19.976775433975	0.00322183	Kevin Fang (TheSnakeFang)
381	19.974977397657	19.976969740406	0.00199234	Kevin Fang (TheSnakeFang)
382	19.988600568289	19.989479729400	0.000879161	Kevin Fang (TheSnakeFang)

For n=339 and n=379, the comparisons use my certificates previously submitted in #506. Counts above 324 are submitted for the beyond-horizon list. These comparisons use published certificates, rather than the frozen construction baseline.

All new certificates are pinned to commit 45966700cf15d3f42e064fd6da51fcb9a5def2be in franciscouzo/square-packing. Each contains an exact rational container side and exactly n rational triples (x, y, t), with t = tan(theta/2), representing unit squares inside the open container. Matching metadata files contain the full certificate hashes and seed provenance.

The certificates for n=154, 302, 379 and 381 were produced with Evan Daniel’s exact contact solver. The remaining certificates are rational witnesses from the decimal poses, with centre dilation 1+1e-11 for n=211 and 339, 1+1e-12 for n=241, and 1+1e-10 for n=380 and 382.

All nine certificates passed both jlevy/squares’ checker and Evan Daniel’s checker, using exact rational arithmetic.

The checkers share 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 through my browser app using fq, then exact finishing. His arrangement descends from my earlier n=155 packing with one square removed.
211 and 241: continued Daniil Ostashev’s arrangements with native search and refinement.
302: continued BuddenPing’s arrangement with native basin hopping and refinement.
339 and 379: continued my L-border constructions reported in 304, 305 and nine counts above 324 (338–381): registration request #506. The latest n=339 improvement came from the browser’s Ellsworth search; n=379 also continued through browser and native refinement.
380–382: continued Kevin Fang’s published arrangements through browser and native searches. Please retain his construction credit.

Evan Daniel’s optimizer, contact solver and verifier, David Ellsworth’s search/refinement ideas, and the upstream sqpack.verify checker were used in this work.

The search implementation, verification orchestration and issue preparation used OpenAI Codex. Earlier search work also used Claude Code. I directed the work.

@franciscouzo

Thanks, @franciscouzo. The acknowledgement for #561, #570, #583 and #586 is one reply, on #586.

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 and replay Couzo's #583 certificates at 4596670 that #586

@franciscouzo

@franciscouzo, thank you; this is the report-order evaluation of every open report at the counts #583 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.

n	Side	Verdict	Best now
154	12.922499814643	not recorded: equal to #570 (Francisco Couzo), reported first	#586 (Francisco Couzo) 12.921206577133
211	14.993558914123	recorded: a new packing, continuing Daniil Ostashev's arrangement (#575); 1.35e-04 below #575 (Daniil Ostashev)	#586 (Francisco Couzo) 14.993558913975
241	15.987117095169	recorded: a new packing, continuing Daniil Ostashev's arrangement (#575); 1.72e-05 below #575 (Daniil Ostashev)	#586 (Francisco Couzo) 15.987117095151
302	17.870013850405	recorded: a new packing, continuing PingYou Ltd's arrangement (#564); at least 2.62e-04 below PR #574 (PingYou Ltd)	this report 17.870013850405
339	18.927383638495	recorded: a new packing, continuing the author's own L-border construction (#506); at least 2.05e-03 below the row on main from #506	#586 (Francisco Couzo) 18.925319360704
379	19.953531531603	recorded: a new packing, continuing the author's own L-border construction (#506); at least 1.11e-05 below #570 (Francisco Couzo)	#586 (Francisco Couzo) 19.953531362123
380	19.973553606628	recorded: a new packing, continuing Kevin Fang's published arrangement (TheSnakeFang/squarepack-certs); 3.22e-03 below Kevin Fang's publication `TheSnakeFang/squarepack-certs@e646c47`	#586 (Francisco Couzo) 19.961611078672
381	19.974977397657	recorded: a new packing, continuing Kevin Fang's published arrangement (TheSnakeFang/squarepack-certs); 1.99e-03 below Kevin Fang's publication `TheSnakeFang/squarepack-certs@e646c47`	this report 19.974977397657
382	19.988600568289	recorded: a new packing, continuing Kevin Fang's published arrangement (TheSnakeFang/squarepack-certs); 8.79e-04 below Kevin Fang's publication `TheSnakeFang/squarepack-certs@c284cd0`	#586 (Francisco Couzo) 19.987713157610

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…

@franciscouzo

@franciscouzo, thank you. With #602 merged, this issue's certificates are registered on main:

T-181, V0/C0, significance S3, recorded: your certificates at 211, 241 and 302, credited Couzo after Daniel, Ostashev, Fang, Ellsworth, Levy and, for the 302 retained from 154, 339, 379, 380, 382; precision refinements at 211 and 241: registration request #586's pin, Couzo after Daniel, Ostashev, BuddenPing, Fang, Ellsworth, Levy. Both of our exact routes replayed them; an independent review of that replay comes next, then adoption on the case pages. At 302 it is the smallest side recorded; at 211 and 241 your 154, 339, 379, 380, 382; precision refinements at 211 and 241: registration request #586 (T-182) tightens it.
154 is the same certificate as 154 and 379: registration request #570's, byte for byte, so it is registered once, as T-172 (V0/C0, significance S2, recorded).
339, 379, 380, 381 and 382 are rows beyond the n ≤ 324 case corpus, which take no register entry. 381 is the current row; 154, 339, 379, 380, 382; precision refinements at 211 and 241: registration request #586 supersedes the other four.

Evidence: E-couzo-583-certificate-report (your report, recorded). On main: RESULTS.md, the packet.

Generated by Claude Code

requests: record #602's post-merge follow-ups and the 14 October verd…

houses: what the 15 October pass moves outside the writer's own files

intake: retain and replay PingYou Ltd's seven certificates of 12 October

intake: retain and replay Francisco Couzo's jlevy#561 certificates at…

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…

@franciscouzo

@franciscouzo, thank you. Where this request stands in the record on main.

Corrections to earlier replies.

The follow-up reply of 2026-10-14 gave T-181 as V0/C0, recorded; it now reads V3/C3, confirmed.
The follow-up reply of 2026-10-14 gave E-couzo-583-certificate-report as recorded; it now reads reviewed.
The follow-up reply of 2026-10-14 gave T-172 as V0/C0, recorded; it now reads V3/C3, confirmed.

What is registered.

s(211) <= 14.993558914123, s(241) <= 15.987117095169 and s(302) <= 17.870013850405, by exact rational certificates:
- T-181, confirmed at V3/C3: re-verified here by an independent implementation (sqpack.verify, run by each case's verify_exact module and the packing-witness command, devtools.check_rational_witness_independent, devtools.evand_arrangement_reports, devtools.upper_bound_reports, devtools.check_half_angle_area, devtools.evand_exact_certificates).
s(154) <= 12.922499814643, the certificate issue 570 names:
- T-172, confirmed at V3/C3 by the same routes, and superseded by your 154, 339, 379, 380, 382; precision refinements at 211 and 241: registration request #586 certificate (T-182).

On the case pages. Our reply of 14 October said adoption would follow the review. On 15 October 2026 T-181 became the house at 302, 2.02e-3 below the packing it replaces (Nate Chaoweeraprasit's, improved by Evan Daniel, T-146), which stays retained as history. At 154, 211 and 241 the house is your #586 certificate (T-182); T-172 and T-181 stay verified there and are not selected.

Smaller certificates that are not adopted: Mykhailo Polkovskyi's of 14 October (T-186, V0/C0) at 154 and 302, and, since #627 merged, your 487b058 certificate at 211 (T-188, V0/C0), 9.29e-6 below T-182.

Beyond the case corpus. 339, 379, 380, 381 and 382 are rows beyond the n ≤ 324 corpus, which take no register entry. All five are now superseded. Four were superseded on 14 October: at 339 by Evan Daniel's #584 composition and then your #586 certificate, and at 379, 380 and 382 by your #586 certificates. The row at 381 was current until #627 merged, when your 487b058 certificate superseded it. The current rows are your 487b058 certificates at 379, 380 and 381 and your #607 certificates at 339 and 382.

Edited: an earlier version of this comment dated all five supersessions to #627; only the row at 381 was superseded then, and the other four on 14 October.

On main. packing/frontier/RESULTS.md, docs/project/reviews/review-2026-10-14-upper-bound-imports-561-593.md, packing/frontier/n-211.md, packing/frontier/n-241.md, packing/frontier/n-302.md, packing/frontier/n-154.md.

Nothing you asked for is queued, so this issue is closed with this comment.

Generated by Claude Code

records: address review A of #637 (the #596 reply, corrected superses…

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154-382: registration request #583

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jlevy commented on Oct 14, 2026

jlevy commented on Oct 14, 2026

jlevy commented on Oct 14, 2026

jlevy commented on Oct 16, 2026

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