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s(130) ≤ 11.902430646: registration request #843
Description
Credit name. Francisco Couzo (franciscouzo/square-packing).
Claim. s(130) ≤ 11.902430645985, the certificate's exact rational side rounded up at 12 places:
466915711841738962256077475351530705109199164124122993/39228601764570445403995003040207131754000000000000000
The register's reported upper bound at 130 is 11.904483032516 (the PR #574 certificate: found by Nate Chaoweeraprasit (itsnaka), improved by Siddharth Gupta and PingYou Ltd), so this improves it by 2.05·10⁻³. Global optimality is not claimed.
Certificate. franciscouzo/square-packing@3a4d95c (full id 3a4d95c72083da3c3fd5acc4b1d0e94479c5422d):
| file | SHA-256 |
|---|---|
certificates/n130.cert (same bytes as certificates/best/n130.cert) |
a2618e1a7a2961cf63bf5a23ac0b006d18ef0dde00dad562b005d82a509c7fcd |
n130.txt (the float packing) |
6d4121d429165db50532a8ee5b1d0a20f9d49df5e9be51c614b1464e37708099 |
Format: a header line n S, then one line x y t per square (centre, and t = tan(θ/2)), all exact rationals. Credits and provenance are in certificates/n130.json.
Checking. Both of the repository's exact checkers accept it, in exact rational arithmetic:
| checker | command | result | time |
|---|---|---|---|
verify_bound_certificate.py (separating axes, projection test) |
python3 verify_bound_certificate.py certificates/n130.cert |
valid and strictly valid (positive wall and pair margins); 1,624 candidate pairs, 280 near pairs | 0.1 s |
exact_finish.py (exact corner replay) |
python3 -c "from pathlib import Path; from exact_finish import exact_replay; print(exact_replay(Path('certificates/n130.cert')))" |
valid; 1,624 pairs tested | 0.3 s |
What the checkers share. Both are this repository's code and read the same certificate format; their geometry tests differ.
Not done. No exact KKT solve, rigidity or local-optimality analysis. Only the upper bound is claimed.
Lineage and credit. The packing was found from the registered PR #574 packing by this project's live searches of 24–25 October. Thirteen successive improvements took the side from 11.904483032516 to 11.902430645985: ten by the web app's fq quench, two by its basin hopping and one by the native SLP refinement, each starting from the previous best. All of them ran on my own computers.
Matched one to one against the PR #574 packing (optimal assignment on centres, best of the eight square symmetries):
- the largest move is 0.704;
- 11 squares move more than 0.1, and 26 more than 0.01;
- 35 squares are tilted, against 32 before.
By your convention that makes it a new packing found from #574's, not a refinement. Please credit it to Francisco Couzo, after the starting packing's credits (Nate Chaoweeraprasit (itsnaka); Siddharth Gupta; PingYou Ltd).
For information: Kaggle's staff per-puzzle leaderboard (run 362304873, coordinates not public) shows 11.902430646006 at 130 for the team Cats and boxes, submitted 24 October 17:28 UTC. That is 2.2·10⁻¹¹ above this certificate.
AI assistance. Yes. The searches ran on my computers under my direction. The certification, the comparison with the register and this report were done by Claude (Anthropic), working in Claude Code at my direction.
Activity
intake(#843-#846, #824 update): replay receipts, identity measurement…
intake(#843-#846, #824 update): register T-252 to T-258 at V0/C0, pac…
intake(#843-#846, #824 update): render the views, verdict comments, #846
intake(#843-#846, #824 update): site URLs, document map, verifiers vi…
intake(#843-#846, #824 update): sharp controls at every count, packet…
intake(#843-#846, #824 update): synopsis status row, verdict drafts n…
intake(#843-#846, #824 update): credits name the project where the so…
records: map the five stage 4 reviews of #852; T-260 split from T-259
Merge origin/main 49dac43 (#849, #850, #853, #854, #855) into the int…
Merge origin/main a8deaf1 (#851, #817) into the intake of #843 to #846
Merge pull request #852 from jlevy/claude/bold-ritchie-xo28us-upper
jlevy commentedon Oct 31, 2026
@franciscouzo, thank you; this is the report-order evaluation of every open report at the counts #843 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.
Your 130 was below everything reported before it, so it is recorded, a new packing found from PR #574's. Mykhailo Polkovskyi's #846, two days later, is your packing re-solved and then dilated by 2e-14, 2.08e-12 below your certificate's side; the ledger records it as a refinement of your packing, which keeps your credit.
The registrations are in the records pull request #852, and a follow-up with the result ids and rungs will come once it is on main.
Generated by Claude Code
jlevy commentedon Oct 31, 2026
@franciscouzo, thank you for #843. Your s(130) certificate is imported and reviewed, and the case at 130 carries your packing. The report-order verdict is in the comment above; this is where the record on
mainstands.Confirmed.
certificates/n130.certat 3a4d95c proves s(130) ≤ 466915711841738962256077475351530705109199164124122993/39228601764570445403995003040207131754000000000000000 = 11.90243064598434…, and your print 11.902430645985 rounds it up. T-254 is confirmed at V3/C3. Two kinds of check re-verified it. This repository's two maintained exact routes share components with your generator:sqpack.verify, run by the case'sverify_exactmodule and the packing-witness command, anddevtools.check_rational_witness_independent, throughdevtools.upper_bound_reports. The stage 4 review (review-2026-10-31-couzo-843-130.md) is an independent implementation:check_certs.py, a clean-room checker that uses two methods. Your own code was not re-run. The review's checker is a Claude agent's, and your certification used Claude too.Your packing is the house at 130. Mykhailo Polkovskyi's New packings: 14 verified upper bounds for square packing (Category A records and Category B refinements, N in [105, 308]): registration request #846 is your packing re-solved and dilated by 2e-14, 2.08e-12 lower; 14 squares move, by up to 1.13e-6. The house rule adopts the smallest validated certificate, so the case at 130 carries New packings: 14 verified upper bounds for square packing (Category A records and Category B refinements, N in [105, 308]): registration request #846's certificate (T-259, V3/C3). The packing is credited to you, found from PR research: submit 148 square-packing certificate refinements with exact endpoints #574's. On the frontier, T-254 is therefore superseded by that later result.
Lineage, measured. Against research: submit 148 square-packing certificate refinements with exact endpoints #574's packing:
The record keeps your word: a new packing found from research: submit 148 square-packing certificate refinements with exact endpoints #574's.
Evidence entries.
E-couzo-843-certificate-report, your certificate as reported, is reviewed.E-couzo-843-exact-feasibility, the maintained routes' replay, andE-couzo-843-review-exact-feasibility, the review's checker, are confirmed.On
mainand the site.packing/frontier/RESULTS.mdpacking/frontier/n-130.mdThe review left three questions. An answer to any of them is welcome, but none holds this issue open:
certificates/n130.jsonand manifest say the packing "refines" PR research: submit 148 square-packing certificate refinements with exact endpoints #574's, while the issue calls it a new packing. Which should the record say?Nothing you asked for is queued, so this issue is closed with this comment.
Generated by Claude Code
requests(#860, review A): T-259 names no finished owner; the confirme…
Merge pull request #860 from jlevy/claude/bold-ritchie-xo28us-post852
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