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Exact rational certificates for 6 packings below register (n = 103, 153, 207, 209, 258, 270): registration request #573
Description
I’m submitting six 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 |
|---|---|---|---|---|
| 103 | 10.679232047362 | 10.679232047511 (#432) | 1.493293 × 10⁻¹⁰ | square-103.cert |
| 153 | 12.870013850405 | 12.870013850408 (#504) | 2.564000 × 10⁻¹² | square-153.cert |
| 207 | 14.880960371558 | 14.880960373044 (#503) | 1.485670 × 10⁻⁹ | square-207.cert |
| 209 | 14.946223226448 | 14.946223654488 (#481) | 4.280399 × 10⁻⁷ | square-209.cert |
| 258 | 16.563448002138 | 16.563448002140 (register) | 1.984000 × 10⁻¹² | square-258.cert |
| 270 | 16.929775353544 | 16.929780126242 (#481) | 4.772697 × 10⁻⁶ | square-270.cert |
All certificates are pinned to commit 336bdf5efab4784e54e0ac32edf3ed12f9c8af7e in Mishapolk/square-packing-records. They contain rational centres and rational t = tan(θ/2), representing exact unit squares inside the open container.
Certificate SHA-256 hashes:
square-103.cert 044ab54af75be78261f64fe7e6bd99f02f0a650fe13c5355714102e31432365c
square-153.cert 8c012a7207a4762c48fbd68577f5b20771d0be66a401a90b7d09b549a50f15bf
square-207.cert 3cc901c7096406d0c1d7a2daf23860ad65758b3b133a103d0e5ebd3ab9a34b41
square-209.cert f5aa5aa77ce5b95914b9048884d519ef03ce2a14fe95a14ab01517a157b8ea1d
square-258.cert 580be390e8307ffc9e3ce1f613098e8c6734f8b5cf9266d2ca29255fc9948a45
square-270.cert 7dd96e6455e03cfab11a6b63d6fbce4b071b16445d1beec0b7f5288c7abe0185
All 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:
103: continued Ryan Xu’s arrangement from #432, refined using SLSQP on active contact graphs followed by exact rational finishing. Please retain his construction credit.
153: new arrangement discovered using basin hopping with tilted grain boundary corridors, refined via exact rational finishing.
207: new arrangement discovered using basin hopping with tilted boundary corridors, refined via exact rational finishing.
209: new arrangement discovered using basin hopping with tilted boundary corridors, refined via exact rational finishing.
258: continued Nate Chaoweeraprasit’s (SQUISH) arrangement from the register, refined using exact finishing.
270: new arrangement discovered using basin hopping and exact rational finishing.
The search implementation, verification orchestration, and issue preparation used Gemini. I directed the work.
Activity
[-]Exact rational certificates for 19 packings below register (n = 103–306): registration request[/-][+]Exact rational certificates for 6 packings below register (n = 103, 153, 207, 209, 258, 270): registration request[/+]jlevy commentedon Oct 14, 2026
@Mishapolk, thank you for the report. We have retained all 19 certificates at 336bdf5e; the six digests listed in the issue match the pinned files. The same 19 files are unchanged at 46f638ce, the pin of #593.
Admission. All six sides you requested are admitted as stated; the issue gives them rounded up at 12 places. We admitted the other 13 certificates at the exact fractions in your README. The binary64 issue with 16-place prints is specific to #593, where we used the exact fractions from
census.json.Replay. We replayed 153, 154, 175 and 207, the counts below the current register entry. All four positives passed both of our exact checkers, and every control was refused.
Comparison against the current register and every other open report:
Another open report is smaller at every count, so this report will not be registered for now. The certificates stay retained here, and your #593 release is tracked in that issue.
One question: you have given two full names, "Mykhailo Polkovskyi" and "Mikhail Polk". Which should the record carry? Until we hear from you, it credits "Mishapolk".
Generated by Claude Code
intake: address the ledger's Fable review: both case lanes in the sta…
requests: record the 14 October replies and entries; read evand to 62…
jlevy commentedon Oct 14, 2026
@Mishapolk, thank you; this is the report-order evaluation of every open report at the counts #573 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.
At 153 and 207 the owner decides the credit: a measurement recorded beside the verdict finds these packings close to PingYou Ltd's registered packings (at 207 every square lies within 2.8e-4 of PingYou's, the same contact topology; at 153, 51 of 153 squares coincide to 1e-6), while the source calls them new.
Where this differs from our earlier reply, which said no count here would be registered, this evaluation replaces it: in report order, #573 came before PR #574's claims at 153 and 207.
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: address the ledger's mathematical review: both case lanes in …
records-1014: review C of #602; T-174 at the #574 lane's final replay
jlevy commentedon Oct 14, 2026
@Mishapolk, thank you. With #602 merged, this issue's 153 and 207 are registered on
main:As the evaluation above says, this replaces our first reply's "will not be registered for now". Two things stay with the owner: whether 153 and 207 are credited as new arrangements, as the issue says, or to PingYou Ltd's packings, whose contact topology a measurement here finds at 207; and adoption against PR #574. This issue stays open while they are pending.
Evidence:
E-mishapolk-573-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…
intake: retain and replay PingYou Ltd's seven certificates of 12 October
intake: retain and replay Mishapolk's jlevy#573 and jlevy#593 certifi…
merge: the Mishapolk intake lane of 14 October (jlevy#573, jlevy#593)
jlevy commentedon Oct 16, 2026
@Mishapolk, thank you. Where this request stands in the record on
main.Corrections to earlier replies.
What is registered.
On the case pages. On 15 October 2026 T-173 became the house at 153 and 207, 2.56e-12 and 1.49e-9 below PingYou Ltd's packings (T-148, T-147), which stay retained as history.
Not registered.
Still with the owner, as our reply of 14 October said:
Edited: an earlier version of this comment gave these two margins without the ledger's "at least".
This issue stays open until those are decided, and a reply follows each change in the record.
On
main.packing/frontier/RESULTS.md,docs/project/reviews/review-2026-10-14-upper-bound-imports-561-593.md,packing/frontier/n-153.md,packing/frontier/n-207.md.Generated by Claude Code
records: address review A of #637 (the #596 reply, corrected superses…
intake-1017-evand: retain #659's s(236) at 5ad0069 and #664's s(271) …