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156-271 and 338-378: registration request #561

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156-271 and 338-378: registration request#561
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@franciscouzo
franciscouzo
opened on Oct 12, 2026

Bounds and comparisons

Every displayed side is rounded upward to 12 decimal places from the certificate’s exact rational side. Improvements are computed before rounding.

n new certified upper bound comparison bound improvement
156 12.979165853835 12.979172613645 6.76e-06
176 13.807637227056 13.808663234387 0.00103
237 15.902947773659 15.902949607678 1.83e-06
271 16.948992356452 16.949116687816 0.000124

The register comparison is pinned to 562fdbdff1d98948f68b36b81b53f9c8165ffd08. The previous 156 bound is Daniil Ostashev’s; 237 is my refinement of SQUISH from #488; 271 is SQUISH’s #500 packing.

For 176, the comparison uses Daniil Ostashev’s smaller published certificate, rather than the larger bound in that register snapshot.

For the beyond-horizon list, these five bounds improve the corresponding rows confirmed from #506. Comparisons use that report’s exact certificates at 337078ca3e05153aceb099237b175cf64af5748a.

n new certified upper bound previously reported in #506 improvement
338 18.906332809853 18.906436500552 0.000104
344 18.993741872920 18.994353244944 0.000611
375 19.901618621328 19.906335145009 0.00472
376 19.904949736499 19.910276586885 0.00533
378 19.942536155970 19.942541777355 5.62e-06

These comparisons are against published packings. The frozen L-border reference used by my search is only a construction baseline.

Certificates

All nine certificates are in franciscouzo/square-packing, pinned to:

0fa0e0de2ef0b414655e871b1baffcfe0d33c815

Each certificates/nN.cert starts with n S, followed by exactly n rational triples (x, y, t), where t = tan(theta/2). The exact S in each header is the authoritative bound.

n certificate SHA-256
156 n156.cert 1b4dfa721e3289c9f55f6920fe10360b75eb56dd03b366c281ddabf2dbf24dd2
176 n176.cert 1b132aa65b3a513267c9bfd260395216c070946c62220cfba663115baf3c901b
237 n237.cert 7b65988e7da36573f7b1318839f0da023c16a730225404a299870898db8cfa70
271 n271.cert 690a1d024f271dffdd0c54d0203f0f1ac1295ccb84f835b7ebe4ff14e5253617
338 n338.cert 20cfd3cab9120d956848b342c378fd04837dfacd6e9c2f37fac294478bf7a519
344 n344.cert 145c020467e1af49210b5f5d815ce7eb7e248f1bbee072c7fe79c5f61c4058ca
375 n375.cert 0252c1ee50315af5065a7ddf7f7a252ea3e5d48ef70e4e3925f7c7b56bcc785c
376 n376.cert 428cf419e40b40758e32ae932b51b4613d34ddb293f233fcdbc6c7499af468e9
378 n378.cert c15aeb0fa927ec749bab7ae22eca36645a2f2343c184ebccb9cf29c3afb7aa03

The certificates for 156, 237, 271, 338 and 376 were produced with Evan Daniel’s exact contact solver.

The certificates for 176, 344, 375 and 378 are rational witnesses from the decimal poses, with centre dilation respectively 1+1e-11, 1+1e-12, 1+1e-10 and 1+1e-12. I also corrected the certificate README’s blanket 1+1e-12 statement in response to the review of #506.

Verification and reproduction

All nine certificates were fetched from the fixed commit above, checked against their complete SHA-256 hashes and exact row counts, and replayed using both checkers with Python’s exact Fraction arithmetic:

Both routes passed all nine certificates. On CT104, geometry checks took 4.52 seconds total for sqpack.verify and 5.56 seconds including interpreter startup for Evan Daniel’s verifier, excluding downloads.

The manifest retains the exact bounds, comparison fractions, certificate hashes and checker hashes. The receipt records every verdict and elapsed time.

Reproduce with Python 3 and network access:

git clone https://github.com/franciscouzo/square-packing.git
cd square-packing
git checkout e9eb44b5aff8fbd4e466d12b1137b25e864060e7
python3 publications/20261012/replay.py --output replay-receipt.json

The replay script downloads the pinned certificates and checker files, verifies their hashes, reconstructs exact unit-square corners, and checks each rational improvement.

Shared assumptions and limits

Both checkers use rational half-angle rotations and separating-axis geometry. The sqpack.verify route is the upstream project’s own checker; Evan Daniel supplies the contact solver and the second verifier.

These certificates establish finite packing feasibility. No local or global optimality proof or independent human review is claimed.

Origins and credit

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

AI disclosure

The continuing search and application work, source audit, exact verification orchestration, and this issue preparation were assisted by OpenAI Codex. Earlier search code and earlier submissions were also prepared with Claude Code. I directed the work; the checker receipts report automated validation.

Activity

  1. jlevy
    added
    intakeTracking intake (saving, validation, tabulation, credits) of new results
    on Oct 14, 2026

  2. jlevy commented on Oct 14, 2026

    @jlevy
    jlevy
    on Oct 14, 2026
    Owner

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

    Generated by Claude Code

  3. jlevy
    added a commit that references this issue on Oct 14, 2026

    requests: record the 14 October replies and entries; read evand to 62…

    60e5ffa

  4. jlevy commented on Oct 14, 2026

    @jlevy
    jlevy
    on Oct 14, 2026
    Owner

    @franciscouzo, thank you; this is the report-order evaluation of every open report at the counts #561 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
    156 12.979165853835 recorded: a new packing, continuing Daniil Ostashev's arrangement (on main); 6.76e-06 below the record on main (Daniil Ostashev) PR #574 (PingYou Ltd) 12.979165853835
    176 13.807637227056 recorded: a new packing, continuing Daniil Ostashev's arrangement (#562's 176); 5.22e-03 below the record on main (Nate Chaoweeraprasit) PR #574 (PingYou Ltd) 13.795872318437
    237 15.902947773659 recorded: a new packing, continuing Nate Chaoweeraprasit's SQUISH arrangement (the author's own, on main); 1.83e-06 below the record on main (Nate Chaoweeraprasit, improved by Francisco Couzo) #593 (Mishapolk) 15.902705057867
    271 16.948992356452 recorded: a new packing, continuing Nate Chaoweeraprasit's SQUISH arrangement (on main); 1.24e-04 below the record on main (Nate Chaoweeraprasit) PR #574 (PingYou Ltd) 16.948992356452
    338 18.906332809853 recorded: a new packing, continuing the author's own L-border construction (#506); at least 1.04e-04 below the row on main from #506 this report 18.906332809853
    344 18.993741872920 recorded: a new packing, continuing Kevin Fang's 344 (#484), through the author's #506; at least 6.11e-04 below the row on main from #506 Francisco Couzo's publication franciscouzo/square-packing@b85dee2 18.993724693587
    375 19.901618621328 recorded: a new packing, continuing the author's own L-border construction (#506); at least 4.72e-03 below the row on main from #506 #584 (Evan Daniel) 19.882451030482
    376 19.904949736499 recorded: a new packing, continuing the author's own L-border construction (#506); at least 5.33e-03 below the row on main from #506 Francisco Couzo's publication franciscouzo/square-packing@4596670 19.904068025747
    378 19.942536155970 recorded: a new packing, continuing the author's own L-border construction (#506); at least 5.62e-06 below the row on main from #506 Francisco Couzo's publication franciscouzo/square-packing@b85dee2 19.942519693846

    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

  5. jlevy commented on Oct 14, 2026

    @jlevy
    jlevy
    on Oct 14, 2026
    Owner

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

    • T-161, V0/C0, significance S2, recorded: your certificates at 156, 176, 237 and 271, credited Couzo after Ostashev, Chaoweeraprasit, Fang, Daniel, Ellsworth, Levy. Both of our exact routes replayed them; an independent review of that replay comes next, then adoption on the case pages, which are unchanged until then. Later entries are smaller at 176 (your T-165) and 237 (T-183), and PR research: submit 148 square-packing certificate refinements with exact endpoints #574 (T-174) tightens 156, 237 and 271 by about 1e-19.
    • 338, 344, 375, 376 and 378 are rows beyond the n ≤ 324 case corpus, which take no register entry. 338 is the current row; later reports supersede the other four.

    Evidence: E-couzo-561-certificate-report (your report, recorded). On main: RESULTS.md, the packet.

    Generated by Claude Code

  6. jlevy
    added a commit that references this issue on Oct 14, 2026

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

    38775ff
  7. BuddenPing
    added 2 commits that reference this issue on Oct 15, 2026

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

    f8ecf21

    merge: the Couzo intake lane of 14 October (jlevy#561, jlevy#570, jle…

    108047d

  8. jlevy commented on Oct 16, 2026

    @jlevy
    jlevy
    on Oct 16, 2026
    Owner

    @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-161 as V0/C0, recorded; it now reads V3/C3, confirmed.
    • The follow-up reply of 2026-10-14 gave E-couzo-561-certificate-report as recorded; it now reads reviewed.

    What is registered.

    • s(156) <= 12.979165853835, s(176) <= 13.807637227056, s(237) <= 15.902947773659 and s(271) <= 16.948992356452, rounded up at 12 places, by exact rational certificates:
      • T-161, 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).

    On the case pages. Our reply of 14 October said adoption would follow the review. On 15 October 2026 T-161 became the house at 156 and 271; the packings it replaces (Daniil Ostashev's T-149 at 156, Nate Chaoweeraprasit's T-151 at 271) stay retained as history. At 176 the house is your exact re-solve of this packing (T-165), and at 237 Mykhailo Polkovskyi's #593 certificate (T-183); T-161 stays verified there and is not selected.

    Smaller certificates that are not adopted: at 156, 176 and 271, PR #574's (T-174), whose houses are held for the owner, and Mykhailo Polkovskyi's of 14 October (T-186, V0/C0). At 237, since #627 merged, your own #607 certificate (T-189) and your 4e4c8ce certificate (T-190) are recorded at V0/C0, 1.01e-4 below T-183, pending review.

    Beyond the case corpus. 338, 344, 375, 376 and 378 are rows beyond the n ≤ 324 corpus, which take no register entry. 338 is still the current row. Your certificates of 13 October supersede the other four. They are still the current rows at 344 and 376; at 375 Evan Daniel's #584 composition is smaller again, and at 378, since #627, your 487b058 certificate. The row at 376 lies above Göbel's classical construction, a question for the owner on #613.

    Edited: an earlier version of this comment said Evan Daniel's #584 composition superseded the row at 375, leaving out your certificate of 13 October, which superseded it first.

    On main. packing/frontier/RESULTS.md, docs/project/reviews/review-2026-10-14-upper-bound-imports-561-593.md, packing/frontier/n-156.md, packing/frontier/n-176.md, packing/frontier/n-237.md, packing/frontier/n-271.md.

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

    Generated by Claude Code

  9. jlevy
    closed this as completedon Oct 16, 2026
  10. jlevy
    added 4 commits that reference this issue on Oct 16, 2026

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

    66e8be6

    intake-1017-evand: replay #659's and #664's certificates on both rout…

    7f8aec7

    houses: adopt Evan Daniel's certificates at 155, 229, 236 and 271; cr…

    be6aa80

    records: credit 271 to Evan Daniel (#664), cite the #669 by-field ans…

    8aa19f6
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