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s(146) ≤ 12.5837822039508342919134679370511513667729: further certificate refinement #566

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s(146) ≤ 12.5837822039508342919134679370511513667729: further certificate refinement#566
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intakeTracking intake (saving, validation, tabulation, credits) of new results

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@BuddenPing
BuddenPing
opened on Oct 12, 2026

Updated 13 October 2026 — further refinement of this existing submission. Please register the improved feasible upper bound

s(146) ≤ 12.5837822039508342919134679370511513667729.

The decimal is rounded upward from the complete exact rational witness. Compared with the witness in our previous submission, the side is reduced by approximately 1.3171282204e-13. The current files below supersede that version.

Method. A high-precision coupled realization of the declared inherited square-corner, square-side and wall contacts produces the complete rational packing. Its raw rational output is already valid; no common dilation repair is needed.

Current files.

Certificate SHA-256: a88ede7e2faa9d62fe8b6d0e46f7d38dde7df1f5a198d15bc6d6d726df77d13d.

Verification and reproduction. Extract the package, enter its top-level directory, and run python3 VERIFY.py using Python 3.10 or later, without -O. All 146 unit squares, all wall conditions and all 10,585 unordered pairs pass exact checks. Separate rational polygon-intersection checks agree. Both unchanged Squares Project native verifiers at commit 074ac28d4ceb9a1897303f936d794771cfc6a7bd accept the native witness. The package retains the relevant receipts and replay instructions. Boundary contacts are permitted; no overlap tolerance is used.

This strengthens the upper bound for the existing record; it does not claim a new value of N or prove local or global optimality. Maintainer review is pending.

Credit and lineage. Ryan Xu: original layout. Robert Barnett: preceding refinement. PingYou Ltd: this further refinement. Evan Daniel: contact-solver source and earlier N146 regularization. Upstream software and schema licenses and credits are retained in the package.

Activity

  1. BuddenPing
    changed the title [-]s(146) ≤ 12.583782203950967: exact certificate refinement[/-] [+]s(146) ≤ 12.5837822039508342919134679370511513667729: further certificate refinement[/+] on Oct 12, 2026

  2. BuddenPing commented on Oct 12, 2026

    @BuddenPing
    BuddenPing
    on Oct 12, 2026
    Author

    Updated this submission to s(146) ≤ 12.5837822039508342919134679370511513667729, improving the previously submitted exact witness by approximately 1.3171282204e-13. The issue body now links the replacement certificate, native witness and verified portable package, pinned to publication commit 820b9ffb11dd602d735f7a03cd472db98a2d3bb6.

    All exact geometric checks and both pinned native verifiers pass. Further refinement credit: PingYou Ltd, with the prior construction and software lineage retained. Please use this version for registration.

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

  4. jlevy commented on Oct 14, 2026

    @jlevy
    jlevy
    on Oct 14, 2026
    Owner

    @BuddenPing, thank you. We have the n146 certificate from your update of 12 October, pinned at 820b9ff (n146.cert.json, SHA-256 a88ede7e…). We retain it as derived exact facts. It replayed and passed both of this project's maintained exact checkers, and both refused the two controls. Its side is 2.119e-13 below the current register entry at 146, which keeps its own claim. Registration comes next. PR #574 states a further n146 certificate; it is a separate import.

    Generated by Claude Code

  5. 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

  6. jlevy commented on Oct 14, 2026

    @jlevy
    jlevy
    on Oct 14, 2026
    Owner

    @BuddenPing, thank you; this is the report-order evaluation of every open report at the counts #566 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
    146 12.583782203951 recorded: a refinement of Ryan Xu's packing; credited to this report's finder, after Ryan Xu; 2.12e-13 below the record on main (Ryan Xu, improved by Robert Barnett) PR #574 (PingYou Ltd) 12.583782203951

    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

  7. jlevy commented on Oct 14, 2026

    @jlevy
    jlevy
    on Oct 14, 2026
    Owner

    @BuddenPing, thank you. With #602 merged, your n146 refinement is registered on main:

    • T-168, V0/C0, significance S2, recorded: a further exact refinement of Ryan Xu's packing of 146 after Robert Barnett's, credited PingYou Ltd after Xu, Barnett, Daniel, Levy and listed as a regularization of T-150, which keeps its own claim. Both of our exact routes replayed it; an independent review of that replay comes next, then adoption on the case page. PR research: submit 148 square-packing certificate refinements with exact endpoints #574 (T-174) tightens it again, by 1.26e-79.

    Evidence: E-pingyou-566-certificate-report (your report, recorded). On main: RESULTS.md, the packet.

    Generated by Claude Code

  8. 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
  9. BuddenPing
    added 2 commits that reference this issue on Oct 15, 2026

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

    6801238

    merge: the PingYou intake lane of 14 October (jlevy#564, jlevy#566-jl…

    02dac55

  10. jlevy commented on Oct 15, 2026

    @jlevy
    jlevy
    on Oct 15, 2026
    Owner

    @BuddenPing, 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-168 as V0/C0, recorded; it now reads V3/C3, confirmed.
    • The follow-up reply of 2026-10-14 gave E-pingyou-566-certificate-report as recorded; it now reads reviewed.

    What is registered.

    • s(146) <= 12.5837822039508342919134679370511513667729, by an exact rational certificate:
      • T-168, 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 page. Our reply of 14 October said adoption would follow the review. On 15 October 2026 T-168 became the house at 146; Ryan Xu's packing as Robert Barnett improved it (T-150) stays retained as history.

    On main. packing/frontier/RESULTS.md, docs/project/reviews/review-2026-10-14-upper-bound-imports-561-593.md, packing/frontier/n-146.md.

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

    Generated by Claude Code

  11. jlevy
    closed this as completedon Oct 15, 2026
  12. jlevy
    added 2 commits that reference this issue on Oct 15, 2026

    requests: the six closed summaries give the confirmed rung; #564 note…

    0b14d0d

    Merge pull request #630 from jlevy/claude/ecstatic-edison-8en33t-repl…

    9f0c1aa
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