Seven fine-net measure certificates: lower bounds for n = 19, 20, 26, 27, 28, 29, 31 (after T-102 to T-111) #446
Description
Seven fine-net measure certificates, in the same format as T-102 to T-111 (the check2 bundles), raise the lower bounds below. All are published in wand125/square-packing: the documents under problems/square-lower-bounds/certificates/<name>/, and the data as certificates__<name>.tar.gz in the release square-lower-bounds-v1.
| n | new lower bound | verified on main now |
certificate | net (directions) |
|---|---|---|---|---|
| 19 | 1931/400 = 4.8275 | 4.825 | mixed_n19_L48275 | 2,073 |
| 20 | 393/80 = 4.9125 | 4.905 | mixed_n20_L49125 | 2,073 |
| 26 | 1111/200 = 5.555 | 5.545 | mixed_n26_L5555 | 2,073 |
| 27 | 2261/400 = 5.6525 | 5.6435 | mixed_n27_L56525 | 2,073 |
| 28 | 287/50 = 5.74 | 5.735 | mixed_n28_L574 | 832 |
| 29 | 1163/200 = 5.815 | 5.81 | mixed_n29_L5815 | 832 |
| 31 | 597/100 = 5.97 | 5.9525 | mixed_n31_L597 | 832 |
Each bundle has the candidate (a nonnegative measure of axis-parallel rectangles, total mass below n, with a declared half-angle net), the receipt of the independent check, a negative control and the verifier source. The check is sqverify_fast (branch wand125/sqverify-proof-net, commit fe12e036c: upstream sqverify-fast plus reading the declared net). Before publication each bundle was checked again on a fresh Ubuntu 24.04 machine from the source in the bundle: every direction of the declared net verified, and the control (every mass × 0.985) was refused in all 32 sampled directions. The receipt of that check is verification/prepublication-receipt.json inside each data asset (it lands in the certificate's folder when the asset is unpacked).
These are lower bounds only, not optimality claims. We would be glad if they could be registered like T-102 to T-111.
Activity
wand125 commentedon Oct 8, 2026
Update for n = 27: the certificate in this issue is superseded by a stronger one in the same format.
Published in wand125/square-packing at commit
bf85d6b, data ascertificates__mixed_n27_L5655.tar.gzin the release square-lower-bounds-v1. Before publication it was checked again on a fresh Ubuntu 24.04 machine withsqverify_fastfrom the source in the bundle: 2,073 of 2,073 directions verified, and the control (every mass × 0.985) was refused in all 32 sampled directions. This is the last step for n = 27 with this method. It is a lower bound only.wand125 commentedon Oct 10, 2026
Update for n = 29: the certificate in this issue is superseded by a stronger one in the same format.
Published in wand125/square-packing at commit
22a23c8, data ascertificates__mixed_n29_L582.tar.gzin the release square-lower-bounds-v1. Before publication it was checked again on a fresh Ubuntu 24.04 machine withsqverify_fastfrom the source in the bundle: 2,073 of 2,073 directions verified, and the control (every mass × 0.985) was refused in all 32 sampled directions. This is the last step for n = 29 with this method. It is a lower bound only.intake: retain wand125's s(29) >= 291/50 fine-net report (#446, think…
intake: register wand125's s(29) >= 291/50 as reported T-132 (#446)
records: correct stale wording left by the 10 October intake
jlevy commentedon Oct 12, 2026
@wand125, thank you. The seven fine-net certificates and your two follow-ups are on
mainas reported results, not yet as lower bounds the case records hold.What is recorded.
E-wand125-fine-net-lower-bounds-446-reportandE-wand125-fine-net-n27-5655-followup-report(reported, recorded). Their mass and net premises have had a conditional review here, and each case record cites the report with an open blocker.E-wand125-fine-net-n29-582-followup-report: s(29) ≥ 291/50 = 5.82 on the 2,073-direction declared net. The maintained readers accepted its exact mass and declared-net premises, andsqverify-fastverified it at eight sampled directions with your node counts and least certified bounds. That is a diagnostic, not a replay, so the value stands as reported.No case lower bound has moved: the case records still hold, for example, 193/40 at n = 19 and T-108's 581/100 at n = 29. None of your programs ran here, and no complete replay has run yet.
What remains, owned by this project:
think-r333), a completesqverify-fastcensus at all 2,073 directions from a retained candidate, with the whole-net control (the 99/100 mutant at every direction) and a review that reads the certificate. The owner set its budget on 11 October, and it is queued after the regularization work now under way; no date is set;think-ndvg) the same for the n = 27 follow-up at 1131/200, and a reviewed native capture of the seven original cases with whole-net controls and full custody.This issue stays open while that work is queued, and a reply follows each change in the record.
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wand125 commentedon Oct 16, 2026
Twenty-one fine-net mixed-measure certificates: 18 published today, and n = 37, 39 and 44 published on 2026-10-13 and not reported here before (this comment was revised to cover all of them; it first listed only n = 38 and 43):
Same bundle format as before (candidate.json, check2/receipt.json, check2/control.json, verifier source under check2/src/). Each was checked with the independent
sqverify-faston a fresh Ubuntu 24.04 machine at every direction of its declared net (2073 or 201), and the negative control (every mass ×0.985, 32 directions) was refused. Data files are in the release square-lower-bounds-v1; ASSET.json in each folder gives the asset name, sha256, and the unpack and check commands."Lifted" certificates start from one of our published certificates at a smaller n (named in provenance/search-notes.md), mapped to the larger side and re-solved by LP; they are checked exactly like the others.
For n = 106, 107, 108 and 110 the previous best claimed lower bound is our closed form (closed-form-v1, #600): 10.4039…, 10.4367…, 10.4840… and 10.6. The bundles' READMEs compare with the lower general bound 1/2 + sqrt(N - floor(sqrt N) + 1/4) (Karakuş 2026, Cor. 6.2); against the closed form the gains are 0.099, 0.143, 0.136 and 0.13.
Hiroaki Hosono (wand125)
register(#446): wand125's 18 fine-net lower bounds of 16 October as r…
jlevy commentedon Oct 19, 2026
The merged intake now maps your later n = 37, 39 and 44 reports to their existing registrations: T-178 at 37, T-176 at 39 and T-177 at 44, all V0/C1. These entries have argument review, while complete replay and controls remain outstanding.
The other 18 certificates in your later report are individually owned for import and validation. Their registration is in the separate open #671; its provisional result numbers should not yet be quoted as merged IDs.
The earlier certificates and the n = 27 and n = 29 follow-ups retain their existing pending dispositions. This intake merge makes no additional lower-bound adoption or verification promotion.
On main: intake request record; results register.
Generated by OpenAI Codex.
Merge pull request #671 from jlevy/claude/intake-2026-10-17-lower-bou…
jlevy commentedon Oct 19, 2026
PR #671 has merged, registering the eighteen submitted lower-bound reports as
T-200–T-217. These are now published in the
results register. The n = 108
bound,
s(108) ≥ 531/50, is T-216and is recorded at V3/C3 from the retained complete 201-direction census, its controls
and the mathematical reviews.
The shared implementation and saved-point checks retain their stated limits; this is not
V4/C4 or an optimality claim.
The other seventeen reports remain V0/C0 pending their complete certificate checks and
reviews. No upper-bound house was changed.
The n108 case now holds that lower
bound in both lanes.
The earlier certificates and n27/n29 follow-ups keep their existing pending
dispositions; this issue stays open for the remaining work.
The actual merge is
6833d05aa44f48140170e631b7766cb295876c31. Itsdeployment audit passed all
4,705 checks; the published eighteen rows and the n108 drawing were also checked against
the merged record.
One small upstream documentation correction remains: the archived README names
check2/control.jsonl.gz, while the retained control file ischeck2/control-197_200.jsonl.gz. Could you correct that filename in the upstreamREADME? We have kept the archived source text unchanged and tracked the correction
separately under
think-f40c.Generated by OpenAI Codex.
Merge origin/main (#645) into the #446 lower-bound landing
Merge origin/main (#658) into the #446 lower-bound landing
Merge origin/main (#646) into the #446 lower-bound landing
22 remaining items
records(think-6m6e): #542's close, ten replies' ids as their text nam…
records(think-6m6e): review A of #833, A1 to A7
jlevy commentedon Oct 31, 2026
@wand125, a follow-up on one entry of this issue.
T-177 is now superseded. Our final comment of 26 October gave T-177, your s(44) ≥ 2799/400 by
mixed_n44_L69975, as V0/C1, reviewed, pending adoption. It now reads V0/C1, reviewed, superseded. #851 merged on 31 October and registered T-252, s(44) = 7, at V3/C3, confirmed: the lower half is Mohsen Khalili and Sara Gharabaghi's closed mixed cover, reported in #842, and its source's sweeps were replayed here in full with the producer's code. Its lower bound of 7 is 1/400 above your 2799/400 = 6.9975, and the n = 44 case now holds 7 in both lower lanes, so your bound is no longer pending adoption there. This replaces that statement.T-177 stays registered at V0/C1 with your credit, and the n = 44 case record keeps it as evidence beside T-090. What remains of its validation, the complete census and its whole-net control, stays with
think-u0av, as that comment said.Everything else on this issue keeps the state our comment of 26 October gave it.
On
main.packing/frontier/n-044.md,packing/frontier/RESULTS.md.The issue stays closed; this brings what the record says up to date.
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Merge pull request #865 from jlevy/claude/bold-ritchie-xo28us-l10
jlevy commentedon Nov 2, 2026
@wand125, a follow-up on one entry of this issue.
T-178 is now confirmed at V3/C3. Our final comment of 26 October gave T-178, your s(37) ≥ 2599/400 = 6.4975 by
mixed_n37_L64975, as V0/C1, reviewed, pending adoption. With #886 merged, it reads V3/C3, confirmed, current, credited Hosono after Tokoharu and Levy.sqverify-proof-netadapts this repository'ssqverify_fastcrate, and the two share the crate apart from their declared-net readers. Our maintainedsqverify-fastcensus verified the certificate at all 2,073 directions of its declared net on 2 November: 864,953,550 boxes, least certified bound 1.0000000000165958 at direction 1919, and each direction's node count and least bound equal to your check2 log.T-176 (s(39) ≥ 533/80) and T-177 (s(44) ≥ 2799/400, superseded by T-252) keep the states our comments of 26 and 31 October gave them, and their censuses stay with
think-u0av. Everything else on this issue keeps the state our comment of 26 October gave it.On
main.packing/frontier/n-037.md,packing/frontier/RESULTS.md, the review of 14 October.The issue stays closed; this brings what the record says up to date.
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Merge pull request #888 from jlevy/claude/bold-ritchie-xo28us-l31
records(think-r333): T-132's candidate is retained; the review that r…
records, atlas, tests: the senior review of #889 at 3878fdb (F1, F3 t…
jlevy commentedon Nov 4, 2026
@wand125, a follow-up on one entry of this issue.
T-176 is now confirmed at V3/C3. Our final comment of 26 October gave T-176, your s(39) ≥ 533/80 = 6.6625 by
mixed_n39_L66625, as V0/C1, reviewed, pending adoption. With #889 merged (69abc50), it reads V3/C3, confirmed, current, credited Hosono after Tokoharu and Levy.sqverify-fastcensus, which shares thesqverify_fastcrate with yoursqverify-proof-netapart from their declared-net readers. On 2 November it verified the certificate at all 2,073 directions of its declared net, with your node count and least certified bound at every direction: the axis by an exact vertex sweep, and the other 2,072 directions over 881,271,470 boxes, least certified bound 1.0000000000654117 at direction 1804.T-177 (s(44) ≥ 2799/400, superseded by T-252) keeps the state our comment of 31 October gave it, and its census stays with
think-u0av. Everything else on this issue keeps the state our comments of 26 October and 2 November gave it.On
main.packing/frontier/n-039.md,packing/frontier/RESULTS.md, the review of 14 October.The issue stays closed; this brings what the record says up to date.
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Merge pull request #904 from jlevy/claude/bold-ritchie-xo28us-l43
Merge origin/main bb5bf6d (#904, #905) into the L42 intake of T-233
fix(#903 review): retained packets list their gzip members; the t-019…
jlevy commentedon Nov 4, 2026
@wand125, a follow-up on one entry of this issue.
T-233 is now confirmed at V3/C3. Our final comment of 26 October gave T-233, your s(19) ≥ 1931/400, s(20) ≥ 393/80 and s(26) ≥ 1111/200 from this issue and s(27) ≥ 1131/200 from your follow-up of 8 October, as V0/C1, reviewed, pending adoption. With #903 merged (c03183f), it reads V3/C3, confirmed, current, credited Hosono after Tokoharu and Levy.
sqverify-fastcensus, which shares thesqverify_fastcrate with yoursqverify-proof-netapart from their declared-net readers. The complete censuses of 23 October verifiedmixed_n19_L48275,mixed_n20_L49125,mixed_n26_L5555andmixed_n27_L5655at all 2,073 directions of each declared net, each with your node total. Each count's replay is its own evidence entry, now confirmed:E-wand125-fine-net-446-n19-48275-sqverify-fast-replay,E-wand125-fine-net-446-n20-49125-sqverify-fast-replay,E-wand125-fine-net-446-n26-5555-sqverify-fast-replayandE-wand125-fine-net-n27-5655-followup-sqverify-fast-replay. The stage 4 review of 23 October read all four certificates.The issue's n = 27 value of 2261/400, which your follow-up supersedes, stays unregistered. Everything else on this issue keeps the state our comments of 26 October, 31 October, 2 November and earlier today gave it.
On
main.packing/frontier/n-019.md,packing/frontier/n-020.md,packing/frontier/n-026.md,packing/frontier/n-027.md,packing/frontier/RESULTS.md, the review of 23 October.The issue stays closed; this brings what the record says up to date.
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Merge pull request #907 from jlevy/claude/bold-ritchie-xo28us-l46
records: #973's reply names its six evidence ids, so record them