Improved rectangle solutions for n=19,20,22-30: five new configurations (n=24,27,28,29,30) and six refinements

[lshhhhhhh]

This PR updates eight entries of the perimeter-4 rectangle circle packing database.

New configurations

n	previous	this PR	improvement
24	2.535344050819014	2.535696915996393	+3.5e-4
27	2.690155081571631	2.691523360670912	+1.4e-3

Both differ structurally from the current entries (radius multisets differ at the 1e-2 level; optimal point-matching distance under all rectangle symmetries exceeds 0.08).

Refinements of known configurations

n=19, 20, 22, 23, 25 (+4e-8 to +8e-8) and n=26 (+1.2e-5): the same configurations as the current entries, converged more tightly. Credit for these configurations remains with their original discoverers.

Verification

All coordinates were verified strictly feasible in 60-digit arithmetic as written: treating each decimal literal as exact, every pairwise distance exceeds the sum of radii (worst slack ~9e-15) and width + height <= 2 holds. Radii include a uniform 5e-15 reduction to guarantee this after 15-decimal rounding. Line 2 of each file is the exact sum of the listed radii, floored at the 15th decimal, so claimed values never exceed actual sums.

A standalone verifier (mpmath only) and full-precision (17 significant digits) coordinates are available at https://github.com/lshhhhhhh/circle-packing-records — or verify with your own checker; the coordinate files are the entire claim.

results.dat is updated for n=24, 26, 27 (5-decimal floors). The per-entry PDFs were not regenerated; happy to add them if you can point me at the rendering script.

Method

Multi-start SLSQP + basin-hopping (16 chains, adaptive step) in plain Python/scipy on a desktop CPU, 1-3 minutes per n. The search pipeline was developed with AI assistance (Anthropic Claude Code); the search itself uses no LLM at run time.

🤖 Generated with Claude Code

[lshhhhhhh]

Pushed three more entries to this PR: n=28 (+3.9e-3), n=29 (+2.3e-3), and n=30 (+1.3e-3), all structurally new configurations (optimal point-matching distance vs the current entries exceeds 0.08 under all rectangle symmetries). Same verification protocol as before; full-precision coordinates and comparison figures at https://github.com/lshhhhhhh/circle-packing-records. The PR title undersells the scope now -- updated summary: new configurations for n=24, 27, 28, 29, 30; refinements for n=19, 20, 22, 23, 25, 26.

[lshhhhhhh]

Correction / clarification on framing. After exchanging email with Erich Friedman we realized the "previous records" in this PR are this database's entries, which for several n lag the curated record page (erich-friedman.github.io/packing/cirRrec/): n=24, 28, 29, 30 have equal-or-better packings by David W. Cantrell (July 2011), n=27 by Everett Dutton (August 2026), n=26 by Aaden Abraham (July 2026).

So this PR should be read as syncing the database toward the known records with full-precision, 60-digit-verified coordinates, not as claiming new records — with one possible exception: our n=26 value 2.639320558987766 appears to exceed the displayed page record 2.63931+, unconfirmed against the page's stored precision.

Our repository README has been corrected accordingly (github.com/lshhhhhhh/circle-packing-records). Apologies for the earlier framing; happy to adjust the PR title/description if you prefer.