Research log — erdos-szekeres-seven

Papers, code, and failed lookups. Forum numbers are leads, not citations.

2026-08-23 — published interval

• The local source of “Green P45” is notes/lists/2026-08-16-proposed-50.md; it is the notebook's green-list label, not a paper citation.
• Erdős and Szekeres's 1960–61 construction: https://renyi.hu/~p_erdos/1960-09.pdf
• A modern exact-coordinate presentation of the construction, used by q1: https://arxiv.org/abs/1602.03075 and https://arxiv.org/pdf/1602.03075
• Mojarrad and Vlachos's upper bound: https://arxiv.org/abs/1510.06255 and https://arxiv.org/pdf/1510.06255
• At k = 7 the two formulas give 33 <= ES(7) <= 113. A 32-point construction is already the published lower witness; a new lower bound needs 33 points with no convex seven-set.

2026-08-23 — Baek and Balko, journal and conference versions

• Journal DOI and publisher page: https://doi.org/10.1016/j.jcta.2026.106195 and https://www.sciencedirect.com/science/article/pii/S0097316526000385
• Crossref and Elsevier API records: https://api.crossref.org/works/10.1016/j.jcta.2026.106195 and https://api.elsevier.com/content/article/PII:S0097316526000385
• Full official SoCG 2025 preliminary version: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.13 and https://drops.dagstuhl.de/storage/00lipics/lipics-vol332-socg2025/LIPIcs.SoCG.2025.13/LIPIcs.SoCG.2025.13.pdf
• The journal record is JCTA 222 (August 2026), article 106195, open access under CC BY. ScienceDirect and its PDF endpoint returned access blocks in this environment. The Elsevier API returned core metadata but not the version-of-record body without an API key. No page-level claim here is attributed to an unread journal PDF; the mathematical checks use the full 15-page official conference version, which the publisher identifies as the preliminary version.
• The conference Theorem 8 proves the conjectured threshold for decomposable sets. At k = 7 it forces a convex seven-set above 32 points, but does not cover arbitrary point sets. Theorem 7's weak-polygon coloring is an abstract coloring, not a geometric lower-bound construction. The new point constructions still have exactly 32 points at k = 7.

2026-08-23 — arXiv:2512.24061 and public code

• Paper: https://arxiv.org/abs/2512.24061, https://arxiv.org/pdf/2512.24061, and https://arxiv.org/e-print/2512.24061
• Code repository and pinned state: https://github.com/bogdan27182/esc-paper and https://github.com/bogdan27182/esc-paper/commit/9520ceac1758120124840e0b66b003c559cec4a7
• Raw released files: https://raw.githubusercontent.com/bogdan27182/esc-paper/main/README.md and https://raw.githubusercontent.com/bogdan27182/esc-paper/main/es_sat_gen.py
• History and archive checks: https://github.com/bogdan27182/esc-paper/commits/main/, https://github.com/bogdan27182/esc-paper/commits/main.atom, https://github.com/bogdan27182/esc-paper/branches, https://github.com/bogdan27182/esc-paper/tags, and https://codeload.github.com/bogdan27182/esc-paper/tar.gz/9520ceac1758120124840e0b66b003c559cec4a7
• python3 scripts/arxiv_fetch.py 2512.24061 --research ... failed at https://export.arxiv.org/api/query with HTTP 429. The PDF was then fetched directly and read in full.
• The repository has exactly two tracked files and no release or tag. It publishes no CNFs, saved configurations, solver version or command, logs, hashes, proof traces, or checker. Its generator SHA-256 is c34fab1327d4c7dbb14a92a143cab657504074e632cfb3fc725dc58eeb354e27.
• The cheapest reported ES(7) slice is layers (5,5,5,5,5,5) with offsets (0,4,4,4,4,4), reported at 2,500 seconds. The public generator emits 578,336 variables and 16,671,498 clauses for that input. Because the paper supplies neither a checked proof nor exhaustive coverage of all layer and offset cases, the table does not change the global upper bound.

2026-08-23 — earlier SAT certificate trail

• Balko and Valtr's public supplement for the earlier SAT attack: https://kam.mff.cuni.cz/~balko/ES_SAT/
• Solver and proof-checker sources used for the local replay: https://github.com/arminbiere/kissat and https://github.com/marijnheule/drat-trim
• It provides older generator/material for strong polygons, but not the Baek–Balko weak-seven coloring certificate or Dumitru's 2025 anchored proof traces. It was useful as a model for what a public replay package should contain, not as evidence for ES(7) = 33.