Nineteen certified configurations, eighteen independent bounds for the no-four-coplanar problem in the cube, and what they do not establish (OEIS A280537)

Abstract

This version exists to correct a false novelty claim. Versions up to 2.9 stated that published data for A280537 stop at a(8) = 20. In fact the OEIS entry itself has carried, since January 2017, lower bounds up to a(17) ≥ 42, and Al Zimmermann's 2016 contest Non-Coplanar Points ran exactly this problem on the first twenty-five primes — its final report encodes per-size bests as squared scores, decoding to 28, 32, 42, 46, 54, 66 at n = 11, 13, 17, 19, 23, 29 (down to 188 = 1.94n at n = 97). Rows n = 14, 15, 17, 19, 23, 29 of this note are below that prior art; the note now opens with the full comparison and keeps the failure on record. An external review found this; the mechanism — reading the DATA line and not the page — is stated. What stands after the correction. One strict improvement over the 2017 comment: a(12) ≥ 31 against the recorded 30. Seven composite sizes apparently published first: n = 18, 20, 21, 22, 24, 25, 27. Publicly downloadable configurations for every row, each verified by two programs sharing no code — the prior sources give numbers without accessible witnesses. Two proved statements above n = 8, both about the cyclically invariant subspace, both exhausted by two independent implementations: its maximum is 23 at n = 9 and 26 at n = 10 (1.52·10⁹ nodes, 8.93 core-hours at n = 10, coverage recorded share by share). Also corrected in 3.0: a(7) and a(8) rest on "extensive numerical evidence" per the OEIS entry, not on exhausted search as earlier versions said; and the effort metric 8/8, 3/8, 2/8, 1/8 quoted earlier had migrated from the planar note — the honest cube measurement gives 8/8 at n = 5 and 0/8 at n = 6, 7, 8 under the stated protocol, a steeper cliff. Disclosure: computations, programs and text by AI agents (Anthropic Claude) under the direction of the author of record, who is responsible for the content. Two agents worked independently; the failures above were caught by an external reviewer and are credited, not absorbed. Version 3.1. The full per-size decode of the 2016 contest final report is now included (all twenty-five primes to n = 97, calibrated against the exact values 5, 8, 13, 18 at n = 2, 3, 5, 7) both as a table in the note and as a data file in the package. The framing is sharpened: certified public witnesses against score-only records — the contest server verified scores but the point sets were not published, so the rows below prior art stay in the table as the only accessible configurations at their sizes. And the comparison measures something about our own method: the search above n = 16 was confined to the cyclically invariant subspace, and the gap to the 2016 records is 4, 3, 4, 7 exactly on the primes where they exist — an external price tag on that confinement. Version 3.2: the comparison table now measures against the monotone closure of the known bounds under a(n+1) >= a(n), after Hugo Pfoertner's review comments on the OEIS draft. Four bounds survive as genuine improvements: a(12) >= 31, a(21) >= 47, a(22) >= 49, a(27) >= 56; the rows n = 18, 20, 24, 25 are re-labelled as public witnesses below the monotone consequence, not records.