No four coplanar in the cube: certified witnesses against the prior art this note initially missed (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.