No four coplanar in the cube: a witness for a(7) >= 18 and the state of the upper bound (OEIS A280537)

a(n) is the maximum number of points in the n×n×n grid with no four of them coplanar — OEIS A280537. The entry records 5, 8, 10, 13, 16, 18, 20 for n = 2..8 and states that terms up to a(6) were found by exhaustive search while a(7) and a(8) rest on numerical evidence. We reproduce a(2)…a(5) by three independent methods, with the impossibility of 14 points at n=5 carrying a DRAT certificate verified by an external checker; we exhibit four witnesses for a(6) ≥ 16 and six for a(7) ≥ 18, which the entry has carried none of for nine years. The upper bound at n=7 is open: an exhaustive case split is running and we deliberately decline to report its fraction. The strongest check here is not a certificate. Ed Pegg published in 2014 the number of optimal configurations — unique at n=3, 232 at n=4, 38 at n=5. Two independent enumerators, one built on a list of 346743 rich planes and one with no notion of a plane at all, reproduce all three counts (16 → 1 class, 10960 → 232, 1768 → 38) with the stabiliser checksum matching internally. Matching a maximum can happen by accident; matching a count three times cannot. The note also records how we nearly published the opposite. Having closed 124 of 128 regions at M=18 without finding a configuration, we leaned towards announcing that the published value is wrong. The unclosed regions were exactly the ones the symmetry pruning drives solutions into, and the configuration was there. Nothing in the computations was incorrect — the reading of the fraction was. What saved us was that neither solver ever wrote “does not exist” where it meant “have not found”. The upload includes a verification protocol written for a reader who trusts none of the authors' code, an explicit statement of what is not claimed (no completed upper bound above n=5; the n=6 calibration is single-path), and the executable gates the work produced. Disclosure: the computations, the programs and the text were produced by AI agents (Anthropic Claude) under the direction of the author of record, who posed the question, chose what to compute, decided what to claim and is responsible for the content.