Field notes
What happened, and when.
Proposed a correction to A079815: under its definition a(8) = 51, and McKay's suggested explanation for 71 fails from n = 5. Found that A239231(13) is 57, where the entry has 56; the remaining terms are being checked before submission. Proposed the rotation-only Gauss diagram count as A398967.
A false comment proposed for A338660 turned into a new sequence, A399316, counting Gauss diagrams of meander curves. Published Sep 12 alongside A338660's first new terms since 2021 and seven new terms of A239300. A091217 gained its first new term since 2008.
The August conjecture is a theorem: a hollow polycube in d dimensions needs 4d − 1 cells, the minimal ones are the spanning trees of the cross-polytope graph, and up to symmetry they are the nets of the d-cube. Two gaps in the first draft of the proof were found in review and closed; exhaustive search confirms every number through four dimensions. Three-page note posted.
Proved the smallest skeleton that cannot be drawn flat has exactly fourteen corners, which is what Knuth conjectured. The argument needs no coordinates: the corners on the line where two faces meet come in pairs, and that condition depends only on how many planes there are.
Adopted Knuth's open questions on signed skeletons. Proved K3,3 and the third prism marking impossible, closed the eight-vertex catalog, and found the marking it was missing. Proofs went through four review rounds.
The two-cavity sequence A398878 was rejected: the editors want four nonzero terms and two are known. a(18) = 590074 was computed for the review. Both values go into A396101 instead; the next terms wait for bigger hardware.
Computed m(n), the smallest polycube that can hide an n-cell cavity, through n = 16 with two independent programs agreeing through n = 13. Submitted the thirteen confirmed terms as a new sequence; published Aug 25 as A399136.
Referee-hardened the paper; found and fixed a proof gap. A355966 corrections published. Resolved the A060966 / A283189 circulant discrepancy: three corrections and five new terms submitted, about seven minutes of wall time. Two-cavity census launched. stephenpursey.com registered.
Submitted all three OEIS contributions; editors reviewed the same day. A357083 (extension) and A396101 (authored) published within hours. Posted the two-bug autopsy of the original A355966 program; the faulty program was removed from the record. Paper drafted to zero TODOs.
84 trillion shapes over three days of pause-and-resume around daily life. Completed and verified August 9. Exactness lemmas closed out August 9–10.
Harvested 2,422 neglected OEIS sequences; chose cavity polycubes. Enumerator built and validated the same day. Discovered the published A355966(14) was wrong. Computed the first genuinely new number, A357083(15) = 422277. Sizes 16 and 17 fell by evening, on two machines.