bibkey: hennessey2024tree authors: Aidan Hennessey year: 2024 title: Tree and Tripod Nim doi: 10.48550/arXiv.2401.07943 claim: Section 9.3 defines D(k,n); printed Conjecture 2 says that each periodic orbit of D(3,n) has a period dividing 2(4n)(4n+1). strata_touched:

• D5/S0/Certificates/TripodNimPeriodRefutation license: citation-only triage: anchor

Tree and Tripod Nim

Source: https://arxiv.org/pdf/2401.07943v1, printed pages 28 and 30. The arXiv version is dated 15 January 2024; the title page is dated September 2023.

Section 9.3 uses k rows and 2n+k columns. Rows are processed from bottom to top, with lower rows representing smaller entries. The transition first shifts left and fills the rightmost column with zeros. Each row whose harvested bit was zero receives a one at its leftmost permitted zero. The leftmost n columns are excluded, and two new ones in one transition cannot occupy the same column. Existing ones in other rows do not by themselves block that column.

Printed page 30 states Conjecture 2 with the expression 2(4n)(4n+1), and Remark 9.2 reports confirmation for n ≤ 9. This note attests that source statement and transition, not its truth or the repository’s counterexample. Only the printed conjecture is at issue; no conclusion about the rest of the paper, the author’s intended claim, or a corrected formula is asserted.

No priority for the counterexample is claimed.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2401.07943
• Preprint: https://arxiv.org/abs/2401.07943