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bibkey: bortnovskyi2025ordered authors: Ivan Bortnovskyi and Michael Lucas and Steven J. Miller and Iana Vranesko and Ren Watson and Cameron White year: 2025 title: The Ordered Zeckendorf Game doi: 10.48550/arXiv.2508.20222 claim: The Long Game Strategy is conjectured to achieve the greatest length among all legal terminating plays of the ordered Zeckendorf game. strata_touched:

  • D5/S1/Digit/Carry
  • D5/S1/Digit/Normalize
  • D5/S0/Rewriting/NewmanConfluence
  • D5/S0/Rewriting/NormalFormFunction license: citation-only triage: anchor

The Ordered Zeckendorf Game

Bortnovskyi, Lucas, Miller, Vranesko, Watson, and White study a variant of the Zeckendorf game whose states are ordered lists of Fibonacci numbers, with combine, split, and inversion-switch moves. Their Conjecture 1.7 states that the Long Game Strategy attains the longest game length; the paper reports that this is supported by exhaustive simulation but that a rigorous optimality proof remains open. It also records that a full resolution of the winner was computationally infeasible beyond n = 25.

This note is the literature anchor for the problem candidate Problems/ordered-zeckendorf-long-game-strategy.md.

Search log

  • 2026-08-18: Queried the arXiv Atom API for id_list=2508.20222. HTTP 200 with totalResults=1; the entry resolved to http://arxiv.org/abs/2508.20222v2, title The Ordered Zeckendorf Game, six authors as recorded above, published 2025-08-27, primary category math.NT. The API reported no arxiv:doi and no arxiv:journal_ref, so the arXiv-assigned DOI is used. The resolved entry is version 2; the DOI above is version-independent, and the problem candidate records the version it quotes.
  • 2026-08-18: Issued HEAD https://doi.org/10.48550/arXiv.2508.20222, which returned HTTP 302 redirecting to https://arxiv.org/abs/2508.20222.

No literature search for a later resolution of Conjecture 1.7 was performed; the open status recorded in the problem candidate is the status stated in this arXiv version.

Verified locator

  • arXiv: https://arxiv.org/abs/2508.20222
  • DOI: https://doi.org/10.48550/arXiv.2508.20222