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Metadata 
bibkey: caochenmiller2025eggdrop
authors: Xiangwen Cao and Zongyun Chen and Steven J. Miller
year: 2025
title: Egg Drop Problems: They Are All They Are Cracked Up To Be!
doi: 10.48550/arXiv.2511.18330
url: https://arxiv.org/abs/2511.18330
claim: Conjecture 1 proposes a real-power ceiling upper bound for multidimensional egg-drop strategies when the egg count is at least the dimension.
strata_touched:
  - D5/S3/Observer/Budget/CaoChenMillerEggDropRefutation
license: citation-only
triage: anchor

Egg Drop Problems: They Are All They Are Cracked Up To Be!

Cao, Chen, and Miller study multidimensional egg-drop strategies. Their Conjecture 1 states that, for positive side lengths and at least as many eggs as dimensions, the worst-case number of drops for the paper’s strategy is bounded by the natural ceiling of a real-power expression. The coordinate model uses a single broken-or-intact answer for each drop and asks for exact recovery of the hidden critical point.

The statement used here is the text of Conjecture 1 on printed page 10 of arXiv version 2, submitted on 2025-12-01. The repository formalization asks whether any deterministic adaptive strategy can meet that budget. This is a weaker existence assertion than success of the paper’s named strategy, so its refutation implies that the printed conjecture is false.

Literature status

The exhaustiveness of this search is ASSUMED-UNVERIFIED.

  • The arXiv API id_list=2511.18330 returned the version-2 work, while the API text queries for the identifier and for an egg-drop counterexample or refutation returned no resolution.
  • Crossref returned a 2026 Fibonacci Quarterly record for the same title, DOI 10.1080/00150517.2026.2681644, with is-referenced-by count zero.
  • OpenAlex work W4416935832 reported zero citations, and its exact cites query returned zero works.
  • The Semantic Scholar DOI citations endpoint returned an empty data array. Its separate paper-metadata endpoint returned HTTP 429, so that metadata request is not a completed check.
  • The publisher DOI redirected to the Taylor and Francis article page; that page returned HTTP 403 in the search environment.

These reached sources contained no published proof or refutation. Zero search and citation hits do not prove absence from the literature.

Verified locator

  • arXiv: https://arxiv.org/abs/2511.18330
  • DOI: https://doi.org/10.48550/arXiv.2511.18330
  • Publisher DOI: https://doi.org/10.1080/00150517.2026.2681644