bibkey: zhang2026sharp authors: Enkai Zhang year: 2026 title: Sharp order-preserving integer models for short additive equalities doi: 10.48550/arXiv.2609.08915 claim: Question 12.5 explicitly restates Shin’s open four-point cardinality-compression question and distinguishes it from weak-type compression. strata_touched:

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

The label-level compression question

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DOI: https://doi.org/10.48550/arXiv.2609.08915

The source is https://arxiv.org/html/2609.08915v1#S12.Thmtheorem5, Question 12.5 (Shin’s label-level question). It asks whether every value of |hA| over four-element integer sets is attained inside [0,D_h^max], for every h>=2. It explicitly says that Theorem 5.1 concerns the finer weak-type invariant and does not answer the question.

The HTML supplied by the public-source intake and read on 2026-09-13 has SHA-256 def8da9ca7df2e381284f9fc175ffb5e0e372ce806d05927cf9643656c061a94. The official https://arxiv.org/abs/2609.08915 version page listed only v1 in the 2026-09-13 public check. Bibliographic details and this short question are paraphrased; no paper text or software is redistributed.

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The same day’s arXiv and GitHub paper-ID checks are described in the shin2026iterated note. No matching solution was found in those bounded queries; that is not an exhaustive novelty claim. This source identifies the question and its then-published open status. Its weak-type theorem is not used as a premise of the cardinality refutation, and the formal result requires no preservation of additive relations.