A failure of the DeTemple complete-monotonicity threshold

We refute the sufficient direction of Yang–Chu–Zhang Conjecture 1(ii) at a strictly positive parameter strictly below 155/294. The literal gamma/digamma quotient violates a positive-input midpoint inequality, hence its proposed negative is not completely monotone. The existential strictly interior source refutation is proved in Lean; the separately calculated rational witness is mathematical evidence, not the formal endpoint. Part (i) and an exact replacement threshold are not claimed. AI-assisted preprint by Myeongjin Kang, with no affiliation. Internal AI review is not external journal peer review. The accompanying Lean certificate covers the precise scoped main statement; inspect the formal endpoint, assumptions and provenance in the supporting package. Prior-art investigations are documented bounded searches, not worldwide-priority certification. Original prose is offered under CC BY 4.0 and original code/Lean under MIT; third-party rights and existing notices are preserved. The public supporting ZIP contains original proof sources and verification evidence, with bibliographic links and hashes instead of redistributed third-party source manuscripts. Recorded prior-art/source-access limits: Bounded independent prior-art screen; closest JMAA gamma-ratio remainder body remains paywalled; no worldwide-priority claim.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23718265
Primary Topic
Mathematical Inequalities and Applications
Type
preprint
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preprint

A failure of the DeTemple complete-monotonicity threshold

Myeongjin Kang
Zenodo (CERN European Organization for Nuclear Research)
Mathematical Inequalities and Applications
preprint

A failure of the DeTemple complete-monotonicity threshold

Myeongjin Kang
preprint en

Abstract

We refute the sufficient direction of Yang–Chu–Zhang Conjecture 1(ii) at a strictly positive parameter strictly below 155/294. The literal gamma/digamma quotient violates a positive-input midpoint inequality, hence its proposed negative is not completely monotone. The existential strictly interior source refutation is proved in Lean; the separately calculated rational witness is mathematical evidence, not the formal endpoint. Part (i) and an exact replacement threshold are not claimed. AI-assisted preprint by Myeongjin Kang, with no affiliation. Internal AI review is not external journal peer review. The accompanying Lean certificate covers the precise scoped main statement; inspect the formal endpoint, assumptions and provenance in the supporting package. Prior-art investigations are documented bounded searches, not worldwide-priority certification. Original prose is offered under CC BY 4.0 and original code/Lean under MIT; third-party rights and existing notices are preserved. The public supporting ZIP contains original proof sources and verification evidence, with bibliographic links and hashes instead of redistributed third-party source manuscripts. Recorded prior-art/source-access limits: Bounded independent prior-art screen; closest JMAA gamma-ratio remainder body remains paywalled; no worldwide-priority claim.

Zenodo (CERN European Organization for Nuclear Research)
Mathematical Inequalities and Applications
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A failure of the DeTemple complete-monotonicity threshold — Myeongjin Kang · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS