Proof of Chen and Chen's parity-positivity conjectures: OEIS A392664–A392666, COMMENTS, and Conjecture 2 (p. 1)

We prove Conjecture 2 on page 1 of Chen and Chen's January 2026 executive summary and the parity-positivity conjectures in OEIS A392664–A392666, COMMENTS: every positive even row is strictly positive for real m <= -3. We also prove the odd-row alternating-sum nonvanishing assertions at m = -4 and -5. The largest root modulus satisfies M_n(-3) ~ 5^(n/2)/sqrt(45), correcting the stated exponent log(2) to log(5)/2 and the proposed scaling constant 1/3. The constants 1/6 and 1/10 at steps -4 and -5 are proved. Companion identities, the integer-step sign classification and boundary cases have written proofs.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23957559
Primary Topic
Advanced Mathematical Identities
Type
preprint
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Proof of Chen and Chen's parity-positivity conjectures: OEIS A392664–A392666, COMMENTS, and Conjecture 2 (p. 1)

Wenlin Zhang, Haobo Ma
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
preprint

Proof of Chen and Chen's parity-positivity conjectures: OEIS A392664–A392666, COMMENTS, and Conjecture 2 (p. 1)

Wenlin Zhang, Haobo Ma
preprint en

Abstract

We prove Conjecture 2 on page 1 of Chen and Chen's January 2026 executive summary and the parity-positivity conjectures in OEIS A392664–A392666, COMMENTS: every positive even row is strictly positive for real m <= -3. We also prove the odd-row alternating-sum nonvanishing assertions at m = -4 and -5. The largest root modulus satisfies M_n(-3) ~ 5^(n/2)/sqrt(45), correcting the stated exponent log(2) to log(5)/2 and the proposed scaling constant 1/3. The constants 1/6 and 1/10 at steps -4 and -5 are proved. Companion identities, the integer-step sign classification and boundary cases have written proofs.

Zenodo (CERN European Organization for Nuclear Research)
National University of Singapore (SG)
Advanced Mathematical Identities
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