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.
Authors
- Wenlin Zhang (ORCID: https://orcid.org/0009-0005-2414-7968)
- Haobo Ma
Institutions
- National University of Singapore (SG)
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