A certified classical-strip comparison for the de Bruijn-Newman constant
Abstract
We give a directed comparison beginning with the classical zero strip lvertIma zrvert≤1 for the de Bruijn--Newman heat deformation. Under explicitly stated complete model-to-function source, localisation and global contact premises, translated-probe estimates imply Λ≤148611789321711/1015 =0.148611789321711<0.148612. The construction uses Raymond's finite source data and 57 fixed translated kernels, independently checked by rational Bernstein certificates. An explicit finite Weyl estimate improves the positive first-head tail and its centred logarithmic moment. A centred cone transfer retains the original physical error allowances, exceptional debit and additive cone reserve, and charges the change in existing phase-surplus credits. Directed tail enclosures are regenerated at 192 and 256 bits; a separate exact-rational auditor accepts all 19,023 comparison steps. The controlled decrease from the complete two-source comparison is 0.000021760452379. We also prove a compatible matched logarithmic tail transfer and identify the finite requirements for stronger exponent pairs. A supplementary section records Raymond's ceiling below 0.116398 under the distinct 7/8 zero-free hypothesis.
Related
- Certified Collision Exclusion and an Unconditional Upper Bound Λ<0.156821 for the de Bruijn--Newman Constant
- Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements
- A conditional bound Λ≤0.13963 for the de Bruijn--Newman constant
- Upper Bounds on the de Bruijn-Newman constant for Dirichlet L-functions with primitive real-valued characters
- An exact hierarchy for Lebesgue's universal covering constant and a certified 0.834 lower bound
BibTeX
@misc{planat2026certified,
title = {{A certified classical-strip comparison for the de Bruijn-Newman constant}},
author = {Michel Planat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18214},
eprint = {2610.18214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18214},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A certified classical-strip comparison for the de Bruijn-Newman constant
AU - Michel Planat
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18214
UR - https://arxiv.org/abs/2610.18214
AB - We give a directed comparison beginning with the classical zero strip lvertIma zrvert≤1 for the de Bruijn--Newman heat deformation. Under explicitly stated complete model-to-function source, localisation and global contact premises, translated-probe estimates imply Λ≤148611789321711/10^15 =0.148611789321711<0.148612. The construction uses Raymond's finite source data and 57 fixed translated kernels, independently checked by rational Bernstein certificates. An explicit finite Weyl estimate improves the positive first-head tail and its centred logarithmic moment. A centred cone transfer retains the original physical error allowances, exceptional debit and additive cone reserve, and charges the change in existing phase-surplus credits. Directed tail enclosures are regenerated at 192 and 256 bits; a separate exact-rational auditor accepts all 19,023 comparison steps. The controlled decrease from the complete two-source comparison is 0.000021760452379. We also prove a compatible matched logarithmic tail transfer and identify the finite requirements for stronger exponent pairs. A supplementary section records Raymond's ceiling below 0.116398 under the distinct 7/8 zero-free hypothesis.
ER -