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arXiv · 2610.18214

A certified classical-strip comparison for the de Bruijn-Newman constant

Michel Planat
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Abstract

We give a directed comparison beginning with the classical zero strip \(\lvert\Ima z\rvert\le1\) for the de Bruijn--Newman heat deformation. Under explicitly stated complete model-to-function source, localisation and global contact premises, translated-probe estimates imply \[ Λ\le\frac{148611789321711}{10^{15}} =0.148611789321711<0.148612. \] 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.

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Michel Planat. 2026-10-13. A certified classical-strip comparison for the de Bruijn-Newman constant. https://arxiv.org/abs/2610.18214

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