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

Source 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.