de Bruijn–Newman 常数 Λ 上界被降至 0.1787854

Jude Gomila 宣布，通过人机协作与计算机辅助证明，将 de Bruijn–Newman 常数 Λ 的上界从 0.2 降至 0.1787854，其精确有理值为 129/800 加上 87677/5,000,000 1。此前 0.2 的上界由 Platt 和 Trudgian 在 2020 年的记录高度推动 1。作者声明该结果是无条件的，不依赖任何未证猜想，期刊发表为剩余步骤 1。

在证明方法上，该研究基于 Terence Tao 领导的 Polymath 15 项目于 2018 至 2019 年间建立的有效热流理论框架 1。同时，研究结合了 Platt 和 Trudgian 验证的黎曼 zeta 零点高度 3,000,175,332,800 的外部计算记录 1。整个证明过程使用了 3,149,013 个区间算术证书、883 个棱柱屏障证书以及 1 个额外证书，均为机器校验的区间证书 1。此外，证明中设定的屏障位置 X/2 比 Platt 和 Trudgian 的记录低 175,239,886.5 1。

该证明已通过 Dan Romik 的独立人类审查，并于 2026 年 7 月进行了对抗性 AI 审查 1。在相关研究背景方面，Rodgers 与 Tao 于 2018 年证明了 de Bruijn–Newman 常数 Λ 大于或等于 0 1。

In 2026, Jude Gomila announced a new upper bound for the de Bruijn–Newman constant Λ, lowering it to 0.1787854, which corresponds to the exact rational value of 129/800 + 87677/5,000,000 1. This achievement improves upon the previous upper bound of 0.2, which was driven by the height records of Platt and Trudgian in 2020 1. The newly established bound was achieved through human-machine collaboration and computer-assisted proofs, and the author asserts that the result is unconditional and does not rely on any unproven conjectures 1.

The mathematical framework for this proof builds on the effective heat flow theory developed by the Polymath 15 project, led by Terence Tao between 2018 and 2019, and integrates Platt and Trudgian's verification of Riemann zeta zeros up to a height of 3,000,175,332,800 1. To execute the proof, the computation utilized 3,149,013 interval arithmetic certificates, 883 prism barrier certificates, and one additional machine-verified certificate, with the barrier position X/2 set 175,239,886.5 lower than the height recorded by Platt and Trudgian 1. The findings have undergone independent human review by Dan Romik and were subjected to adversarial AI review in July 2026 1. Building upon the foundational work of Rodgers and Tao, who proved that Λ ≥ 0 in 2018, Gomila states that the only remaining step for this unconditional result is formal journal publication 1.