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The paper aims to complete the remaining support windows in the Hilbert–Pólya program and establish a quantitative temporal-resonance law.

July 30, 2026Open Access

An Arithmetic-Fluctuation Hilbert–Pólya Mechanism: Outward-Rounded Endpoint-Seven Residual Closure and a Quantitative Cofinal Temporal-Resonance Law

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Preprint demonstrates closures of prime-power support windows, implying significant advancements in numerical analysis.

The paper aims to complete the remaining support windows in the Hilbert–Pólya program and establish a quantitative temporal-resonance law.
Introduced Hilbert–Pólya operator post positivity verification of arithmetic form.
Completed analysis for endpoint-seven with identified nonzero von Mangoldt labels.
Accumulated finite residual rows using IEEE binary128 arithmetic for infinite tail expansion.
Closed the first three prime-power support windows within validated-numerics trust boundary.
Established rigorous bounds for continuum positivity and inverse estimates from high-block analysis.
Demonstrated a cofinal temporal-resonance framework with polynomial endpoint margin and coefficient decay.

Tosho Lazarov Karadzhov (2026) studied this question.

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