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This work aims to construct a mathematical framework that isolates a positivity problem related to the Riemann Hypothesis.

June 28, 2026Open Access

Arithmetic Dirac Packets, Fargues-Fontaine Slopes, and Weil Positivity: A Conditional Spectral Route Toward the Riemann Hypothesis

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Conditional reduction explores positivity in arithmetic structures to propose insights on the Riemann Hypothesis.

This work aims to construct a mathematical framework that isolates a positivity problem related to the Riemann Hypothesis.
Develop a framework integrating finite prime-orbit Dirac packets and Fargues-Fontaine slopes.
Utilize Weil positivity criteria to approach the Riemann Hypothesis.
Construct conditional reductions for verifying the proposed forms and compatibility.
If the Fargues-Fontaine Dirac package satisfies the conditions, then the Riemann Hypothesis follows.
Identified a definitive positivity problem that is essential for the Riemann Hypothesis implication.

Ying Ye (2026) studied this question.

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