What question did this study set out to answer?

To establish a conditional topological transfer framework for analyzing prime gaps at the Legendre exponent and formally identify the exact mathematical barrier to an unconditional geometric resolution.

August 16, 2026Open Access

The Geometry of Prime Gaps: A Topological Blueprint for the Legendre Scale

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HVHuynh Hai Dang Vo

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Implication

Theoretical framework uncovers topological barriers to resolving prime gaps at the Legendre scale, suggesting a unified geometric pathway toward classical conjectures.

Key Points

To establish a conditional topological transfer framework for analyzing prime gaps at the Legendre exponent and formally identify the exact mathematical barrier to an unconditional geometric resolution.
Leveraged liquid and solid modules from condensed mathematics alongside Clausen's Weil-Moore anima.
Imported the unconditional architecture of global shtukas over function fields to construct a blueprint over Spec(Z).
Identified the missing global dynamical absolute Frobenius endofunctor over Spec(Z) as the exact obstruction, requiring an Absolute Analytic Prismatization Stack.
Showed that resolving this obstruction guarantees maximal monodromy via a non-degenerate 2D Hessian phase, condensing the Legendre, Oppermann, and Andrica conjectures into a single universality class.

Cite This Study

Huynh Hai Dang Vo (2026) studied this question.

synapsesocial.com/papers/6a8179bcf2fb91fc834ad081 https://doi.org/10.5281/zenodo.21934336

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Implication

Theoretical framework uncovers topological barriers to resolving prime gaps at the Legendre scale, suggesting a unified geometric pathway toward classical conjectures.

The Geometry of Prime Gaps: A Topological Blueprint for the Legendre Scale

Discussion

Member takes

Implication

Key Points

Cite This Study

The Geometry of Prime Gaps: A Topological Blueprint for the Legendre Scale

Discussion

Member takes

Implication

Key Points

Cite This Study

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