What question did this study set out to answer?

To construct a structural and topological framework for prime distribution at the critical short-interval Legendre scale and isolate the geometric barriers to an unconditional resolution.

August 14, 2026Open Access

Primes at the Legendre Scale: Condensed Mathematics, the Absolute Liquid Frobenius, and Topological Degeneration

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HVHuynh Hai Dang Vo

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Implication

Theoretical analysis demonstrates the unification of classical prime gap conjectures, suggesting a single topological universality class governs distribution at the Legendre scale.

Key Points

To construct a structural and topological framework for prime distribution at the critical short-interval Legendre scale and isolate the geometric barriers to an unconditional resolution.
Integrated liquid and solid modules, Clausen's Weil-Moore anima, and function field global shtuka architectures.
Analyzed the non-degenerate 2D Hessian of the underlying continuous phase to establish maximal monodromy.
Identified the lack of a global dynamical absolute Frobenius endofunctor over Spec(Z) as the exact barrier blocking unconditional resolution.
Showed that resolving this barrier causes the Legendre, Oppermann, and Andrica Conjectures to degenerate into a single topologically governed universality class.

Cite This Study

Huynh Hai Dang Vo (2026) studied this question.

synapsesocial.com/papers/6a7ec78db70b84ec8b913fe1 https://doi.org/10.5281/zenodo.21907515

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Implication

Theoretical analysis demonstrates the unification of classical prime gap conjectures, suggesting a single topological universality class governs distribution at the Legendre scale.

Primes at the Legendre Scale: Condensed Mathematics, the Absolute Liquid Frobenius, and Topological Degeneration

Discussion

Member takes

Implication

Key Points

Cite This Study

Primes at the Legendre Scale: Condensed Mathematics, the Absolute Liquid Frobenius, and Topological Degeneration

Discussion

Member takes

Implication

Key Points

Cite This Study

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