What question did this study set out to answer?

The central aim is to provide a geometric and spectral proof for the Riemann Hypothesis by utilizing the properties of Weyl partitions and Ak−1 root systems.

April 10, 2026Open Access

The Simplicial Geometry Of Weyl Partitions: A Geometric And Spectral Proof Of The Riemann Hypothesis Via Ak−1 Root Systems

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Authors

ABAntonio Bonelli

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Implication

Demonstrates a geometric and spectral resolution of the Riemann Hypothesis, indicating fundamental connections between topology and analytic number theory.

Key Points

The central aim is to provide a geometric and spectral proof for the Riemann Hypothesis by utilizing the properties of Weyl partitions and Ak−1 root systems.
Introduced the Kaleidoscopic Filter to isolate features of the partition manifold.
Applied Ehrhart-Macdonald Reciprocity and Faulhaber summation to condense geometric defects into polynomials.
Developed a 5-step synthesis linking the Riemann Hypothesis to symmetric operator theory.
Mapped Weyl reflections onto a real symmetric matrix for spectral analysis.
Used the Spectral Theorem to affirm the existence of real eigenvalues.
Proven that the non-trivial zeros of the Zeta function lie on the critical line ℜ(s) = 1/2.
Demonstrated that the discrete Laplacian imposes constraints aligning with the dispersion relation λ = s(1−s).
Showed that the geometric invariance in the Arakelov-Adelic lattice establishes connections between topology and spectral theory.

Cite This Study

Antonio Bonelli (2026) studied this question.

synapsesocial.com/papers/69d8948f6c1944d70ce05779 https://doi.org/10.5281/zenodo.19456765

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Implication

Demonstrates a geometric and spectral resolution of the Riemann Hypothesis, indicating fundamental connections between topology and analytic number theory.

The Simplicial Geometry Of Weyl Partitions: A Geometric And Spectral Proof Of The Riemann Hypothesis Via Ak−1 Root Systems

Discussion

Member takes

Implication

Key Points

Cite This Study

The Simplicial Geometry Of Weyl Partitions: A Geometric And Spectral Proof Of The Riemann Hypothesis Via Ak−1 Root Systems

Discussion

Member takes

Implication

Key Points

Cite This Study

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