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May 27, 2026Open Access

The Kaleidoscopic Framework and the Simplicial Geometry of Weyl Partitions: A Spectral Proof of the Riemann Hypothesis via A₊-₁ Root Systems

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Authors

ABAntonio Bonelli

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Implication

This theoretical framework demonstrates the Riemann Hypothesis through simplicial geometry in integer partitions, suggesting a novel geometric approach.

Key Points

  • This work aims to provide a geometric proof of the Riemann Hypothesis by translating the problem into simplicial geometry and integer partitions.
  • Theoretical framework connecting continuous complex analysis with simplicial geometry.
  • Application of Bonelli's Kaleidoscopic Filter Theorem to partition coefficients.
  • Construction of a combinatorial Hamiltonian operator based on the scattering of partitions.
  • The proposed framework conclusively places all non-trivial zeros of the Riemann zeta function on the critical line $c3 = 1/2$.
  • The geometric operator is compact, strictly self-adjoint, and belongs to the Schatten-von Neumann nuclear class $S_1$.
  • The polarization on the primitive cohomology of the operator is strictly positive definite, precluding asymmetric complex eigenvalues.

Cite This Study

Antonio Bonelli (2026) studied this question.

synapsesocial.com/papers/6a168b160c924ddd1bd59fa2https://doi.org/10.5281/zenodo.20368902
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The Simplicial Geometry of Weyl Partitions: An Algebraic Proof of the Riemann Hypothesis via A_{k-1} Root Systems2026
  2. 2The Kaleidoscopic Filter, Part II : A Geometric And Spectral Proof Of The Riemann Hypothesis Via Aₖ₋₁ Root Systems2026
  3. 3The Simplicial Geometry of Weyl Partitions (revised): A Geometric and Spectral Proof of the Riemann Hypothesis2026
  4. 4The Kaleidoscopic Filter: Exact $\mathcal{O}(1)$ Formula for $P_k(n)$, The Exact Riemann Zeta Zeroes, Berry-Keating Regularization, and the Proof of the Riemann Hypothesis2026
  5. 5Subdivision of the Partition Manifold: From Lower-Dimensional Geometry to the Spectral Realization of the Riemann Zeros2026