What question did this study set out to answer?

To prove the Riemann Hypothesis using a novel kernel-theoretic approach based on tensor methods.

March 24, 2026Open Access

On the Riemann Hypothesis: A Kernel-Theoretic Approach via Tensor Contraction, Self-Adjoint Extension, and Dixon-Algebraic Realization

Key Points

To prove the Riemann Hypothesis using a novel kernel-theoretic approach based on tensor methods.
Developed eleven lemmas to establish the dynamical zeta function Z(s).
Identified Z(s) with the arithmetic kernel to confirm Z(s)=ζ(s).
Realized the functional equation through the vanishing of an adjunction tensor.
Demonstrated the Berry-Keating operator's essential self-adjointness using ε-tensor methods.
Applied global CCR and Stone-von Neumann to derive the spectrum's discreteness.
Successfully proved the Riemann Hypothesis through the established framework.
Validated that the critical line σ=1/2 is a unique fixed point within the Cayley-Dickson hierarchy.
Confirmed the essential self-adjointness of the Berry-Keating operator on specified subspaces.

Abstract

We prove the Riemann Hypothesis via a kernel-theoretic approach. Starting from a dynamical system (S,Φ), eleven lemmas yield the dynamical zeta function Z(s). Identifying with the arithmetic kernel gives Z(s)=ζ(s). The functional equation is realized as vanishing of an adjunction tensor; the Berry-Keating operator is shown essentially self-adjoint on the J-invariant subspace via ε-tensor annihilation of deficiency elements. Discreteness of the spectrum follows via global CCR (Sonde argument) and Stone-von Neumann. A Dixon-algebraic extension realizes the critical line σ=1/2 as the unique fixed point of an e1-reflection in the Cayley-Dickson hierarchy C→H→O→S, valid at every assembly level.

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