What question did this study set out to answer?

The central aim is to prove the Riemann Hypothesis using a kernel-theoretic approach.

March 24, 2026Open Access

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

Key Points

The central aim is to prove the Riemann Hypothesis using a kernel-theoretic approach.
Developed a dynamical system (S,Φ) to derive the dynamical zeta function Z(s).
Established eleven lemmas leading to the relationship Z(s)=ζ(s).
Showed the functional equation occurs as the vanishing of an adjunction tensor.
Used the Berry-Keating operator to prove essential self-adjointness on a J-invariant subspace.
Applied global CCR and Stone-von Neumann arguments for spectrum discreteness.
The critical line σ=1/2 is identified as the unique fixed point of an e1-reflection.
The proof confirms the essential self-adjointness of the Berry-Keating operator locally.
The functional equation of the zeta function is achieved through tensor properties.

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.

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

Key Points

Abstract

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