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The aim is to provide a complete proof of the Riemann Hypothesis using adelic spectral methods within Zermelo-Fraenkel set theory.

August 6, 2026Open Access

A Complete Conditional Proof of the Riemann Hypothesis via Adelic Spectral Duality

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The aim is to provide a complete proof of the Riemann Hypothesis using adelic spectral methods within Zermelo-Fraenkel set theory.
Constructs a self-adjoint operator HR on the adelic automorphic quotient XA.
Proves self-adjointness and conducts geometric derivations from the Arthur-Selberg trace formula.
Verifies the first zero of the zeta function through autonomous computations using hyperbolic geodesic data.
Establishes spectral rigidity with a unique parameter b=2 compatible with Selberg asymptotics.
Derives the critical zeros of the Riemann zeta function ζ(s), including E1 ≈ 14.134725 while verifying the necessary group structure.
Affirms the conditional nature of the proof based on well-known results regarding congruence subgroups.

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Randomized trial demonstrates connection between spectral operators and critical zeros of zeta function, implying Riemann Hypothesis validity.

Carlos Mario Acevedo Carvajal (2026) studied this question.

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Randomized trial demonstrates connection between spectral operators and critical zeros of zeta function, implying Riemann Hypothesis validity.