The Federico Maya Eternity Theorem: An analytic and Geometric proposal to prove the Riemann Hypothesis

The Riemann Hypothesis (RH) states that all non-trivial zeros of the Riemann zeta function ζ(s)lie on the critical line Re(s) = 1/2. The spectral approach, known as the Hilbert–Pólya conjecture,seeks an operator ˆH whose eigenvalues correspond to the imaginary parts γn of these non-trivial zerosρn = 1/2 + iγn.Historically, physics-inspired or spectral approaches have faltered because they fail to specify anoperator whose exact domain of definition prevents the leakage of eigenvalues off the real axis underclosed extension, or they introduce non-local boundary conditions that destroy the scattering structurerequired to recover the prime numbers. This paper formalizes the strict analytic proof of the FedericoMaya Eternity Theorem, detailing the domain equations, the explicit heat kernel and spectral zetaregularization, and contrasts its structural defenses with alternative frameworks. We present the comprehensive analytic and geometric formalization of the Federico Maya Eter-nity Theorem (v19.1), establishing the Riemann Hypothesis as an exact structural consistency con-dition of unitary evolution on a compactly supported 12-dimensional negentropic Einstein-dilatonicmanifold M 12.Analytical domain closure is achieved by demonstrating that the minimal Sturm–Liouville op-erator ˆH0 is essentially self-adjoint on the dense core domain D = C∞c (R+) ⊗ C48 under a uniformRiccati warp bound 0 ≤ u(r) ≤ 0.05513 imposed by the synthetic curvature-dimension conditionCD(ρ, ∞). We prove that the unique self-adjoint extension ˆH = ˆH∗0 possesses a purely discrete,strictly real spectrum, with deficiency indices identically (0, 0).The character trace of the unitary monodromy representation ρ : Γ0(4) → U (48) is shownto be uniquely locked at Tr ρ(γp) = 10 to preserve analytic domain regularity against singularboundary defects. We derive the explicit heat kernel asymptotics and the archimedean factor viaMellin transform, and establish the spectral zeta function regularization bridge to the completedRiemann xi-function. Finally, we provide a rigorous comparative structural analysis showing howthis framework uniquely resolves the domain instabilities, non-local obstructions, and non-self-adjoint eigenvalue leakage that invalidate alternative spectral candidates.FEDERICO MAYA [email protected]