The Hilbert–Pólya Operator as an Emergent Boundary Operator in Generalized Universe Holography (GUH)

This note reinterprets the classical Hilbert–Pólya conjecture within the framework of Generalized Universe Holography (GUH).

Rather than postulating a fundamental self-adjoint operator whose spectrum reproduces the nontrivial zeros of the Riemann zeta function, we argue that such an operator emerges naturally as an effective boundary operator enforcing minimal-entropy encoding.

In this framework, the critical line $\Re(s)=1/2$ is identified as an effective boundary manifold, while off-critical zeros correspond to transverse defects that increase informational entropy and violate minimal variance conditions derived from prime–zero duality. Self-adjointness of the Hilbert–Pólya operator is not assumed a priori, but arises as a structural consequence of boundary completeness and entropy minimization.

The note positions the Hilbert–Pólya conjecture as a consequence rather than a foundation, bridging analytic number theory, holographic principles, and emergent spacetime. The proposal remains falsifiable through variance bounds in analytic number theory and observational constraints on holographic entropy.