From the TEBAC Hilbert–Pólya Determinant to the Riemann Hypothesis (E4: the final HP ⇒ RH bridge)

This preprint isolates the final functional-analytic bridge in the TEBAC Hilbert--Pólya program for GL(1). Assuming the baseline construction (E2/GS5) of a canonically normalized Hilbert--Pólya determinant DGL(1)(s) and the E3 closure DGL(1)(s)≡ξ(s), we reduce the remaining step to a spectral-determinant identification: DGL(1)(12+z) coincides with the zeta-regularized spectral determinant of a self-adjoint Hilbert--Pólya operator on the zeta channel. Under explicit operator-theoretic verification items (B1)--(B3) (reduction, compact resolvent, and heat-trace interface) for a fixed final arithmetic generator Lₐᵣᵢₜₕ, the zeros of ξ(s) lie on s=12, yielding the Riemann Hypothesis.