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 D₆₋ (₁) (s) and the E3 closure D₆₋ (₁) (s) (s), we reduce the remaining step to a spectral-determinant identification: D₆₋ (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 L₀ₑ₈ₓ₇, the zeros of (s) lie on s=12, yielding the Riemann Hypothesis.