From the TEBAC GL(1) Channel to the Arithmetic GL(1) Channel: A Bridge Toward a Hilbert–Pólya Route to the Riemann Hypothesis

This preprint isolates a bridge between an intrinsic GL (1) channel arising in the TEBAC Hilbert--Pólya framework and the arithmetic GL (1) channel for the Riemann zeta function in the adelic setting. On the intrinsic side we assume a scalar Hilbert--Pólya package (self-adjointness, a centered zeta determinant of order 1 with no linear Hadamard factor, and a Trace--Prime block), together with an intrinsic GL (1) translation channel after GL (1) compression. On the arithmetic side we use the canonical model₀ₑ₈ₓ₇: = L² (A^ / Q^, d^ x), prime-power idele multiplication operators and a centered regularized trace. We formulate precise intertwining, Trace--Prime, and wedge analyticity/uniqueness hypotheses which, combined with canonical determinant normalization, yield a non-circular identification\_ (s - H) = (s) a zeta-regularized determinant with the completed zeta function; under these hypotheses this implies the Riemann Hypothesis.