TEBAC Hilbert–Pólya for GL(1): E3 determinant–ξ identity (canonical normalization and rigidity)

This module (E3) fixes a single canonical normalization for the frozen $\mathrm{GL}(1)$ reduced determinant $D_{\mathrm{GL}(1)}(\sigma)$ (primitive spectral shift $\sigma$, with $\Re \sigma \ge 0$) and proves the determinant\textendash$\xi$ identity in the form $D_{\mathrm{GL}(1)}(s)=\xi(s)$ (with $D_{\mathrm{GL}(1)}(s):=D_{\mathrm{GL}(1)}(s(1-s))$) by a rigidity argument. All determinant inputs (HT2/HT3, kernel-centering, cutoffs $\chi,\rho$ and subtraction $P_{\mathrm{ref}}^{\mathrm{final}}$) are imported from the frozen E2 determinant package closure. The log-derivative match on $\Re(s)>1$ is imported from the Trace\textendash Prime modules. The basepoint/normalization is fixed \emph{only} via $\lim_{\Re s\to +\infty} Q(s)=1$ for the quotient $Q(s):=D_{\mathrm{GL}(1)}(s)/\xi(s)$, eliminating any ambiguity. Appendices record the formal complex-analytic lemmas, E2 integral convergence facts, Trace\textendash Prime glue identities, a formal wedge continuation/rigidity package, and (optionally) standard $\xi$-function facts.