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 GL(1) reduced determinant DGL(1)(σ) (primitive spectral shift σ, with σ ≥ 0) and proves the determinantξ identity in the form DGL(1)(s)=ξ(s) (with DGL(1)(s):=DGL(1)(s(1-s))) by a rigidity argument. All determinant inputs (HT2/HT3, kernel-centering, cutoffs χ,ρ and subtraction Prefᶠⁱⁿᵃˡ) are imported from the frozen E2 determinant package closure. The log-derivative match on (s)>1 is imported from the Trace Prime modules. The basepoint/normalization is fixed only via lims→ +∞ Q(s)=1 for the quotient Q(s):=DGL(1)(s)/ξ(s), eliminating any ambiguity. Appendices record the formal complex-analytic lemmas, E2 integral convergence facts, Trace Prime glue identities, a formal wedge continuation/rigidity package, and (optionally) standard ξ-function facts.