Closing E3 in the TEBAC Hilbert–Pólya Program: Complex-Time Heat Bounds ⇒ Wedge(GL1) ⇒ Vanishing of the Odd Remainder

We close the E3 uniqueness step in the TEBAC Hilbert--Pólya program for GL(1) by deriving a full Wedge(GL₁) package for the reference-subtracted remainder kernel $R(t)$ from complex-time heat kernel bounds of Davies type. These sectorial complex-time estimates on the remainder channel imply that the associated odd remainder transform $H(s)$ (in the centred variable s=12+z) extends to an entire function of order ≤ 1 with uniform strip and half-plane control, and a concrete Phragmén--Lindelöf uniqueness argument then forces H≡ 0. An interface lemma identifies ∂ₛlog Q(s) in terms of $H(s)/z$, so that the determinant quotient Q(s)=DGL(1)(s)/ξ(s) is forced to be constant; the canonical normalization finally fixes Q≡ 1, and hence DGL(1)(s)≡ ξ(s). Build: pdflatex (run twice for cross-references).\\ Companion baseline: ''TEBAC Hilbert--Pólya for GL(1): baseline construction (E2/GS5 companion paper)''.