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 ₛ Q (s) in terms of H (s) /z, so that the determinant quotient Q (s) =D₆₋ (₁) (s) / (s) is forced to be constant; the canonical normalization finally fixes Q 1, and hence D₆₋ (₁) (s) (s). Build: pdflatex (run twice for cross-references). \\ Companion baseline: ''TEBAC Hilbert--Pólya for GL (1): baseline construction (E2/GS5 companion paper) ''.
Tosho Lazarov Karadzhov (Thu,) studied this question.