TEBAC HP IV: Complex-Time Wedge Continuation and Rigidity (E3 Closure)

This module develops the complex-time (CT) Laplace representation and wedge bounds for the HP--III discrepancy transformₓ₏ (s) \;: =\;ₛ \! (D₂₎₌₏ (ₒ) R (s) ),: = s-12. express the normalized transform (z) \;=\;Eₓ₏\! (₁₂+ₙ) 2z a Laplace transform of an L¹ kernel and derive boundary/sector control on CT rays. We then formulate a resolvent/Laplace forcing functional (Route~B) whose vanishing implies Eₓ₏ 0 on the wedge, hence D₂₎₌₏/R is constant and fixed by the E2N normalization. The Route~B forcing step is discharged in HP--III by the tight-frame/Parseval package: combining the exact bookkeeping identity with the seed-cancellation proposition yields N (z) 0 on an interval z>0 and hence identically by the identity theorem; see HP--III (Prop. ~III-seed-cancel, Thm. ~III-parseval-force). This Zenodo record contains the LaTeX source and compiled PDF of the HP-IV module. Cross-module references to HP-III are resolved in the master build (shared bibliography/aux files).