Forced Residual Reinjection Block

TA38 derives the reinjection block \ (C ₁: HR HM\) of the barrier-scattering matrix from the Q5 admissibility architecture. Given the residual state circulated by TA36 and TA37, only the component of residual return lying in the \ (Y\) -admissible gate subspace may re-enter the coherent carrier sector. This forces the reinjection block to take the form ₁=Y\, Uₑ₄ₓₔₑ₍| ₇ₑ. theorem also gives the exact nonvanishing condition: reinjection occurs precisely when the residual return transport has nonzero overlap with \ (im (Y) \). The resulting carrier output consists of direct carrier transport plus a lagged residual reinforcement term, \M^out (t) =A ₁M+C ₁e^tE ₁D ₁M. with TA36 and TA37, this completes the forced off-diagonal block trilogy: extraction, mediated circulation, and admissible reinjection. The result shows that the residual sector of the barrier-scattering matrix is geometrically constrained by the Q5 architecture rather than introduced as a phenomenological model. Status: solid for the forced structure of \ (C ₁\) ; conditional for nontrivial reinjection pending explicit computation of the leakage generator \ (AL\).