GL1 IV - A T5-Replacement Lemma from Carrier Capture and Shift Regimes

We formulate, inside the mod-6 ±1 support space U6, an operator-facing T5-replacement input for the GL1 program: the missing step geometry ⇒uniform residual/tail control. We work with b-adic shells Lℓ = [bℓ, bℓ+1) ∩U6 (typically b= 5), model composites by branch-aware displacement branches, and allow an optional p4 filament/switch layer. The empirical input is a finite carrier-capture depth, stable shift regimes, mass guards, and null-model separation. The formal core is a pushforward covariance statement for LPF-filtered branch profiles under the transition ℓ→ℓ+ 1, up to a controlled defect. From capture, carrier transport, and guards we obtain a relative transport lemma for bad-set indicators; with an additional lift step µB ⇒µdiag this becomes a GL1-compatible control of residual energy, for example of lineᵣatio. The paper remains strictly below an RH claim. Its role in the suite is to isolate the formal T5-style bridge and to reduce the remaining work to two hard knots: (K1) arithmetic pushforward covariance / (M+) and (K2) the operator lift or embedding into the whitened band metric.