Shrinking-Layer Terminal Saturation with Companion Escape and Finite-Width Results

We study the exact-versus-relaxed defect associated with integers having a prescribed number r of distinct prime factors and prescribed prime-index support gap K. The central result concerns an arbitrary canonical feasible moving sequence with r→∞ and η = log N / [r(r+1)] → 0, with the integer K fixed before the sequence is chosen: the relaxed prime-height layer law concentrates on the terminal layer and the global defect tends to one along the whole sequence. Two companion results cover domains left outside the previously published finite-parameter baselines: for fixed, or more generally bounded, integer r, the escape condition K/M_r(N)→∞ forces global defect saturation; and in the moving-r positive finite-width domain, with η confined eventually to any fixed compact subset of (0,∞), the global defect tends to one uniformly over every integer K≥0. The latter two regimes yield the corresponding exact-count vanishing statements, and the positive finite-width regime has normalization ZN,r∼binom(J,r). The statements are kept separate from the lower-edge observable of P3 and the finite-τ fixed-r law of P4; no all-regime classification, moving-K shrinking theorem, or raw shrinking tail-tightness theorem is asserted.