The Matrix, Generation by Generation: The Stagger at the Stricter Bench

AF-20 completed the gauge running — stepped thresholds, Yukawa terms — and printed one input as its least exact: the electroweak two-loop entries were stepped at the top threshold by proxy shares (the top's declared fraction of each whole entry, from one-loop charge sums), with the full Machacek–Vaughn generation-resolved matrix named as the stricter bench still owed. This paper builds that bench. The matrix is decomposed as the Machacek–Vaughn formulas structure it: each entry = a pure gauge+Higgs constant plus a part linear in the fermion content (the five purely fermionic entries were already flavour-exact in AF-20's V1); the electroweak entries' fermion parts are declared from the standard evaluation (b₁₁: 19/15 of 199/50; b₁₂: 9/10 of 27/10; b₂₁: 3/10 of 9/10; b₂₂: 3/2 of 35/6), and the stepping removes exactly the third generation's quark share of each fermion part, computed from the declared one-generation charge table (ΣY⁴ for b₁₁'s structure, ΣY² for the mixed and b₂₂ structures — shares 0.3605 and 0.5500). The Yukawa sector is completed to the full trace Y2 = Tr(Y_u Y_u†) + Tr(Y_d Y_d†) + Tr(Y_e Y_e†), with y_b and y_τ run beside y_t at their declared m_Z prints. The result is the stillest verdict in the line: the resolved removals differ from AF-20's proxies entry by entry (0.457 vs 0.564; 0.495 vs 0.225; 0.165 vs 0.0375; 0.825 vs 0.486 — one proxy was 4.4× too small, another 1.2× too large), and the completed running does not care: at E_ind the inverses stand at 47.786 / 38.300 / 28.410 against AF-20 V3's 47.786 / 38.300 / 28.409, the crossings at 13.05 / 14.20 / 16.35 unmoved, spacings 1.15 and 2.151 dex, zero crossings at or below the wall, no coincidence. The added Yukawa flavours are 0.036% of Y2 at m_Z and less as they run down. The stagger was never the proxies' artifact; it is the running's geometry, now certified at the bench AF-20 itself demanded.