{"baseline": "3/4", "conditional_fidelity": "547/726", "copies": 4, "critical_inequality": "547/726 > 3/4", "delta": "1/2", "fidelity_gain": "5/1452", "n2_n3_gain_controls": {"2": "-5/52", "3": "-1/25"}, "numerator": "547/7680", "scope": "success-weighted Haar mean, not pointwise purification", "source_S25_Pauli_equations_checked": 1024, "status": "passed", "success_probability": "121/1280", "unnormalized_gain": "1/3072"}
{"copies": 5, "delta_pointwise": "2/3", "fixed_Z_delta_half_comparator": "2305/3072 > 3/4", "fixed_Z_delta_half_fidelity": "2305/3072", "haar_comparator_at_delta_2_over_3": "325/486 > 2/3", "haar_fidelity_at_delta_2_over_3": "325/486", "haar_gain_at_delta_2_over_3": "1/486", "pointwise_comparator": "11693/17496 > 2/3", "pointwise_fidelity_lower_bound": "11693/17496", "pointwise_gain_lower_bound": "29/17496", "proof_scope": "Universal r inequality separately follows from S4>=1/3; no numerical grid substitutes for that proof", "status": "passed", "success_probability_on_every_input": "1"}