{ "weak_coupling_prediction": [ { "gap": 0.5, "eps": 5e-06, "observed_shift_over_eps2": 2.0000001654807416, "predicted_limit_1_over_gap": 2.0, "certificate_ratio": 1.000000082840371 }, { "gap": 1.0, "eps": 1e-05, "observed_shift_over_eps2": 1.0000000827403708, "predicted_limit_1_over_gap": 1.0, "certificate_ratio": 1.000000082840371 }, { "gap": 2.0, "eps": 2e-05, "observed_shift_over_eps2": 0.5000000413701854, "predicted_limit_1_over_gap": 0.5, "certificate_ratio": 1.000000082840371 }, { "gap": 4.0, "eps": 4e-05, "observed_shift_over_eps2": 0.2500000206850927, "predicted_limit_1_over_gap": 0.25, "certificate_ratio": 1.000000082840371 } ], "strong_coupling_prediction": [ { "eps": 1, "observed_shift_over_eps": 0.6180339887498949, "predicted_limit": 1.0, "certificate_ratio": 1.0000000000000002 }, { "eps": 3, "observed_shift_over_eps": 0.8471270883830367, "predicted_limit": 1.0, "certificate_ratio": 1.0 }, { "eps": 10, "observed_shift_over_eps": 0.9512492197250394, "predicted_limit": 1.0, "certificate_ratio": 1.0000000000000002 }, { "eps": 30, "observed_shift_over_eps": 0.9834722125784999, "predicted_limit": 1.0, "certificate_ratio": 1.0 }, { "eps": 100, "observed_shift_over_eps": 0.9950124999218759, "predicted_limit": 1.0, "certificate_ratio": 1.0 } ], "zero_gap_prediction": [ { "eps": 0.01, "observed_shift": 0.01, "predicted_eps": 0.01, "certificate_ratio": 1.0 }, { "eps": 0.1, "observed_shift": 0.1, "predicted_eps": 0.1, "certificate_ratio": 1.0 }, { "eps": 1.0, "observed_shift": 1.0, "predicted_eps": 1.0, "certificate_ratio": 1.0 }, { "eps": 10.0, "observed_shift": 10.0, "predicted_eps": 10.0, "certificate_ratio": 1.0 } ], "rank_one_frobenius_check": { "trials": 100, "max_actual_over_bound": 0.7408804083528778, "violations": 0 }, "adaptive_merge_demo": { "gap": 1.0, "threshold": 0.08, "rows": [ { "eps": 0.01, "certificate_fro": 0.00014140721692940602, "decision": "retain separate blocks" }, { "eps": 0.03, "certificate_fro": 0.0012716487504459695, "decision": "retain separate blocks" }, { "eps": 0.1, "certificate_fro": 0.014003473906250336, "decision": "retain separate blocks" }, { "eps": 0.3, "certificate_fro": 0.11751434393698458, "decision": "merge blocks" }, { "eps": 1.0, "certificate_fro": 0.8740320488976421, "decision": "merge blocks" } ] } }