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mathematics
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semidefinite-programming
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| {"case_id": "rigidity-001", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.3862901399452014,\"defect_sum\":4.772580279890403,\"distance_squared\":1.5852855757376076,\"identity_error\":5.329070518200751e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.3333333333333335,\"nearest_formula_error\":6.661338147750939e-16,\"off_complement_mass\":4.476983890285696,\"repetition\":0,\"residual_sum\":38.180642239123245,\"support\":\"central_4\"}"} | |
| {"case_id": "rigidity-002", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.701432168150607,\"defect_sum\":5.402864336301214,\"distance_squared\":1.898590267902197,\"identity_error\":3.552713678800501e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.3333333333333335,\"nearest_formula_error\":0.0,\"off_complement_mass\":5.016394354612732,\"repetition\":1,\"residual_sum\":43.22291469040971,\"support\":\"central_4\"}"} | |
| {"case_id": "rigidity-003", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.858977942349093,\"defect_sum\":5.717955884698186,\"distance_squared\":1.6320574255876525,\"identity_error\":1.7763568394002505e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.3333333333333335,\"nearest_formula_error\":2.220446049250313e-16,\"off_complement_mass\":4.4575773738022,\"repetition\":2,\"residual_sum\":45.743647077585486,\"support\":\"central_4\"}"} | |
| {"case_id": "rigidity-004", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":15.23576465891236,\"defect_sum\":30.47152931782472,\"distance_squared\":8.146660127578116,\"identity_error\":7.105427357601002e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.2000000000000013,\"nearest_formula_error\":1.7763568394002505e-15,\"off_complement_mass\":19.13472386689478,\"repetition\":0,\"residual_sum\":243.77223454259786,\"support\":\"central_6\"}"} | |
| {"case_id": "rigidity-005", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":15.318467774973865,\"defect_sum\":30.63693554994773,\"distance_squared\":8.16798973004714,\"identity_error\":1.4210854715202004e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.2000000000000013,\"nearest_formula_error\":1.7763568394002505e-15,\"off_complement_mass\":19.165418436054885,\"repetition\":1,\"residual_sum\":245.09548439958186,\"support\":\"central_6\"}"} | |
| {"case_id": "rigidity-006", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":15.41868180104753,\"defect_sum\":30.83736360209506,\"distance_squared\":8.330938857095319,\"identity_error\":1.4210854715202004e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.2000000000000013,\"nearest_formula_error\":3.552713678800501e-15,\"off_complement_mass\":19.30037369629614,\"repetition\":2,\"residual_sum\":246.69890881676048,\"support\":\"central_6\"}"} | |
| {"case_id": "rigidity-007", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_8", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":70.41357169203964,\"defect_sum\":140.82714338407928,\"distance_squared\":31.288155378439058,\"identity_error\":5.684341886080802e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.1428571428571441,\"nearest_formula_error\":1.0658141036401503e-14,\"off_complement_mass\":69.02296477168558,\"repetition\":0,\"residual_sum\":1126.6171470726347,\"support\":\"central_8\"}"} | |
| {"case_id": "rigidity-008", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_8", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":70.28446490784879,\"defect_sum\":140.56892981569757,\"distance_squared\":31.55579621829544,\"identity_error\":5.684341886080802e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.1428571428571441,\"nearest_formula_error\":7.105427357601002e-15,\"off_complement_mass\":69.08083010788728,\"repetition\":1,\"residual_sum\":1124.5514385255806,\"support\":\"central_8\"}"} | |
| {"case_id": "rigidity-009", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "central_8", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":69.30138822567395,\"defect_sum\":138.6027764513479,\"distance_squared\":30.639565175955365,\"identity_error\":5.684341886080802e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.1428571428571441,\"nearest_formula_error\":3.552713678800501e-15,\"off_complement_mass\":68.60841245535259,\"repetition\":2,\"residual_sum\":1108.8222116107831,\"support\":\"central_8\"}"} | |
| {"case_id": "rigidity-010", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "even_parity_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":3.7675006603529315,\"defect_sum\":7.535001320705863,\"distance_squared\":2.806037195856188,\"identity_error\":3.552713678800501e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.0,\"nearest_formula_error\":0.0,\"off_complement_mass\":7.115074264102671,\"repetition\":0,\"residual_sum\":60.28001056564689,\"support\":\"even_parity_4\"}"} | |
| {"case_id": "rigidity-011", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "even_parity_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":3.19080183625427,\"defect_sum\":6.38160367250854,\"distance_squared\":2.223400032673778,\"identity_error\":7.105427357601002e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.0,\"nearest_formula_error\":4.440892098500626e-16,\"off_complement_mass\":6.203639296180321,\"repetition\":1,\"residual_sum\":51.052829380068296,\"support\":\"even_parity_4\"}"} | |
| {"case_id": "rigidity-012", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "even_parity_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":3.849484718600291,\"defect_sum\":7.698969437200582,\"distance_squared\":2.839107134016127,\"identity_error\":8.881784197001252e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.0,\"nearest_formula_error\":4.440892098500626e-16,\"off_complement_mass\":7.306768228646982,\"repetition\":2,\"residual_sum\":61.59175549760462,\"support\":\"even_parity_4\"}"} | |
| {"case_id": "rigidity-013", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "even_parity_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":22.734161807311672,\"defect_sum\":45.468323614623344,\"distance_squared\":13.968150799784272,\"identity_error\":2.1316282072803006e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.0,\"nearest_formula_error\":0.0,\"off_complement_mass\":31.339964914062076,\"repetition\":0,\"residual_sum\":363.7465889169868,\"support\":\"even_parity_6\"}"} | |
| {"case_id": "rigidity-014", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "even_parity_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":23.194755525834804,\"defect_sum\":46.38951105166961,\"distance_squared\":12.753348851173955,\"identity_error\":1.4210854715202004e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.0,\"nearest_formula_error\":0.0,\"off_complement_mass\":30.52291432515799,\"repetition\":1,\"residual_sum\":371.11608841335686,\"support\":\"even_parity_6\"}"} | |
| {"case_id": "rigidity-015", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "even_parity_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":23.76071138459493,\"defect_sum\":47.52142276918986,\"distance_squared\":13.455691083135596,\"identity_error\":2.842170943040401e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.0,\"nearest_formula_error\":3.552713678800501e-15,\"off_complement_mass\":30.911582825620556,\"repetition\":2,\"residual_sum\":380.1713821535189,\"support\":\"even_parity_6\"}"} | |
| {"case_id": "rigidity-016", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_4_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.6219653168181203,\"defect_sum\":3.2439306336362406,\"distance_squared\":1.0968241403182015,\"identity_error\":0.0,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":2.0,\"nearest_formula_error\":0.0,\"off_complement_mass\":3.1374286085684133,\"repetition\":0,\"residual_sum\":25.951445069089925,\"support\":\"two_orbit_4_2\"}"} | |
| {"case_id": "rigidity-017", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_4_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.9213229797823645,\"defect_sum\":3.842645959564729,\"distance_squared\":1.273384472156573,\"identity_error\":3.552713678800501e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":2.0,\"nearest_formula_error\":0.0,\"off_complement_mass\":3.4064994637498547,\"repetition\":1,\"residual_sum\":30.741167676517826,\"support\":\"two_orbit_4_2\"}"} | |
| {"case_id": "rigidity-018", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_4_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.4880105499626115,\"defect_sum\":2.976021099925223,\"distance_squared\":0.9003099219911006,\"identity_error\":6.217248937900877e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":2.0,\"nearest_formula_error\":6.661338147750939e-16,\"off_complement_mass\":2.7879349642415896,\"repetition\":2,\"residual_sum\":23.808168799401763,\"support\":\"two_orbit_4_2\"}"} | |
| {"case_id": "rigidity-019", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_6_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.301533801253954,\"defect_sum\":4.603067602507908,\"distance_squared\":1.142010025421166,\"identity_error\":3.552713678800501e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":3.999999999999999,\"nearest_formula_error\":4.440892098500626e-16,\"off_complement_mass\":3.26293484913774,\"repetition\":0,\"residual_sum\":36.82454082006325,\"support\":\"two_orbit_6_2\"}"} | |
| {"case_id": "rigidity-020", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_6_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.3907319580521733,\"defect_sum\":4.781463916104347,\"distance_squared\":0.8218165645499773,\"identity_error\":7.105427357601002e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":3.999999999999999,\"nearest_formula_error\":8.881784197001252e-16,\"off_complement_mass\":2.5556887991697703,\"repetition\":1,\"residual_sum\":38.25171132883474,\"support\":\"two_orbit_6_2\"}"} | |
| {"case_id": "rigidity-021", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_6_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.7443673129845836,\"defect_sum\":5.488734625969167,\"distance_squared\":1.2184372581156055,\"identity_error\":1.7763568394002505e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":3.999999999999999,\"nearest_formula_error\":0.0,\"off_complement_mass\":3.1399886879527745,\"repetition\":2,\"residual_sum\":43.90987700775335,\"support\":\"two_orbit_6_2\"}"} | |
| {"case_id": "rigidity-022", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_6_3", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.7552315960627871,\"defect_sum\":5.265694788188362,\"distance_squared\":1.296161968756612,\"identity_error\":8.881784197001252e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":2.9999999999999996,\"nearest_formula_error\":8.881784197001252e-16,\"off_complement_mass\":3.5044581318203485,\"repetition\":0,\"residual_sum\":42.125558305506864,\"support\":\"two_orbit_6_3\"}"} | |
| {"case_id": "rigidity-023", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_6_3", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":0.7986195649658145,\"defect_sum\":2.3958586948974436,\"distance_squared\":0.48889410514130216,\"identity_error\":8.881784197001252e-16,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":2.9999999999999996,\"nearest_formula_error\":1.1102230246251565e-16,\"off_complement_mass\":1.5912498221710205,\"repetition\":1,\"residual_sum\":19.166869559179545,\"support\":\"two_orbit_6_3\"}"} | |
| {"case_id": "rigidity-024", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_6_3", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.1894659438342805,\"defect_sum\":3.5683978315028417,\"distance_squared\":0.7495265592988649,\"identity_error\":2.6645352591003757e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":2.9999999999999996,\"nearest_formula_error\":2.220446049250313e-16,\"off_complement_mass\":2.3769307388565,\"repetition\":2,\"residual_sum\":28.547182652022727,\"support\":\"two_orbit_6_3\"}"} | |
| {"case_id": "rigidity-025", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_8_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":3.7673697490319564,\"defect_sum\":7.534739498063913,\"distance_squared\":0.9291122952857397,\"identity_error\":5.329070518200751e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":5.999999999999999,\"nearest_formula_error\":3.3306690738754696e-16,\"off_complement_mass\":2.8530074471412705,\"repetition\":0,\"residual_sum\":60.27791598451126,\"support\":\"two_orbit_8_2\"}"} | |
| {"case_id": "rigidity-026", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_8_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":3.232014086742863,\"defect_sum\":6.464028173485726,\"distance_squared\":0.9022541719107953,\"identity_error\":1.7763568394002505e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":5.999999999999999,\"nearest_formula_error\":4.440892098500626e-16,\"off_complement_mass\":2.7949004471290206,\"repetition\":1,\"residual_sum\":51.71222538788581,\"support\":\"two_orbit_8_2\"}"} | |
| {"case_id": "rigidity-027", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_8_2", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.2390889493823813,\"defect_sum\":2.4781778987647627,\"distance_squared\":0.6106650583708573,\"identity_error\":8.881784197001252e-16,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":5.999999999999999,\"nearest_formula_error\":2.220446049250313e-16,\"off_complement_mass\":2.0635820054180574,\"repetition\":2,\"residual_sum\":19.825423190118105,\"support\":\"two_orbit_8_2\"}"} | |
| {"case_id": "rigidity-028", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_8_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.8240327607105467,\"defect_sum\":7.296131042842187,\"distance_squared\":1.203634267263367,\"identity_error\":8.881784197001252e-16,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":3.999999999999999,\"nearest_formula_error\":0.0,\"off_complement_mass\":3.3657657987741834,\"repetition\":0,\"residual_sum\":58.36904834273749,\"support\":\"two_orbit_8_4\"}"} | |
| {"case_id": "rigidity-029", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_8_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.1446394769137864,\"defect_sum\":8.578557907655146,\"distance_squared\":1.371247006503242,\"identity_error\":7.105427357601002e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":3.999999999999999,\"nearest_formula_error\":4.440892098500626e-16,\"off_complement_mass\":3.599547808919945,\"repetition\":1,\"residual_sum\":68.62846326124121,\"support\":\"two_orbit_8_4\"}"} | |
| {"case_id": "rigidity-030", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "two_orbit_8_4", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.836196877117987,\"defect_sum\":7.344787508471948,\"distance_squared\":1.1867880398608601,\"identity_error\":0.0,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":3.999999999999999,\"nearest_formula_error\":0.0,\"off_complement_mass\":3.292501088149211,\"repetition\":2,\"residual_sum\":58.758300067775586,\"support\":\"two_orbit_8_4\"}"} | |
| {"case_id": "rigidity-031", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "paired_random_subset_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":12.660485479005033,\"defect_sum\":25.320970958010065,\"distance_squared\":6.687520406600256,\"identity_error\":7.105427357601002e-15,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.5000000000000009,\"nearest_formula_error\":8.881784197001252e-16,\"off_complement_mass\":15.490890193786766,\"repetition\":0,\"residual_sum\":202.56776766408052,\"support\":\"paired_random_subset_6\"}"} | |
| {"case_id": "rigidity-032", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "paired_random_subset_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":11.561749363703115,\"defect_sum\":23.12349872740623,\"distance_squared\":6.262922406916063,\"identity_error\":1.0658141036401503e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.5000000000000009,\"nearest_formula_error\":1.7763568394002505e-15,\"off_complement_mass\":15.07513291592828,\"repetition\":1,\"residual_sum\":184.9879898192498,\"support\":\"paired_random_subset_6\"}"} | |
| {"case_id": "rigidity-033", "suite": "rigidity", "kind": "random_projection_rigidity", "case_name": "paired_random_subset_6", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":11.830037748322527,\"defect_sum\":23.660075496645053,\"distance_squared\":5.875834212100083,\"identity_error\":1.4210854715202004e-14,\"kind\":\"random_projection_rigidity\",\"largest_covariance_eigenvalue\":1.5000000000000009,\"nearest_formula_error\":1.7763568394002505e-15,\"off_complement_mass\":14.703867002221337,\"repetition\":2,\"residual_sum\":189.28060397316037,\"support\":\"paired_random_subset_6\"}"} | |
| {"case_id": "rigidity-034", "suite": "rigidity", "kind": "sharp_constant", "case_name": "sharp_constant", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.0,\"defect_sum\":4.0,\"delta\":2,\"distance_squared\":2.0,\"identity_error\":0.0,\"kind\":\"sharp_constant\",\"largest_covariance_eigenvalue\":2.0,\"n\":4,\"nearest_formula_error\":0.0,\"off_complement_mass\":4.0,\"residual_sum\":32.0}"} | |
| {"case_id": "rigidity-035", "suite": "rigidity", "kind": "sharp_constant", "case_name": "sharp_constant", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.0,\"defect_sum\":4.0,\"delta\":2,\"distance_squared\":2.0,\"identity_error\":0.0,\"kind\":\"sharp_constant\",\"largest_covariance_eigenvalue\":3.999999999999999,\"n\":6,\"nearest_formula_error\":0.0,\"off_complement_mass\":4.0,\"residual_sum\":32.0}"} | |
| {"case_id": "rigidity-036", "suite": "rigidity", "kind": "sharp_constant", "case_name": "sharp_constant", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.0,\"defect_sum\":6.0,\"delta\":3,\"distance_squared\":2.0,\"identity_error\":0.0,\"kind\":\"sharp_constant\",\"largest_covariance_eigenvalue\":2.9999999999999996,\"n\":6,\"nearest_formula_error\":0.0,\"off_complement_mass\":4.0,\"residual_sum\":48.0}"} | |
| {"case_id": "rigidity-037", "suite": "rigidity", "kind": "sharp_constant", "case_name": "sharp_constant", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.0,\"defect_sum\":8.0,\"delta\":4,\"distance_squared\":2.0,\"identity_error\":0.0,\"kind\":\"sharp_constant\",\"largest_covariance_eigenvalue\":3.999999999999999,\"n\":8,\"nearest_formula_error\":0.0,\"off_complement_mass\":4.0,\"residual_sum\":64.0}"} | |
| {"case_id": "rigidity-038", "suite": "rigidity", "kind": "exact_erasure_recovery", "case_name": "exact_erasure_recovery", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"erasure_locations_checked\":4,\"kind\":\"exact_erasure_recovery\",\"maximum_density_recovery_error\":2.185138360293623e-16,\"maximum_kl_error\":1.923402235133598e-16,\"maximum_post_erasure_collective_phase_error\":3.427483507053832e-16,\"maximum_recovery_completeness_error\":2.746544248410882e-16,\"n\":4,\"rank\":3}"} | |
| {"case_id": "rigidity-039", "suite": "rigidity", "kind": "exact_erasure_recovery", "case_name": "exact_erasure_recovery", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"erasure_locations_checked\":6,\"kind\":\"exact_erasure_recovery\",\"maximum_density_recovery_error\":1.217687788433933e-16,\"maximum_kl_error\":3.9253637702709275e-16,\"maximum_post_erasure_collective_phase_error\":1.5890470772125876e-16,\"maximum_recovery_completeness_error\":5.551115123125783e-16,\"n\":6,\"rank\":10}"} | |
| {"case_id": "rigidity-040", "suite": "rigidity", "kind": "exact_erasure_recovery", "case_name": "exact_erasure_recovery", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"erasure_locations_checked\":8,\"kind\":\"exact_erasure_recovery\",\"maximum_density_recovery_error\":5.494057971869168e-17,\"maximum_kl_error\":6.707834488976634e-16,\"maximum_post_erasure_collective_phase_error\":6.600545094896479e-17,\"maximum_recovery_completeness_error\":8.459621780138418e-16,\"n\":8,\"rank\":35}"} | |
| {"case_id": "rigidity-041", "suite": "rigidity", "kind": "central_sector_sharp_half_constant", "case_name": "central_sector_sharp_half_constant", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":2.0,\"defect_sum\":4.0,\"distance_squared\":2.0,\"expected_noncomplement_mass\":4,\"identity_error\":0.0,\"kind\":\"central_sector_sharp_half_constant\",\"largest_covariance_eigenvalue\":1.3333333333333335,\"n\":4,\"nearest_formula_error\":0.0,\"off_complement_mass\":4.0,\"residual_sum\":32.0}"} | |
| {"case_id": "rigidity-042", "suite": "rigidity", "kind": "central_sector_sharp_half_constant", "case_name": "central_sector_sharp_half_constant", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":6.0,\"defect_sum\":12.0,\"distance_squared\":6.0,\"expected_noncomplement_mass\":12,\"identity_error\":0.0,\"kind\":\"central_sector_sharp_half_constant\",\"largest_covariance_eigenvalue\":1.2000000000000013,\"n\":6,\"nearest_formula_error\":0.0,\"off_complement_mass\":12.0,\"residual_sum\":96.0}"} | |
| {"case_id": "rigidity-043", "suite": "rigidity", "kind": "central_sector_sharp_half_constant", "case_name": "central_sector_sharp_half_constant", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":20.0,\"defect_sum\":40.0,\"distance_squared\":20.0,\"expected_noncomplement_mass\":40,\"identity_error\":0.0,\"kind\":\"central_sector_sharp_half_constant\",\"largest_covariance_eigenvalue\":1.1428571428571441,\"n\":8,\"nearest_formula_error\":0.0,\"off_complement_mass\":40.0,\"residual_sum\":320.0}"} | |
| {"case_id": "rigidity-044", "suite": "rigidity", "kind": "central_four_noncomplement_swap_witness", "case_name": "central_four_noncomplement_swap_witness", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"bound\":1.9999999999999982,\"defect_sum\":3.9999999999999964,\"distance_squared\":1.9999999999999996,\"identity_error\":7.105427357601002e-15,\"kind\":\"central_four_noncomplement_swap_witness\",\"largest_covariance_eigenvalue\":1.3333333333333335,\"nearest_formula_error\":4.440892098500626e-16,\"off_complement_mass\":3.9999999999999982,\"residual_sum\":31.999999999999986}"} | |
| {"case_id": "rigidity-045", "suite": "rigidity", "kind": "balanced_joint_signatures", "case_name": "balanced_joint_signatures", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"antipodal_pairs\":2,\"kind\":\"balanced_joint_signatures\",\"maximum_scalar_compression_error\":3.163757407787533e-17}"} | |
| {"case_id": "rigidity-046", "suite": "rigidity", "kind": "individually_balanced_but_no_antipodal_joint_signature", "case_name": "individually_balanced_but_no_antipodal_joint_signature", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"anticommuting_matrix_kernel_dimension\":0,\"conclusion\":\"No nonzero matrix anticommutes with all three signature observables; hence no rank-two zero-compression projector.\",\"kind\":\"individually_balanced_but_no_antipodal_joint_signature\"}"} | |
| {"case_id": "rigidity-047", "suite": "rigidity", "kind": "sharp_joint_signature_imbalance_obstruction", "case_name": "sharp_joint_signature_imbalance_obstruction", "passed": true, "tolerance": 2e-09, "source_report": "results/recorded/verification_results.json", "details_json": "{\"defect_sum\":2.0,\"gamma\":1.0,\"gamma_delta_over_two\":2.0,\"identity_error\":0.0,\"kind\":\"sharp_joint_signature_imbalance_obstruction\",\"signature_imbalance_delta\":4}"} | |
| {"case_id": "real_minimax-001", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "complete_dephasing_2", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":2,\"duality_gap\":0.0,\"extremal_trace_norm_identity_error\":2.220446049250313e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"complete_dephasing_2\",\"simplex_minimum_lower\":0.5,\"simplex_minimum_upper\":0.5}"} | |
| {"case_id": "real_minimax-002", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "complete_dephasing_3", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":3,\"duality_gap\":0.0,\"extremal_trace_norm_identity_error\":0.0,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"complete_dephasing_3\",\"simplex_minimum_lower\":0.3333333333333333,\"simplex_minimum_upper\":0.3333333333333333}"} | |
| {"case_id": "real_minimax-003", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "complete_dephasing_5", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":5,\"duality_gap\":5.551115123125783e-17,\"extremal_trace_norm_identity_error\":2.220446049250313e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"complete_dephasing_5\",\"simplex_minimum_lower\":0.19999999999999998,\"simplex_minimum_upper\":0.20000000000000004}"} | |
| {"case_id": "real_minimax-004", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "complete_dephasing_8", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":8,\"duality_gap\":0.0,\"extremal_trace_norm_identity_error\":4.440892098500626e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"complete_dephasing_8\",\"simplex_minimum_lower\":0.125,\"simplex_minimum_upper\":0.125}"} | |
| {"case_id": "real_minimax-005", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "identity_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":5,\"duality_gap\":0.0,\"extremal_trace_norm_identity_error\":0.0,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"identity_channel\",\"simplex_minimum_lower\":1.0,\"simplex_minimum_upper\":1.0}"} | |
| {"case_id": "real_minimax-006", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "equicorrelation_3_0.15", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":3,\"duality_gap\":0.0,\"extremal_trace_norm_identity_error\":1.6653345369377348e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"equicorrelation_3_0.15\",\"simplex_minimum_lower\":0.8999999999999999,\"simplex_minimum_upper\":0.8999999999999999}"} | |
| {"case_id": "real_minimax-007", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "equicorrelation_4_0.5", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":4,\"duality_gap\":0.0,\"extremal_trace_norm_identity_error\":0.0,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"equicorrelation_4_0.5\",\"simplex_minimum_lower\":0.625,\"simplex_minimum_upper\":0.625}"} | |
| {"case_id": "real_minimax-008", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "equicorrelation_6_0.8", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":6,\"duality_gap\":1.1102230246251565e-16,\"extremal_trace_norm_identity_error\":0.0,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"equicorrelation_6_0.8\",\"simplex_minimum_lower\":0.33333333333333326,\"simplex_minimum_upper\":0.33333333333333337}"} | |
| {"case_id": "real_minimax-009", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "equicorrelation_7_1.0", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":7,\"duality_gap\":5.551115123125783e-17,\"extremal_trace_norm_identity_error\":0.0,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"equicorrelation_7_1.0\",\"simplex_minimum_lower\":0.14285714285714285,\"simplex_minimum_upper\":0.1428571428571429}"} | |
| {"case_id": "real_minimax-010", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "positive_gram_0", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":3,\"duality_gap\":1.9984014443252818e-15,\"extremal_trace_norm_identity_error\":8.881784197001252e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"positive_gram_0\",\"simplex_minimum_lower\":0.6213700328488412,\"simplex_minimum_upper\":0.6213700328488432}"} | |
| {"case_id": "real_minimax-011", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "positive_gram_1", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":4,\"duality_gap\":4.440892098500626e-16,\"extremal_trace_norm_identity_error\":2.220446049250313e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"positive_gram_1\",\"simplex_minimum_lower\":0.7404167206384591,\"simplex_minimum_upper\":0.7404167206384595}"} | |
| {"case_id": "real_minimax-012", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "positive_gram_2", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":5,\"duality_gap\":6.699179433411473e-09,\"extremal_trace_norm_identity_error\":2.7755575615628914e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"positive_gram_2\",\"simplex_minimum_lower\":0.8141084611961469,\"simplex_minimum_upper\":0.8141084678953263}"} | |
| {"case_id": "real_minimax-013", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "positive_gram_3", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":6,\"duality_gap\":2.4539518195254573e-08,\"extremal_trace_norm_identity_error\":9.43689570931383e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"positive_gram_3\",\"simplex_minimum_lower\":0.7937782047922277,\"simplex_minimum_upper\":0.7937782293317459}"} | |
| {"case_id": "real_minimax-014", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "positive_gram_4", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":3,\"duality_gap\":7.534185497704016e-09,\"extremal_trace_norm_identity_error\":1.1102230246251565e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"positive_gram_4\",\"simplex_minimum_lower\":0.8091438646799711,\"simplex_minimum_upper\":0.8091438722141566}"} | |
| {"case_id": "real_minimax-015", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "positive_gram_5", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":4,\"duality_gap\":0.0,\"extremal_trace_norm_identity_error\":4.440892098500626e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"positive_gram_5\",\"simplex_minimum_lower\":0.6626395688977935,\"simplex_minimum_upper\":0.6626395688977935}"} | |
| {"case_id": "real_minimax-016", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "positive_gram_6", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":5,\"duality_gap\":1.4980240825579472e-08,\"extremal_trace_norm_identity_error\":1.1657341758564144e-15,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"positive_gram_6\",\"simplex_minimum_lower\":0.8751023118594269,\"simplex_minimum_upper\":0.8751023268396677}"} | |
| {"case_id": "real_minimax-017", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "gaussian_phase_kernel_0", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":6,\"duality_gap\":2.4343192794873403e-08,\"extremal_trace_norm_identity_error\":2.220446049250313e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"gaussian_phase_kernel_0\",\"simplex_minimum_lower\":0.3979758079878891,\"simplex_minimum_upper\":0.3979758323310819}"} | |
| {"case_id": "real_minimax-018", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "gaussian_phase_kernel_1", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":6,\"duality_gap\":5.675690428752489e-08,\"extremal_trace_norm_identity_error\":8.881784197001252e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"gaussian_phase_kernel_1\",\"simplex_minimum_lower\":0.31554655229237527,\"simplex_minimum_upper\":0.31554660904927956}"} | |
| {"case_id": "real_minimax-019", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "gaussian_phase_kernel_2", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":6,\"duality_gap\":5.7524907060013675e-08,\"extremal_trace_norm_identity_error\":1.1102230246251565e-15,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"gaussian_phase_kernel_2\",\"simplex_minimum_lower\":0.22829575867965507,\"simplex_minimum_upper\":0.22829581620456213}"} | |
| {"case_id": "real_minimax-020", "suite": "real_minimax", "kind": "nonnegative_schur", "case_name": "nonnegative_five_cycle_correlation", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":5,\"duality_gap\":1.1102230246251565e-16,\"extremal_trace_norm_identity_error\":2.220446049250313e-16,\"kind\":\"nonnegative_schur\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"nonnegative_five_cycle_correlation\",\"simplex_minimum_lower\":0.43999999999999995,\"simplex_minimum_upper\":0.44000000000000006}"} | |
| {"case_id": "real_minimax-021", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.08409280341068093,\"closed_formula_error\":0.0,\"dimension\":2,\"duality_gap\":0.0,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":0.5678712915560191,\"minimum_eigenvalue\":-0.22032802231004056}"} | |
| {"case_id": "real_minimax-022", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.05824410756239129,\"closed_formula_error\":7.771561172376096e-16,\"dimension\":3,\"duality_gap\":4.440892098500626e-16,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":-0.031640835351991026,\"minimum_eigenvalue\":-0.6575866205242655}"} | |
| {"case_id": "real_minimax-023", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.3149194880223344,\"closed_formula_error\":1.1102230246251565e-16,\"dimension\":4,\"duality_gap\":2.220446049250313e-16,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":0.42425556093520056,\"minimum_eigenvalue\":-0.929857222247942}"} | |
| {"case_id": "real_minimax-024", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.06954378327834387,\"closed_formula_error\":2.220446049250313e-16,\"dimension\":5,\"duality_gap\":0.0,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":0.18988433688232376,\"minimum_eigenvalue\":-0.5305389985009228}"} | |
| {"case_id": "real_minimax-025", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.008150999047626506,\"closed_formula_error\":4.440892098500626e-16,\"dimension\":6,\"duality_gap\":2.220446049250313e-16,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":-0.20538770130919892,\"minimum_eigenvalue\":-0.44609034043043594}"} | |
| {"case_id": "real_minimax-026", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.038122120447065866,\"closed_formula_error\":2.220446049250313e-16,\"dimension\":2,\"duality_gap\":2.220446049250313e-16,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":-0.20984035222854214,\"minimum_eigenvalue\":-0.6928460416705158}"} | |
| {"case_id": "real_minimax-027", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.01864719952584548,\"closed_formula_error\":0.0,\"dimension\":3,\"duality_gap\":0.0,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":-0.6607170273803238,\"minimum_eigenvalue\":-0.89508039206931}"} | |
| {"case_id": "real_minimax-028", "suite": "real_minimax", "kind": "binary_closed_formula", "case_name": "binary_closed_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"closed_form_diamond_error\":0.15205795056509364,\"closed_formula_error\":2.220446049250313e-16,\"dimension\":4,\"duality_gap\":6.661338147750939e-16,\"kind\":\"binary_closed_formula\",\"maximum_eigenvalue\":0.9061344396037196,\"minimum_eigenvalue\":0.01664235623996535}"} | |
| {"case_id": "real_minimax-029", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":2,\"dimension\":2,\"duality_gap\":0.0,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":7.850462293418876e-17}"} | |
| {"case_id": "real_minimax-030", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":3,\"dimension\":3,\"duality_gap\":4.440892098500626e-16,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":3.1031676915590914e-17}"} | |
| {"case_id": "real_minimax-031", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":4,\"dimension\":4,\"duality_gap\":3.679029125791544e-08,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":8.312656720654792e-17}"} | |
| {"case_id": "real_minimax-032", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":2,\"dimension\":5,\"duality_gap\":2.220446049250313e-16,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":4.3394099949984434e-17}"} | |
| {"case_id": "real_minimax-033", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":3,\"dimension\":2,\"duality_gap\":0.0,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":1.1188630228279524e-16}"} | |
| {"case_id": "real_minimax-034", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":4,\"dimension\":3,\"duality_gap\":1.2972239504804861e-08,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":5.890401654755922e-17}"} | |
| {"case_id": "real_minimax-035", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":2,\"dimension\":4,\"duality_gap\":2.220446049250313e-16,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":4.291468873614597e-17}"} | |
| {"case_id": "real_minimax-036", "suite": "real_minimax", "kind": "orthogonal_flagged_commuting_channel", "case_name": "orthogonal_flagged_commuting_channel", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"branches\":3,\"dimension\":5,\"duality_gap\":2.220446049250313e-16,\"kind\":\"orthogonal_flagged_commuting_channel\",\"maximum_random_recovery_fidelity_excess\":0.0,\"polar_channel_identity_error\":4.366579663241769e-17}"} | |
| {"case_id": "real_minimax-037", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":3.734332842952881e-09,\"joint_simplex_minimum\":0.7169078557591799,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.7169078557591797,\"product_witness_duality_gap\":2.220446049250313e-16,\"tensorization_error\":2.220446049250313e-16}"} | |
| {"case_id": "real_minimax-038", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":4.815410070690973e-09,\"joint_simplex_minimum\":0.6793244932106453,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.6793244932106449,\"product_witness_duality_gap\":2.7028863591738173e-09,\"tensorization_error\":3.3306690738754696e-16}"} | |
| {"case_id": "real_minimax-039", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":1.944627059380366e-08,\"joint_simplex_minimum\":0.7748895194432603,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.7748895194432557,\"product_witness_duality_gap\":8.881784197001252e-16,\"tensorization_error\":4.6629367034256575e-15}"} | |
| {"case_id": "real_minimax-040", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":3.70505375268948e-08,\"joint_simplex_minimum\":0.548194885235034,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.548194885235033,\"product_witness_duality_gap\":1.043755126772794e-08,\"tensorization_error\":9.992007221626409e-16}"} | |
| {"case_id": "real_minimax-041", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":7.692072978571218e-09,\"joint_simplex_minimum\":0.740239207422857,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.7402392074228565,\"product_witness_duality_gap\":6.009549746721632e-09,\"tensorization_error\":4.440892098500626e-16}"} | |
| {"case_id": "real_minimax-042", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":1.6908874300725074e-09,\"joint_simplex_minimum\":0.5441104839685315,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.5441104839685321,\"product_witness_duality_gap\":1.0564919605826617e-08,\"tensorization_error\":6.661338147750939e-16}"} | |
| {"case_id": "real_minimax-043", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":2.077271243905443e-09,\"joint_simplex_minimum\":0.6598659779553401,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.6598659779553404,\"product_witness_duality_gap\":1.5019582022546274e-08,\"tensorization_error\":3.3306690738754696e-16}"} | |
| {"case_id": "real_minimax-044", "suite": "real_minimax", "kind": "tensorization", "case_name": "tensorization", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimensions\":[3,4],\"duality_gap\":4.259274333229257e-08,\"joint_simplex_minimum\":0.664207805279966,\"kind\":\"tensorization\",\"product_of_simplex_minima\":0.6642078052799629,\"product_witness_duality_gap\":6.783711370417222e-10,\"tensorization_error\":3.1086244689504383e-15}"} | |
| {"case_id": "real_minimax-045", "suite": "real_minimax", "kind": "real_schur_fixed_channel_only", "case_name": "signed_real_gram_0", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":4,\"duality_gap\":2.220446049250313e-16,\"extremal_trace_norm_identity_error\":6.661338147750939e-16,\"kind\":\"real_schur_fixed_channel_only\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"signed_real_gram_0\",\"simplex_minimum_lower\":0.5099269448398991,\"simplex_minimum_upper\":0.5099269448398993}"} | |
| {"case_id": "real_minimax-046", "suite": "real_minimax", "kind": "real_schur_fixed_channel_only", "case_name": "signed_real_gram_1", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":4,\"duality_gap\":2.7755575615628914e-17,\"extremal_trace_norm_identity_error\":0.0,\"kind\":\"real_schur_fixed_channel_only\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"signed_real_gram_1\",\"simplex_minimum_lower\":0.0915638764502865,\"simplex_minimum_upper\":0.09156387645028653}"} | |
| {"case_id": "real_minimax-047", "suite": "real_minimax", "kind": "real_schur_fixed_channel_only", "case_name": "signed_real_gram_2", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":4,\"duality_gap\":6.44247100736739e-08,\"extremal_trace_norm_identity_error\":6.661338147750939e-16,\"kind\":\"real_schur_fixed_channel_only\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"signed_real_gram_2\",\"simplex_minimum_lower\":0.026649081140140748,\"simplex_minimum_upper\":0.02664914556485082}"} | |
| {"case_id": "real_minimax-048", "suite": "real_minimax", "kind": "real_schur_fixed_channel_only", "case_name": "signed_real_gram_3", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"dimension\":4,\"duality_gap\":2.220446049250313e-16,\"extremal_trace_norm_identity_error\":4.440892098500626e-16,\"kind\":\"real_schur_fixed_channel_only\",\"maximum_random_input_bound_excess\":0.0,\"maximum_random_recovery_fidelity_excess\":0.0,\"name\":\"signed_real_gram_3\",\"simplex_minimum_lower\":0.3982457847096085,\"simplex_minimum_upper\":0.3982457847096087}"} | |
| {"case_id": "real_minimax-049", "suite": "real_minimax", "kind": "negative_phase_counterexample_to_identity_optimality", "case_name": "negative_phase_counterexample_to_identity_optimality", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"fixed_channel_diamond_error\":2.0,\"kind\":\"negative_phase_counterexample_to_identity_optimality\",\"phase_unitary_corrected_diamond_error\":0.0}"} | |
| {"case_id": "real_minimax-050", "suite": "real_minimax", "kind": "complex_phase_counterexample_to_real_distance_formula", "case_name": "complex_phase_counterexample_to_real_distance_formula", "passed": true, "tolerance": 5e-07, "source_report": "results/recorded/minimax_results.json", "details_json": "{\"fixed_channel_diamond_error\":1.4142135623730954,\"invalid_real_formula_value\":1.0,\"kind\":\"complex_phase_counterexample_to_real_distance_formula\"}"} | |
| {"case_id": "extensions-001", "suite": "extensions", "kind": "exact_tail_noncompletion", "case_name": "exact_tail_noncompletion", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"ambient_dimension\":8,\"check_method\":\"Exact tail counts, exhaustive cube-edge check, exact parity sum, and small covariance matrix; no global code projector allocated.\",\"complement_fourier_coefficient\":0.0,\"covariance_error\":0.0,\"even_count\":1,\"forbidden_cube_edges\":0,\"kind\":\"exact_tail_noncompletion\",\"largest_covariance_eigenvalue\":2.0,\"logical_coordinates\":3,\"maximum_code_rank_K\":4,\"nearest_maximal_code_squared_distance\":4,\"normalized_squared_distance\":1.0,\"odd_count\":1,\"physical_coordinates\":6,\"rank_deficit\":2,\"rank_fraction\":0.5,\"tail_code_rank_k\":2}"} | |
| {"case_id": "extensions-002", "suite": "extensions", "kind": "exact_tail_noncompletion", "case_name": "exact_tail_noncompletion", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"ambient_dimension\":128,\"check_method\":\"Exact tail counts, exhaustive cube-edge check, exact parity sum, and small covariance matrix; no global code projector allocated.\",\"complement_fourier_coefficient\":0.0,\"covariance_error\":0.0,\"even_count\":22,\"forbidden_cube_edges\":0,\"kind\":\"exact_tail_noncompletion\",\"largest_covariance_eigenvalue\":2.0,\"logical_coordinates\":7,\"maximum_code_rank_K\":64,\"nearest_maximal_code_squared_distance\":64,\"normalized_squared_distance\":1.0,\"odd_count\":22,\"physical_coordinates\":14,\"rank_deficit\":20,\"rank_fraction\":0.6875,\"tail_code_rank_k\":44}"} | |
| {"case_id": "extensions-003", "suite": "extensions", "kind": "exact_tail_noncompletion", "case_name": "exact_tail_noncompletion", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"ambient_dimension\":2048,\"check_method\":\"Exact tail counts, exhaustive cube-edge check, exact parity sum, and small covariance matrix; no global code projector allocated.\",\"complement_fourier_coefficient\":0.0,\"covariance_error\":0.0,\"even_count\":386,\"forbidden_cube_edges\":0,\"kind\":\"exact_tail_noncompletion\",\"largest_covariance_eigenvalue\":2.0,\"logical_coordinates\":11,\"maximum_code_rank_K\":1024,\"nearest_maximal_code_squared_distance\":1024,\"normalized_squared_distance\":1.0,\"odd_count\":386,\"physical_coordinates\":22,\"rank_deficit\":252,\"rank_fraction\":0.75390625,\"tail_code_rank_k\":772}"} | |
| {"case_id": "extensions-004", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.7805525878714797,\"ambient_dimension\":6,\"epsilon\":1.0407367838286397,\"eta\":3.9027629393573986,\"filter_distance\":1.1760053175324614,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_0\",\"largest_absolute_alpha\":0.4043164544894224,\"maximum_cs_spectral_error\":1.1102230246251565e-15,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":1.1102230246251565e-15,\"n\":4,\"phase_rounding_distance\":0.8267912736889521,\"rank\":3,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.7716113231648191}"} | |
| {"case_id": "extensions-005", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.8082136219589429,\"ambient_dimension\":6,\"epsilon\":1.077618162611924,\"eta\":4.041068109794715,\"filter_distance\":1.249490305143437,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_1\",\"largest_absolute_alpha\":0.11981175687913807,\"maximum_cs_spectral_error\":1.7763568394002505e-15,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":1.9984014443252818e-15,\"n\":4,\"phase_rounding_distance\":0.8344453737656846,\"rank\":3,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.985313265131095}"} | |
| {"case_id": "extensions-006", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.7528350099781873,\"ambient_dimension\":6,\"epsilon\":1.0037800133042498,\"eta\":3.764175049890937,\"filter_distance\":1.1738843926294478,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_2\",\"largest_absolute_alpha\":0.18929830839752568,\"maximum_cs_spectral_error\":8.881784197001252e-16,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":3.1086244689504383e-15,\"n\":4,\"phase_rounding_distance\":0.8980991841417518,\"rank\":3,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.9223042516552351}"} | |
| {"case_id": "extensions-007", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.7287188822997392,\"ambient_dimension\":6,\"epsilon\":0.9716251763996523,\"eta\":3.6435944114986962,\"filter_distance\":1.2462339792001271,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_3\",\"largest_absolute_alpha\":0.07775214972670193,\"maximum_cs_spectral_error\":6.123573870198129e-16,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":6.661338147750939e-16,\"n\":4,\"phase_rounding_distance\":0.5649611673296677,\"rank\":3,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.7871771036808791}"} | |
| {"case_id": "extensions-008", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.0004678397685157989,\"ambient_dimension\":6,\"epsilon\":0.0006237863580210652,\"eta\":0.0023391988425789947,\"filter_distance\":0.0009344720101306273,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"near_optimal_angle_0.001\",\"largest_absolute_alpha\":0.00024708909745892096,\"maximum_cs_spectral_error\":5.108760636751697e-16,\"maximum_filter_step_excess\":2.800494211530058e-16,\"maximum_operator_identity_error\":1.2899837448232532e-15,\"n\":4,\"phase_rounding_distance\":2.3986490262494946e-07,\"rank\":3,\"repair_bound\":0.0023391988425789947,\"repair_bound_is_nontrivial\":true,\"repair_distance\":0.00046721701957185094}"} | |
| {"case_id": "extensions-009", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.004679462812841089,\"ambient_dimension\":6,\"epsilon\":0.006239283750454786,\"eta\":0.02339731406420545,\"filter_distance\":0.009350244790147169,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"near_optimal_angle_0.01\",\"largest_absolute_alpha\":0.0024738499691705222,\"maximum_cs_spectral_error\":2.4296970685400154e-16,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":1.4866580189121237e-15,\"n\":4,\"phase_rounding_distance\":2.403562473968974e-05,\"rank\":3,\"repair_bound\":0.02339731406420545,\"repair_bound_is_nontrivial\":true,\"repair_distance\":0.004673245808919342}"} | |
| {"case_id": "extensions-010", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.02341827232658486,\"ambient_dimension\":6,\"epsilon\":0.031224363102113146,\"eta\":0.1170913616329243,\"filter_distance\":0.046863648029332024,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"near_optimal_angle_0.05\",\"largest_absolute_alpha\":0.012430131253702672,\"maximum_cs_spectral_error\":4.926614671774132e-16,\"maximum_filter_step_excess\":2.636779683484747e-16,\"maximum_operator_identity_error\":1.0408340855860843e-15,\"n\":4,\"phase_rounding_distance\":0.0006061581688637102,\"rank\":3,\"repair_bound\":0.1170913616329243,\"repair_bound_is_nontrivial\":true,\"repair_distance\":0.023387417222115285}"} | |
| {"case_id": "extensions-011", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.8672872992202268,\"ambient_dimension\":20,\"epsilon\":1.0407447590642722,\"eta\":6.071011094541587,\"filter_distance\":1.1664729014585378,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_0\",\"largest_absolute_alpha\":0.043870482654385534,\"maximum_cs_spectral_error\":1.3322676295501878e-15,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":1.3322676295501878e-15,\"n\":6,\"phase_rounding_distance\":0.9324325077135568,\"rank\":10,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.9991657041380794}"} | |
| {"case_id": "extensions-012", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.9087657498353113,\"ambient_dimension\":20,\"epsilon\":1.0905188998023736,\"eta\":6.361360248847179,\"filter_distance\":1.2999762929956797,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_1\",\"largest_absolute_alpha\":0.10671377769967356,\"maximum_cs_spectral_error\":1.6653345369377348e-15,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":1.7763568394002505e-15,\"n\":6,\"phase_rounding_distance\":0.9109838133132024,\"rank\":10,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.9919782639765727}"} | |
| {"case_id": "extensions-013", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.8948006988946718,\"ambient_dimension\":20,\"epsilon\":1.0737608386736062,\"eta\":6.263604892262702,\"filter_distance\":1.181851295269572,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_2\",\"largest_absolute_alpha\":0.07730720662095499,\"maximum_cs_spectral_error\":1.6653345369377348e-15,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":1.3322676295501878e-15,\"n\":6,\"phase_rounding_distance\":0.9464017037879779,\"rank\":10,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.981688835221462}"} | |
| {"case_id": "extensions-014", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.8889233213453149,\"ambient_dimension\":20,\"epsilon\":1.066707985614378,\"eta\":6.2224632494172045,\"filter_distance\":1.1898690100889715,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"random_3\",\"largest_absolute_alpha\":0.08854867093229488,\"maximum_cs_spectral_error\":1.6653345369377348e-15,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":1.3322676295501878e-15,\"n\":6,\"phase_rounding_distance\":0.9133317946688062,\"rank\":10,\"repair_bound\":1.0,\"repair_bound_is_nontrivial\":false,\"repair_distance\":0.9871340851640318}"} | |
| {"case_id": "extensions-015", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.0008573478690833191,\"ambient_dimension\":20,\"epsilon\":0.001028817442899983,\"eta\":0.0060014350835832335,\"filter_distance\":0.0013614446440653213,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"near_optimal_angle_0.001\",\"largest_absolute_alpha\":0.00010731135669441445,\"maximum_cs_spectral_error\":3.211406834902064e-16,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":3.622102617839573e-15,\"n\":6,\"phase_rounding_distance\":3.6801321963594164e-07,\"rank\":10,\"repair_bound\":0.0060014350835832335,\"repair_bound_is_nontrivial\":true,\"repair_distance\":0.0006807160470301857}"} | |
| {"case_id": "extensions-016", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.008569521769096927,\"ambient_dimension\":20,\"epsilon\":0.01028342612291631,\"eta\":0.05998665238367848,\"filter_distance\":0.013614408428943792,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"near_optimal_angle_0.01\",\"largest_absolute_alpha\":0.0010743476173559867,\"maximum_cs_spectral_error\":5.685556192513985e-16,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":2.4390212072233908e-15,\"n\":6,\"phase_rounding_distance\":3.683500782206512e-05,\"rank\":10,\"repair_bound\":0.05998665238367848,\"repair_bound_is_nontrivial\":true,\"repair_distance\":0.006806653282143295}"} | |
| {"case_id": "extensions-017", "suite": "extensions", "kind": "central_operator_repair", "case_name": "central_operator_repair", "passed": true, "tolerance": 3e-09, "source_report": "results/recorded/extensions_results.json", "details_json": "{\"alpha_bound\":0.042743795612027013,\"ambient_dimension\":20,\"epsilon\":0.05129255473443242,\"eta\":0.2992065692841891,\"filter_distance\":0.0680421120366015,\"filter_selection_error\":0.0,\"kind\":\"central_operator_repair\",\"label\":\"near_optimal_angle_0.05\",\"largest_absolute_alpha\":0.005396865984554082,\"maximum_cs_spectral_error\":4.0939474033052647e-16,\"maximum_filter_step_excess\":0.0,\"maximum_operator_identity_error\":2.5396351688300456e-15,\"n\":6,\"phase_rounding_distance\":0.0009243464851576485,\"rank\":10,\"repair_bound\":0.2992065692841891,\"repair_bound_is_nontrivial\":true,\"repair_distance\":0.03401579511491887}"} | |
| {"case_id": "complex-001", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "phase_unitary_2", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":1.0,\"analytic_value_error\":3.1611047113244695e-10,\"diamond_formula_error\":6.004783375066515e-10,\"dimension\":2,\"direct_diamond_value\":3.174260475824232e-11,\"dual_value\":0.9999999999501948,\"explicit_decoder_lower_value\":0.999999999,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":9.516731847014626e-11,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":3.466747473946242e-16,\"largest_raw_psd_violation\":2.4902385709069108e-11,\"name\":\"phase_unitary_2\",\"packing_reciprocity_error\":9.122922417503787e-10,\"packing_value\":0.9999999999925404,\"primal_dual_gap\":2.663053111362501e-10,\"primal_value\":0.9999999996838895,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":1.0000000199999999,\"rounded_gap\":8.021678898906259e-08,\"rounded_primal_lower\":0.9999999397832109,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":1.0000000003941025,\"state_cap_duality_gap\":1.2989351816372618e-09,\"state_cap_hadamard_value_error\":5.887221821154753e-10,\"state_cap_rank\":1,\"state_cap_value\":0.9999999990951673}"} | |
| {"case_id": "complex-002", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "phase_unitary_3", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":1.0,\"analytic_value_error\":7.599176843342548e-11,\"diamond_formula_error\":2.360597202354364e-10,\"dimension\":3,\"direct_diamond_value\":-8.407618336858542e-11,\"dual_value\":0.9999999998307021,\"explicit_decoder_lower_value\":0.9999999989999994,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":1.1118739262627741e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":1.5967962526346484e-15,\"largest_raw_psd_violation\":5.643255307496986e-11,\"name\":\"phase_unitary_3\",\"packing_reciprocity_error\":1.1159331236854086e-09,\"packing_value\":0.9999999999952549,\"primal_dual_gap\":9.330614059166464e-11,\"primal_value\":0.9999999999240082,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":1.00000003,\"rounded_gap\":1.0666666583336593e-07,\"rounded_primal_lower\":0.9999999233333342,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":1.0000000001466423,\"state_cap_duality_gap\":1.25783028437354e-09,\"state_cap_hadamard_value_error\":1.0351962620447352e-09,\"state_cap_rank\":1,\"state_cap_value\":0.999999998888812}"} | |
| {"case_id": "complex-003", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "phase_unitary_4", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":1.0,\"analytic_value_error\":3.677164128745858e-10,\"diamond_formula_error\":7.451339103421473e-10,\"dimension\":4,\"direct_diamond_value\":-9.701084592975723e-12,\"dual_value\":0.9999999992120239,\"explicit_decoder_lower_value\":0.9999999989999991,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":9.905721798375566e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":4.245000760025271e-16,\"largest_raw_psd_violation\":1.9699263054118177e-10,\"name\":\"phase_unitary_4\",\"packing_reciprocity_error\":9.33142452197444e-12,\"packing_value\":1.0000000000000973,\"primal_dual_gap\":4.2025971591641564e-10,\"primal_value\":0.9999999996322836,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":1.00000004,\"rounded_gap\":1.250668232311014e-07,\"rounded_primal_lower\":0.9999999149331767,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":1.000000000003724,\"state_cap_duality_gap\":1.3152590128129305e-11,\"state_cap_hadamard_value_error\":3.582877328156542e-10,\"state_cap_rank\":1,\"state_cap_value\":0.9999999999905713}"} | |
| {"case_id": "complex-004", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "phase_unitary_5", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":1.0,\"analytic_value_error\":8.282956542871034e-10,\"diamond_formula_error\":1.0837798008724403e-09,\"dimension\":5,\"direct_diamond_value\":5.728115077017664e-10,\"dual_value\":0.9999999986294694,\"explicit_decoder_lower_value\":0.9999999989999993,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":9.927474398097047e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":2.5226461455635714e-16,\"largest_raw_psd_violation\":2.741169929931786e-10,\"name\":\"phase_unitary_5\",\"packing_reciprocity_error\":6.295408638834488e-12,\"packing_value\":1.000000000000958,\"primal_dual_gap\":5.422349236283708e-10,\"primal_value\":0.9999999991717043,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":1.00000005,\"rounded_gap\":1.4025931327488195e-07,\"rounded_primal_lower\":0.9999999097406866,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":1.000000000010374,\"state_cap_duality_gap\":1.7627233006578535e-11,\"state_cap_hadamard_value_error\":8.210423452226223e-10,\"state_cap_rank\":1,\"state_cap_value\":0.9999999999927467}"} | |
| {"case_id": "complex-005", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "complete_dephasing_2", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.5,\"analytic_value_error\":7.77279351993343e-11,\"diamond_formula_error\":1.764990376074138e-10,\"dimension\":2,\"direct_diamond_value\":0.9999999999789568,\"dual_value\":0.5000000000070328,\"explicit_decoder_lower_value\":0.4999999994802036,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":5.750132037185551e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":0.0,\"largest_raw_psd_violation\":5.35879673968509e-12,\"name\":\"complete_dephasing_2\",\"packing_reciprocity_error\":1.8812795765654755e-10,\"packing_value\":1.9999999999672606,\"primal_dual_gap\":8.476075397112481e-11,\"primal_value\":0.49999999992227206,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.5000000200177505,\"rounded_gap\":2.501775048235899e-08,\"rounded_primal_lower\":0.499999995,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.500000000394106,\"state_cap_duality_gap\":3.388891389732862e-10,\"state_cap_hadamard_value_error\":1.32944766306764e-10,\"state_cap_rank\":2,\"state_cap_value\":0.5000000000552168}"} | |
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| {"case_id": "complex-018", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "random_complex_1", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":3.988296914947398e-09,\"dimension\":3,\"direct_diamond_value\":0.5825807613110184,\"dual_value\":0.708709619236958,\"explicit_decoder_lower_value\":0.7087096179697886,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":8.000516915629419e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":6.018197365098367e-16,\"largest_raw_psd_violation\":3.691523329343099e-11,\"name\":\"random_complex_1\",\"packing_reciprocity_error\":1.0855365495388014e-09,\"packing_value\":1.4110151361659855,\"primal_dual_gap\":1.8866156414887314e-09,\"primal_value\":0.7087096173503423,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.7087096492378366,\"rounded_gap\":7.340317165205335e-08,\"rounded_primal_lower\":0.708709575834665,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.7087096192621339,\"state_cap_duality_gap\":4.922936502893549e-10,\"state_cap_hadamard_value_error\":1.4194979636172889e-09,\"state_cap_rank\":3,\"state_cap_value\":0.7087096187698403}"} | |
| {"case_id": "complex-019", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "random_complex_2", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":3.6221083909993013e-09,\"dimension\":4,\"direct_diamond_value\":0.7902123866690445,\"dual_value\":0.6048938081655473,\"explicit_decoder_lower_value\":0.6048938053631085,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":1.0435686759180385e-09,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":5.821568012393098e-16,\"largest_raw_psd_violation\":1.5957077751531876e-10,\"name\":\"random_complex_2\",\"packing_reciprocity_error\":5.155460280903412e-09,\"packing_value\":1.653182734374341,\"primal_dual_gap\":3.311123708549246e-09,\"primal_value\":0.6048938048544236,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.6048938485117732,\"rounded_gap\":8.282091379374634e-08,\"rounded_primal_lower\":0.6048937656908594,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.6048938082941454,\"state_cap_duality_gap\":1.887468181749341e-09,\"state_cap_hadamard_value_error\":1.5522536589429592e-09,\"state_cap_rank\":4,\"state_cap_value\":0.6048938064066772}"} | |
| {"case_id": "complex-020", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "random_complex_3", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":3.3174356595111476e-09,\"dimension\":5,\"direct_diamond_value\":1.0000000073965611,\"dual_value\":0.49999999711715115,\"explicit_decoder_lower_value\":0.4999999994900978,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":5.087593679675706e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":8.817194000891222e-16,\"largest_raw_psd_violation\":8.606853954723178e-10,\"name\":\"random_complex_3\",\"packing_reciprocity_error\":8.471245926955362e-11,\"packing_value\":1.999999999919859,\"primal_dual_gap\":2.4741496074121017e-09,\"primal_value\":0.49999999464300154,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.5000000519255641,\"rounded_gap\":7.715789612783297e-08,\"rounded_primal_lower\":0.49999997476766794,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.5000000000415373,\"state_cap_duality_gap\":4.26801372022112e-11,\"state_cap_hadamard_value_error\":5.3558556478705555e-09,\"state_cap_rank\":2,\"state_cap_value\":0.4999999999988572}"} | |
| {"case_id": "complex-021", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "random_complex_4", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":1.0695311303265953e-10,\"dimension\":2,\"direct_diamond_value\":0.5213858186422347,\"dual_value\":0.7393070907560944,\"explicit_decoder_lower_value\":0.7393070899160371,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":7.585003736210183e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":8.319568169893044e-17,\"largest_raw_psd_violation\":4.599010061667741e-11,\"name\":\"random_complex_4\",\"packing_reciprocity_error\":2.927391662410628e-11,\"packing_value\":1.3526178939606357,\"primal_dual_gap\":1.3068823800921336e-10,\"primal_value\":0.7393070906254061,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.7393071108480742,\"rounded_gap\":5.1516509724791604e-08,\"rounded_primal_lower\":0.7393070593315645,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.7393070906947642,\"state_cap_duality_gap\":2.0226709196435877e-11,\"state_cap_hadamard_value_error\":4.913136564255183e-11,\"state_cap_rank\":2,\"state_cap_value\":0.7393070906745375}"} | |
| {"case_id": "complex-022", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "random_complex_5", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":1.0669147565423032e-08,\"dimension\":3,\"direct_diamond_value\":1.1431581011093,\"dual_value\":0.42842095025905,\"explicit_decoder_lower_value\":0.42842094913614914,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":4.0456099581476224e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":5.330399243400339e-16,\"largest_raw_psd_violation\":6.550185347597354e-10,\"name\":\"random_complex_5\",\"packing_reciprocity_error\":5.4749107469831415e-09,\"packing_value\":2.3341528903441495,\"primal_dual_gap\":6.148273778983082e-09,\"primal_value\":0.42842094411077625,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.4284209807964783,\"rounded_gap\":4.855037799567086e-08,\"rounded_primal_lower\":0.4284209322461003,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.4284209505351903,\"state_cap_duality_gap\":9.944801648842372e-10,\"state_cap_hadamard_value_error\":5.429933891409888e-09,\"state_cap_rank\":3,\"state_cap_value\":0.42842094954071014}"} | |
| {"case_id": "complex-023", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "random_complex_6", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":4.212760029709273e-09,\"dimension\":4,\"direct_diamond_value\":0.9324888725877328,\"dual_value\":0.5337555634921769,\"explicit_decoder_lower_value\":0.5337555628538896,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":6.331989377272862e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":1.006501637075875e-15,\"largest_raw_psd_violation\":1.7056037929037684e-10,\"name\":\"random_complex_6\",\"packing_reciprocity_error\":9.289629065989402e-10,\"packing_value\":1.8735167704314726,\"primal_dual_gap\":1.892423329152848e-09,\"primal_value\":0.5337555615997536,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.5337556046073543,\"rounded_gap\":6.413455277964886e-08,\"rounded_primal_lower\":0.5337555404728015,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.5337555637583671,\"state_cap_duality_gap\":2.712785551750585e-10,\"state_cap_hadamard_value_error\":1.887334954986386e-09,\"state_cap_rank\":2,\"state_cap_value\":0.5337555634870885}"} | |
| {"case_id": "complex-024", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "random_complex_7", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":2.7276463310244026e-09,\"dimension\":5,\"direct_diamond_value\":1.0950511035104127,\"dual_value\":0.4524744472077895,\"explicit_decoder_lower_value\":0.4524744487571359,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":4.932340091912124e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":3.2969024564432995e-16,\"largest_raw_psd_violation\":1.7332298819235644e-09,\"name\":\"random_complex_7\",\"packing_reciprocity_error\":1.3567205137121618e-09,\"packing_value\":2.210069543247919,\"primal_dual_gap\":3.2681901629416643e-10,\"primal_value\":0.4524744468809705,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.4524745022948905,\"rounded_gap\":7.821333919411089e-08,\"rounded_primal_lower\":0.4524744240815513,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.4524744496090266,\"state_cap_duality_gap\":3.5865671543788835e-10,\"state_cap_hadamard_value_error\":2.3693993989049034e-09,\"state_cap_rank\":3,\"state_cap_value\":0.4524744492503699}"} | |
| {"case_id": "complex-025", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "sic_analytic_t_0.0", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.25,\"analytic_value_error\":2.203809357226305e-10,\"diamond_formula_error\":1.4276373194732628e-08,\"dimension\":4,\"direct_diamond_value\":1.4999999861643887,\"dual_value\":0.24999999993351613,\"explicit_decoder_lower_value\":0.24999999975,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":2.4286817001950567e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":1.1107649934270853e-16,\"largest_raw_psd_violation\":1.3060948156340402e-11,\"name\":\"sic_analytic_t_0.0\",\"packing_reciprocity_error\":1.4023404659724292e-10,\"packing_value\":3.9999999999738756,\"primal_dual_gap\":1.5389706176094364e-10,\"primal_value\":0.24999999977961906,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.25000004000951404,\"rounded_gap\":4.250951404771719e-08,\"rounded_primal_lower\":0.2499999975,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.250000000008567,\"state_cap_duality_gap\":1.5698803368380254e-11,\"state_cap_hadamard_value_error\":2.1324911281261905e-10,\"state_cap_rank\":4,\"state_cap_value\":0.24999999999286818}"} | |
| {"case_id": "complex-026", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "sic_analytic_t_0.2", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.3,\"analytic_value_error\":9.572008741187688e-10,\"diamond_formula_error\":1.9013008945023557e-09,\"dimension\":4,\"direct_diamond_value\":1.400000000013101,\"dual_value\":0.2999999910536818,\"explicit_decoder_lower_value\":0.29999999949005424,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":1.9051987765195122e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":4.94053036697312e-16,\"largest_raw_psd_violation\":2.6058782718849685e-09,\"name\":\"sic_analytic_t_0.2\",\"packing_reciprocity_error\":3.021577210660098e-09,\"packing_value\":3.333333333860933,\"primal_dual_gap\":7.989117312146021e-09,\"primal_value\":0.2999999990427991,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.30000004000000635,\"rounded_gap\":4.830873651107126e-08,\"rounded_primal_lower\":0.29999999169126984,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.2999999999774441,\"state_cap_duality_gap\":2.968699730487856e-10,\"state_cap_hadamard_value_error\":6.377749994790349e-10,\"state_cap_rank\":4,\"state_cap_value\":0.2999999996805741}"} | |
| {"case_id": "complex-027", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "sic_analytic_t_0.65", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.4125,\"analytic_value_error\":7.652431466276255e-10,\"diamond_formula_error\":7.916802768903608e-10,\"dimension\":4,\"direct_diamond_value\":1.175000000738806,\"dual_value\":0.4124999998118796,\"explicit_decoder_lower_value\":0.4124999995874999,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":3.5596692260497775e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":3.631494990456004e-16,\"largest_raw_psd_violation\":3.61518873984314e-11,\"name\":\"sic_analytic_t_0.65\",\"packing_reciprocity_error\":6.564864207803112e-10,\"packing_value\":2.4242424239181806,\"primal_dual_gap\":5.771227939987966e-10,\"primal_value\":0.41249999923475683,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.41250004000044055,\"rounded_gap\":6.088663051517784e-08,\"rounded_primal_lower\":0.41249997911381003,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.4125000003180374,\"state_cap_duality_gap\":3.745705967617141e-10,\"state_cap_hadamard_value_error\":7.08709979591049e-10,\"state_cap_rank\":4,\"state_cap_value\":0.4124999999434668}"} | |
| {"case_id": "complex-028", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "sic_analytic_t_1.0", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.5,\"analytic_value_error\":1.7789070216878144e-10,\"diamond_formula_error\":6.508993344311875e-11,\"dimension\":4,\"direct_diamond_value\":1.0000000002906915,\"dual_value\":0.49999999996101074,\"explicit_decoder_lower_value\":0.49999999933755834,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":6.130574381479903e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":3.920759305987645e-16,\"largest_raw_psd_violation\":2.510233942370124e-11,\"name\":\"sic_analytic_t_1.0\",\"packing_reciprocity_error\":2.083366812399845e-10,\"packing_value\":1.9999999999892004,\"primal_dual_gap\":1.3890144590078535e-10,\"primal_value\":0.4999999998221093,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.500000040061421,\"rounded_gap\":7.018147796244989e-08,\"rounded_primal_lower\":0.499999969879943,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.5000000000185154,\"state_cap_duality_gap\":6.789963036268887e-11,\"state_cap_hadamard_value_error\":1.2850648323237124e-10,\"state_cap_rank\":2,\"state_cap_value\":0.4999999999506158}"} | |
| {"case_id": "complex-029", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "harmonic_tight_frame_t_0.0", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.2,\"analytic_value_error\":2.537708931882321e-10,\"diamond_formula_error\":6.136819274971117e-09,\"dimension\":5,\"direct_diamond_value\":1.5999999943707224,\"dual_value\":0.19999999989851774,\"explicit_decoder_lower_value\":0.19999999980000002,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":1.8941376245251718e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":0.0,\"largest_raw_psd_violation\":1.5166333466876125e-11,\"name\":\"harmonic_tight_frame_t_0.0\",\"packing_reciprocity_error\":2.992583958416617e-10,\"packing_value\":4.999999999965397,\"primal_dual_gap\":1.5228862615401795e-10,\"primal_value\":0.19999999974622912,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.2000000500109675,\"rounded_gap\":5.2010967505067285e-08,\"rounded_primal_lower\":0.19999999799999998,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.20000000000660162,\"state_cap_duality_gap\":1.7187834489007514e-11,\"state_cap_hadamard_value_error\":2.431846668482507e-10,\"state_cap_rank\":5,\"state_cap_value\":0.19999999998941378}"} | |
| {"case_id": "complex-030", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "harmonic_tight_frame_t_0.35", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.305,\"analytic_value_error\":1.8028245563073142e-11,\"diamond_formula_error\":5.368037125919045e-10,\"dimension\":5,\"direct_diamond_value\":1.3900000005728603,\"dual_value\":0.30499997402148016,\"explicit_decoder_lower_value\":0.30499999945754663,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":1.7096107862712984e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":2.606477468364402e-16,\"largest_raw_psd_violation\":1.0209008128583515e-08,\"name\":\"harmonic_tight_frame_t_0.35\",\"packing_reciprocity_error\":4.279054000022597e-09,\"packing_value\":3.2786885243045774,\"primal_dual_gap\":2.5960491589760437e-08,\"primal_value\":0.30499999998197175,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.3050000561596411,\"rounded_gap\":6.971786986609274e-08,\"rounded_primal_lower\":0.30499998644177123,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.30500000000196476,\"state_cap_duality_gap\":3.734570430680151e-10,\"state_cap_hadamard_value_error\":3.534640358182628e-10,\"state_cap_rank\":5,\"state_cap_value\":0.3049999996285077}"} | |
| {"case_id": "complex-031", "suite": "complex", "kind": "independent_primal_dual_direct_sdp", "case_name": "harmonic_tight_frame_t_1.0", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"analytic_value\":0.5,\"analytic_value_error\":1.7131371876644153e-09,\"diamond_formula_error\":5.71354963341264e-10,\"dimension\":5,\"direct_diamond_value\":1.0000000028549194,\"dual_value\":0.499999999526008,\"explicit_decoder_lower_value\":0.4999999993744942,\"explicit_decoder_psd_violation\":0.0,\"explicit_decoder_value_gap\":6.047742862058669e-10,\"kind\":\"independent_primal_dual_direct_sdp\",\"kraus_composition_error\":5.414660748592615e-16,\"largest_raw_psd_violation\":8.84679284291806e-11,\"name\":\"harmonic_tight_frame_t_1.0\",\"packing_reciprocity_error\":8.986322796999957e-11,\"packing_value\":1.9999999999930629,\"primal_dual_gap\":1.2391451753579474e-09,\"primal_value\":0.4999999982868628,\"rounded_dual_psd_violation\":0.0,\"rounded_dual_upper\":0.5000000500009861,\"rounded_gap\":8.636127735162091e-08,\"rounded_primal_lower\":0.4999999636397088,\"rounded_primal_psd_violation\":0.0,\"state_cap_dual_value\":0.5000000000167826,\"state_cap_duality_gap\":3.751410293517665e-11,\"state_cap_hadamard_value_error\":1.6924056600586823e-09,\"state_cap_rank\":2,\"state_cap_value\":0.4999999999792685}"} | |
| {"case_id": "complex-032", "suite": "complex", "kind": "complex_tensorization", "case_name": "complex_tensorization", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":1.5696247968044474e-08,\"dimensions\":[2,3],\"joint_value\":0.6517392955819638,\"kind\":\"complex_tensorization\",\"largest_raw_psd_violation\":1.3836261326939629e-09,\"primal_dual_gap\":6.404140884264109e-09,\"product_value\":0.6517393015030947,\"tensorization_error\":5.92113091890667e-09}"} | |
| {"case_id": "complex-033", "suite": "complex", "kind": "complex_tensorization", "case_name": "complex_tensorization", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":1.7719216538480964e-08,\"dimensions\":[2,4],\"joint_value\":0.5562688271024971,\"kind\":\"complex_tensorization\",\"largest_raw_psd_violation\":2.1568664903259883e-08,\"primal_dual_gap\":7.43123519386657e-08,\"product_value\":0.5562688246468183,\"tensorization_error\":2.455678882462564e-09}"} | |
| {"case_id": "complex-034", "suite": "complex", "kind": "complex_tensorization", "case_name": "complex_tensorization", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"diamond_formula_error\":1.101110660428617e-07,\"dimensions\":[3,4],\"joint_value\":0.428694058753619,\"kind\":\"complex_tensorization\",\"largest_raw_psd_violation\":6.405247020922599e-09,\"primal_dual_gap\":2.5488577859444916e-08,\"product_value\":0.4286940569759712,\"tensorization_error\":1.7776478067332846e-09}"} | |
| {"case_id": "complex-035", "suite": "complex", "kind": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "case_name": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":2,\"fidelity_upper_violation\":0.0,\"kind\":\"arbitrary_cptp_recovery_worst_fidelity_upper_check\",\"optimal_recovery_upper\":0.9196140210182415,\"random_recovery_worst_fidelity\":0.09102763382487988}"} | |
| {"case_id": "complex-036", "suite": "complex", "kind": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "case_name": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":3,\"fidelity_upper_violation\":0.0,\"kind\":\"arbitrary_cptp_recovery_worst_fidelity_upper_check\",\"optimal_recovery_upper\":0.708709619236958,\"random_recovery_worst_fidelity\":0.03843430858812062}"} | |
| {"case_id": "complex-037", "suite": "complex", "kind": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "case_name": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":4,\"fidelity_upper_violation\":0.0,\"kind\":\"arbitrary_cptp_recovery_worst_fidelity_upper_check\",\"optimal_recovery_upper\":0.6048938081655473,\"random_recovery_worst_fidelity\":0.016208266603478804}"} | |
| {"case_id": "complex-038", "suite": "complex", "kind": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "case_name": "arbitrary_cptp_recovery_worst_fidelity_upper_check", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":5,\"fidelity_upper_violation\":0.0,\"kind\":\"arbitrary_cptp_recovery_worst_fidelity_upper_check\",\"optimal_recovery_upper\":0.49999999711715115,\"random_recovery_worst_fidelity\":5.615635281812756e-12}"} | |
| {"case_id": "complex-039", "suite": "complex", "kind": "optimal_recovery_worst_fidelity_equality", "case_name": "optimal_recovery_worst_fidelity_equality", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":2,\"fidelity_equality_error\":4.1755761071016195e-08,\"kind\":\"optimal_recovery_worst_fidelity_equality\",\"optimized_worst_fidelity\":0.9196139800487645,\"sdp_value\":0.9196140218045256}"} | |
| {"case_id": "complex-040", "suite": "complex", "kind": "optimal_recovery_worst_fidelity_equality", "case_name": "optimal_recovery_worst_fidelity_equality", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":3,\"fidelity_equality_error\":3.4102941248725926e-08,\"kind\":\"optimal_recovery_worst_fidelity_equality\",\"optimized_worst_fidelity\":0.7087095832474011,\"sdp_value\":0.7087096173503423}"} | |
| {"case_id": "complex-041", "suite": "complex", "kind": "optimal_recovery_worst_fidelity_equality", "case_name": "optimal_recovery_worst_fidelity_equality", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":4,\"fidelity_equality_error\":3.270771720131904e-08,\"kind\":\"optimal_recovery_worst_fidelity_equality\",\"optimized_worst_fidelity\":0.6048937721467064,\"sdp_value\":0.6048938048544236}"} | |
| {"case_id": "complex-042", "suite": "complex", "kind": "optimal_recovery_worst_fidelity_equality", "case_name": "optimal_recovery_worst_fidelity_equality", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"dimension\":5,\"fidelity_equality_error\":1.4844316220674614e-08,\"kind\":\"optimal_recovery_worst_fidelity_equality\",\"optimized_worst_fidelity\":0.4999999797986853,\"sdp_value\":0.49999999464300154}"} | |
| {"case_id": "complex-043", "suite": "complex", "kind": "phase_unitary_recovery_contrast", "case_name": "phase_unitary_recovery_contrast", "passed": true, "tolerance": 3e-06, "source_report": "results/recorded/complex_recovery_results.json", "details_json": "{\"kind\":\"phase_unitary_recovery_contrast\",\"optimal_corrected_diamond_error\":0.0,\"recovered_correlation_residual\":0.0,\"uncorrected_diamond_error\":1.4142135623730951}"} | |