{ "release": "3.0.0", "seed": 2026101303, "status": "PASS", "python": "3.13.5", "numpy": "2.3.5", "scipy": "1.17.0", "groups": [ { "name": "two_matrix_primal_dual_certificates", "status": "PASS", "cases": 150, "max_residual": 1.636954875243968e-14, "interpretation": "" }, { "name": "determinant_budget_reconstruction", "status": "PASS", "cases": 400, "max_residual": 6.661338147750939e-15, "interpretation": "" }, { "name": "noncommuting_closed_form_frontier", "status": "PASS", "cases": 61, "max_residual": 9.931705480248354e-08, "interpretation": "All B regimes, including the transition." }, { "name": "primal_dual_frontier_bracketing", "status": "PASS", "cases": 4, "max_residual": 8.871813453881217e-07, "interpretation": "Floating bounds; exact formula is an independent comparator." }, { "name": "general_noncommuting_envelope_solver", "status": "PASS", "cases": 45, "max_residual": 3.600000001185988e-06, "interpretation": "Known-certificate families, d=2..6." }, { "name": "tensor_envelope_certificates", "status": "PASS", "cases": 35, "max_residual": 7.549516567451064e-15, "interpretation": "Includes ten independent 4D barrier comparisons." }, { "name": "direct_sum_envelope_composition", "status": "PASS", "cases": 25, "max_residual": 4.596917872165076e-07, "interpretation": "" }, { "name": "nonassociative_memory_witness", "status": "PASS", "cases": 1, "max_residual": 1.414216598501613e-07, "interpretation": "" }, { "name": "common_envelope_memory_domination", "status": "PASS", "cases": 150, "max_residual": 0.0, "interpretation": "" }, { "name": "exact_infinite_ellipsoid_witness", "status": "PASS", "cases": 300, "max_residual": 4.440892098500626e-16, "interpretation": "" }, { "name": "ellipsoid_two_resource_primal_dual_LP", "status": "PASS", "cases": 120, "max_residual": 1.1102230246251565e-16, "interpretation": "" }, { "name": "passive_unitary_dilation_identity", "status": "PASS", "cases": 200, "max_residual": 7.689044769142466e-15, "interpretation": "Standard operator identity, no hardware." }, { "name": "calibration_spectral_Lipschitz", "status": "PASS", "cases": 200, "max_residual": 0.0, "interpretation": "" }, { "name": "falsification_average_is_not_robust", "status": "PASS", "cases": 1, "max_residual": 0.0, "interpretation": "Naive average overstates the weakest floor by a factor 5000.5." } ], "group_count": 14, "total_cases": 1692, "elapsed_seconds": 3.959585189819336, "frontier_curve": [ { "B": 0.0, "exact": 1.3944487245360109, "computed": 1.3944487231368736, "uniform": 1.3944487245360109 }, { "B": 0.05, "exact": 1.3820139810077046, "computed": 1.3820139796256896, "uniform": 1.3264406577361443 }, { "B": 0.1, "exact": 1.3680006321548133, "computed": 1.368000630786812, "uniform": 1.261749383492701 }, { "B": 0.15000000000000002, "exact": 1.3521977603342679, "computed": 1.3521977589818097, "uniform": 1.2002131399238927 }, { "B": 0.2, "exact": 1.334370888551228, "computed": 1.334370887216856, "uniform": 1.1416780543679994 }, { "B": 0.25, "exact": 1.3142636426359324, "computed": 1.3142636413216675, "uniform": 1.085997758621567 }, { "B": 0.30000000000000004, "exact": 1.2916024478551391, "computed": 1.2916024465635345, "uniform": 1.0330330229426585 }, { "B": 0.35000000000000003, "exact": 1.2661057057367502, "computed": 1.2661057044706416, "uniform": 0.982651407903978 }, { "B": 0.4, "exact": 1.2374990622761834, "computed": 1.2374990610386836, "uniform": 0.9347269332253173 }, { "B": 0.45, "exact": 1.2055381374692533, "computed": 1.2055381362637043, "uniform": 0.8891397627572359 }, { "B": 0.5, "exact": 1.1700390798430118, "computed": 1.1700390786728816, "uniform": 0.8457759048282669 }, { "B": 0.55, "exact": 1.1309152201616677, "computed": 1.130915219030751, "uniform": 0.804526927206363 }, { "B": 0.6000000000000001, "exact": 1.0882149796890466, "computed": 1.0882149786008288, "uniform": 0.7652896859618364 }, { "B": 0.65, "exact": 1.0421528979798131, "computed": 1.0421528969376601, "uniform": 0.7279660675538099 }, { "B": 0.7000000000000001, "exact": 0.9931706075828189, "computed": 0.9931705082657641, "uniform": 0.6924627434952584 }, { "B": 0.75, "exact": 0.9447331054820294, "computed": 0.9447330110087245, "uniform": 0.6586909369831803 }, { "B": 0.8, "exact": 0.8986579282344431, "computed": 0.8986578383686558, "uniform": 0.6265662009103466 }, { "B": 0.8500000000000001, "exact": 0.8548298638974533, "computed": 0.854829778414472, "uniform": 0.5960082067035478 }, { "B": 0.9, "exact": 0.8131393194811982, "computed": 0.8131392381672712, "uniform": 0.5669405434603184 }, { "B": 0.9500000000000001, "exact": 0.7734820469090024, "computed": 0.7734819695608023, "uniform": 0.5392905268818806 }, { "B": 1.0, "exact": 0.7357588823428847, "computed": 0.7357588087670008, "uniform": 0.5129890175245382 }, { "B": 1.05, "exact": 0.6998754982223107, "computed": 0.6998754282347651, "uniform": 0.4879702479150531 }, { "B": 1.1, "exact": 0.6657421673961591, "computed": 0.6657421008219464, "uniform": 0.4641716580977068 }, { "B": 1.1500000000000001, "exact": 0.6332735387581063, "computed": 0.6332734754307563, "uniform": 0.4415337392018237 }, { "B": 1.2000000000000002, "exact": 0.602388423824404, "computed": 0.6023883635855654, "uniform": 0.4199998846385991 }, { "B": 1.25, "exact": 0.5730095937203802, "computed": 0.5730095364194243, "uniform": 0.39951624855514095 }, { "B": 1.3, "exact": 0.5450635860680252, "computed": 0.5450635315616699, "uniform": 0.38003161119179096 }, { "B": 1.35, "exact": 0.518480521291783, "computed": 0.518480469443734, "uniform": 0.36149725080604644 }, { "B": 1.4000000000000001, "exact": 0.49319392788321287, "computed": 0.4931938785638231, "uniform": 0.34386682184282574 }, { "B": 1.4500000000000002, "exact": 0.46914057618759525, "computed": 0.46914052927354044, "uniform": 0.3270962390464407 }, { "B": 1.5, "exact": 0.44626032029685964, "computed": 0.4462602756708303, "uniform": 0.3111435672244938 }, { "B": 1.55, "exact": 0.4244959476534861, "computed": 0.4244959052038939, "uniform": 0.29596891638805445 }, { "B": 1.6, "exact": 0.40379303598931077, "computed": 0.4037929956100096, "uniform": 0.281534342005909 }, { "B": 1.6500000000000001, "exact": 0.38409981724150816, "computed": 0.38409977883152874, "uniform": 0.26780375012346797 }, { "B": 1.7000000000000002, "exact": 0.3653670481054692, "computed": 0.3653670115687666, "uniform": 0.2547428071090794 }, { "B": 1.75, "exact": 0.3475478869008903, "computed": 0.3475478521461037, "uniform": 0.2423188538020661 }, { "B": 1.8, "exact": 0.33059777644317306, "computed": 0.3305977433833974, "uniform": 0.23050082384781198 }, { "B": 1.85, "exact": 0.3144743326272552, "computed": 0.31447430117982383, "uniform": 0.21925916601569465 }, { "B": 1.9000000000000001, "exact": 0.29913723844527007, "computed": 0.299137208531548, "uniform": 0.2085657703056157 }, { "B": 1.9500000000000002, "exact": 0.28454814317302707, "computed": 0.28454811471821445, "uniform": 0.1983938976583589 }, { "B": 2.0, "exact": 0.2706705664732254, "computed": 0.2706705394061704, "uniform": 0.18871811309401434 }, { "B": 2.0500000000000003, "exact": 0.25746980717560836, "computed": 0.2574697814286292, "uniform": 0.17951422211127988 }, { "B": 2.1, "exact": 0.2449128565059638, "computed": 0.24491283201467964, "uniform": 0.17075921018860615 }, { "B": 2.15, "exact": 0.23296831554699393, "computed": 0.23296829225016377, "uniform": 0.1624311852359043 }, { "B": 2.2, "exact": 0.22160631672466774, "computed": 0.2216062945640374, "uniform": 0.1545093228529181 }, { "B": 2.25, "exact": 0.21079844912372867, "computed": 0.21079842804388502, "uniform": 0.1469738142573763 }, { "B": 2.3000000000000003, "exact": 0.2005176874456074, "computed": 0.2005176673938399, "uniform": 0.13980581675271886 }, { "B": 2.35, "exact": 0.19073832443109923, "computed": 0.19073830535726793, "uniform": 0.13298740661154107 }, { "B": 2.4000000000000004, "exact": 0.18143590657882494, "computed": 0.1814358884352354, "uniform": 0.12650153425693864 }, { "B": 2.45, "exact": 0.172587172998741, "computed": 0.17258715574002473, "uniform": 0.12033198162968511 }, { "B": 2.5, "exact": 0.1641699972477976, "computed": 0.16416998083079887, "uniform": 0.11446332163463589 }, { "B": 2.5500000000000003, "exact": 0.15616333200230625, "computed": 0.156163316385974, "uniform": 0.10888087956495478 }, { "B": 2.6, "exact": 0.14854715642866775, "computed": 0.14854714157395302, "uniform": 0.10357069640770351 }, { "B": 2.6500000000000004, "exact": 0.14130242612085914, "computed": 0.14130241199061738, "uniform": 0.09851949393903794 }, { "B": 2.7, "exact": 0.1344110254794995, "computed": 0.13441101203839778, "uniform": 0.09371464152173267 }, { "B": 2.75, "exact": 0.12785572241341514, "computed": 0.12785570962784368, "uniform": 0.0891441245220085 }, { "B": 2.8000000000000003, "exact": 0.1216201252504359, "computed": 0.12162011308842412, "uniform": 0.0847965142666901 }, { "B": 2.85, "exact": 0.11568864174967691, "computed": 0.11568863018081343, "uniform": 0.08066093946557024 }, { "B": 2.9000000000000004, "exact": 0.11004644011281442, "computed": 0.11004642910817107, "uniform": 0.07672705902752129 }, { "B": 2.95, "exact": 0.10467941189686476, "computed": 0.10467940142892421, "uniform": 0.07298503620238139 }, { "B": 3.0, "exact": 0.09957413673572789, "computed": 0.09957412677831481, "uniform": 0.06942551398395505 } ], "bracket_examples": [ { "B": 0.07, "lower": 1.3766092016798188, "upper": 1.376609920928412, "iterations": 17, "trace": [ { "target": 1.3473120487345596, "primal_capacity_twice": 0.32862416794544524, "dual_capacity_twice": 0.32863016794544586, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3708803866352852, "primal_capacity_twice": 0.18040319744978606, "dual_capacity_twice": 0.18040919744978667, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3826645555856478, "primal_capacity_twice": 0.09505039956646189, "dual_capacity_twice": 0.09505639956646383, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.3767724711104665, "primal_capacity_twice": 0.13881737872341238, "dual_capacity_twice": 0.13882337872341122, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.3738264288728759, "primal_capacity_twice": 0.15986958609730229, "dual_capacity_twice": 0.15987558609730002, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.375299449991671, "primal_capacity_twice": 0.14940990088193085, "dual_capacity_twice": 0.14941590088193213, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3760359605510688, "primal_capacity_twice": 0.1441304498988103, "dual_capacity_twice": 0.14413644989881114, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3764042158307677, "primal_capacity_twice": 0.14147814292334748, "dual_capacity_twice": 0.1414841429233491, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3765883434706172, "primal_capacity_twice": 0.140148821263128, "dual_capacity_twice": 0.14015482126312873, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3766804072905419, "primal_capacity_twice": 0.13948336551566276, "dual_capacity_twice": 0.1394893655156646, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.3766343753805796, "primal_capacity_twice": 0.1398161597183627, "dual_capacity_twice": 0.13982215971836032, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.3766113594255984, "primal_capacity_twice": 0.13998250706654047, "dual_capacity_twice": 0.1399885070665411, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.3765998514481077, "primal_capacity_twice": 0.14006566830797829, "dual_capacity_twice": 0.1400716683079798, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3766056054368532, "primal_capacity_twice": 0.14002408872314476, "dual_capacity_twice": 0.14003008872314482, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3766084824312257, "primal_capacity_twice": 0.1400032981538274, "dual_capacity_twice": 0.14000929815382623, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.376609920928412, "primal_capacity_twice": 0.13999290267493192, "dual_capacity_twice": 0.13999890267493076, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.3766092016798188, "primal_capacity_twice": 0.14000107040084864, "dual_capacity_twice": 0.14000113040103668, "barrier": 1e-08, "decision": "feasible" } ], "status": "floating-point primal/dual bracket, not an interval certificate" }, { "B": 0.3, "lower": 1.2916017862135236, "upper": 1.291602475559268, "iterations": 19, "trace": [ { "target": 1.2137408737393345, "primal_capacity_twice": 0.8753423413815951, "dual_capacity_twice": 0.8753483413815952, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.3040947991376726, "primal_capacity_twice": 0.5463468098624915, "dual_capacity_twice": 0.5463528098624921, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.2589178364385036, "primal_capacity_twice": 0.7262123516128148, "dual_capacity_twice": 0.7262183516128146, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.281506317788088, "primal_capacity_twice": 0.6410025321896697, "dual_capacity_twice": 0.6410085321896697, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.2928005584628803, "primal_capacity_twice": 0.5949967943865865, "dual_capacity_twice": 0.5950027943865867, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.2871534381254843, "primal_capacity_twice": 0.6183107414600139, "dual_capacity_twice": 0.6183167414600154, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.2899769982941822, "primal_capacity_twice": 0.6067338446319099, "dual_capacity_twice": 0.6067398446319108, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.2913887783785314, "primal_capacity_twice": 0.6008856374349831, "dual_capacity_twice": 0.6008916374349831, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.292094668420706, "primal_capacity_twice": 0.597946333409304, "dual_capacity_twice": 0.5979523334093053, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.2917417233996187, "primal_capacity_twice": 0.5994172600140372, "dual_capacity_twice": 0.5994232600140371, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.2915652508890751, "primal_capacity_twice": 0.6001517667773348, "dual_capacity_twice": 0.6001577667773346, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.2916534871443468, "primal_capacity_twice": 0.5997845929831666, "dual_capacity_twice": 0.5997905929831672, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.291609369016711, "primal_capacity_twice": 0.5999681997678293, "dual_capacity_twice": 0.5999741997678295, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.291587309952893, "primal_capacity_twice": 0.6000599882433157, "dual_capacity_twice": 0.6000659882433166, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.291598339484802, "primal_capacity_twice": 0.6000140952484005, "dual_capacity_twice": 0.6000200952484014, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.2916038542507566, "primal_capacity_twice": 0.5999911478188397, "dual_capacity_twice": 0.5999971478188387, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.2916010968677794, "primal_capacity_twice": 0.6000026216112989, "dual_capacity_twice": 0.6000086216112989, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.291602475559268, "primal_capacity_twice": 0.5999998547198947, "dual_capacity_twice": 0.5999999147199145, "barrier": 1e-08, "decision": "infeasible" }, { "target": 1.2916017862135236, "primal_capacity_twice": 0.600002723163155, "dual_capacity_twice": 0.6000027831631555, "barrier": 1e-08, "decision": "feasible" } ], "status": "floating-point primal/dual bracket, not an interval certificate" }, { "B": 0.6, "lower": 1.088214783506988, "upper": 1.0882153835198038, "iterations": 20, "trace": [ { "target": 1.0798692052489236, "primal_capacity_twice": 1.2186488648969307, "dual_capacity_twice": 1.2186548648969304, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.2371589648924672, "primal_capacity_twice": 0.8011207006792742, "dual_capacity_twice": 0.8011267006792744, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.1585140850706954, "primal_capacity_twice": 1.0304374768644697, "dual_capacity_twice": 1.0304434768644697, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.1191916451598094, "primal_capacity_twice": 1.1282880344071657, "dual_capacity_twice": 1.128294034407165, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.0995304252043665, "primal_capacity_twice": 1.1742767577663085, "dual_capacity_twice": 1.1742827577663084, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.089699815226645, "primal_capacity_twice": 1.196650913572715, "dual_capacity_twice": 1.1966569135727156, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.0847845102377844, "primal_capacity_twice": 1.2076952749479934, "dual_capacity_twice": 1.2077012749479934, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.0872421627322146, "primal_capacity_twice": 1.2021846412045185, "dual_capacity_twice": 1.202190641204519, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.08847098897943, "primal_capacity_twice": 1.1994206895709743, "dual_capacity_twice": 1.199426689570974, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.0878565758558223, "primal_capacity_twice": 1.200803390235221, "dual_capacity_twice": 1.2008093902352215, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.088163782417626, "primal_capacity_twice": 1.2001122215136408, "dual_capacity_twice": 1.2001182215136408, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.088317385698528, "primal_capacity_twice": 1.1997665009948726, "dual_capacity_twice": 1.199772500994873, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.0882405840580769, "primal_capacity_twice": 1.1999393726111525, "dual_capacity_twice": 1.199945372611153, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.0882021832378515, "primal_capacity_twice": 1.2000257999008401, "dual_capacity_twice": 1.2000317999008403, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.0882213836479642, "primal_capacity_twice": 1.199982586965705, "dual_capacity_twice": 1.1999885869657054, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.0882117834429077, "primal_capacity_twice": 1.200004193610688, "dual_capacity_twice": 1.2000101936106886, "barrier": 1e-06, "decision": "feasible" }, { "target": 1.088216583545436, "primal_capacity_twice": 1.1999933903325515, "dual_capacity_twice": 1.199999390332551, "barrier": 1e-06, "decision": "infeasible" }, { "target": 1.0882141834941719, "primal_capacity_twice": 1.2000017619451744, "dual_capacity_twice": 1.2000018219451742, "barrier": 1e-08, "decision": "feasible" }, { "target": 1.0882153835198038, "primal_capacity_twice": 1.1999990611243772, "dual_capacity_twice": 1.1999991236460257, "barrier": 1e-08, "decision": "infeasible" }, { "target": 1.088214783506988, "primal_capacity_twice": 1.2000004115347143, "dual_capacity_twice": 1.200000471534715, "barrier": 1e-08, "decision": "feasible" } ], "status": "floating-point primal/dual bracket, not an interval certificate" }, { "B": 1.1, "lower": 0.6657419213175227, "upper": 0.6657428084988681, "iterations": 20, "trace": [ { "target": 0.9293101913168587, "primal_capacity_twice": 1.5329177567532966, "dual_capacity_twice": 1.5329237567532965, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.6967409247072827, "primal_capacity_twice": 2.108975636889536, "dual_capacity_twice": 2.108981636889536, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.5804562914024947, "primal_capacity_twice": 2.474173911964467, "dual_capacity_twice": 2.474179911964468, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6385986080548887, "primal_capacity_twice": 2.283250717895802, "dual_capacity_twice": 2.283256717895802, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6676697663810857, "primal_capacity_twice": 2.1942155398986882, "dual_capacity_twice": 2.194221539898688, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.6531341872179872, "primal_capacity_twice": 2.2382377158717097, "dual_capacity_twice": 2.2382437158717097, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6604019767995364, "primal_capacity_twice": 2.216105508331622, "dual_capacity_twice": 2.216111508331622, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.664035871590311, "primal_capacity_twice": 2.2051305760947617, "dual_capacity_twice": 2.2051365760947617, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6658528189856983, "primal_capacity_twice": 2.199665611880018, "dual_capacity_twice": 2.1996716118800186, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.6649443452880046, "primal_capacity_twice": 2.2023962273733537, "dual_capacity_twice": 2.202402227373354, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6653985821368514, "primal_capacity_twice": 2.2010304536104117, "dual_capacity_twice": 2.2010364536104112, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6656257005612749, "primal_capacity_twice": 2.2003479163206574, "dual_capacity_twice": 2.2003539163206574, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6657392597734866, "primal_capacity_twice": 2.200006735004129, "dual_capacity_twice": 2.2000127350041283, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6657960393795924, "primal_capacity_twice": 2.1998361661692623, "dual_capacity_twice": 2.199842166169262, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.6657676495765394, "primal_capacity_twice": 2.1999214487683374, "dual_capacity_twice": 2.199927448768338, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.665753454675013, "primal_capacity_twice": 2.1999640914316245, "dual_capacity_twice": 2.1999700914316245, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.6657463572242498, "primal_capacity_twice": 2.199985413104222, "dual_capacity_twice": 2.1999914131042217, "barrier": 1e-06, "decision": "infeasible" }, { "target": 0.6657428084988681, "primal_capacity_twice": 2.1999980540219517, "dual_capacity_twice": 2.199998114021952, "barrier": 1e-08, "decision": "infeasible" }, { "target": 0.6657410341361774, "primal_capacity_twice": 2.2000014045078413, "dual_capacity_twice": 2.2000074045078413, "barrier": 1e-06, "decision": "feasible" }, { "target": 0.6657419213175227, "primal_capacity_twice": 2.2000007192612157, "dual_capacity_twice": 2.2000007792612166, "barrier": 1e-08, "decision": "feasible" } ], "status": "floating-point primal/dual bracket, not an interval certificate" } ], "scope": "Finite seeded consistency checks. Not formal proof verification, exhaustive novelty validation or physical validation." }