{ "results": [ { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "1225/1633", "polynomial": [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ], "decomposition_seconds": 0.03013103600096656, "degree_bound": 34, "elapsed_seconds": 0.03280243300105212, "improvements": 0, "initial_bound": "1225/1633", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 35 ], "integral_over_2pi_display": 2.5469988851611736, "lambda": "3/2", "leaves": 1, "node_limit": 10000000, "nodes": 296, "normalized_best": "1225/1633", "normalized_minimum": "1225/1633", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], "polynomial_degree": 34, "python_version": "3.12.14", "real_relaxation_minimum": "10889035741470030830827987437816582766592/34731117519826359353974846380413253246165", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 190, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "260100/664631", "polynomial": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] ], "decomposition_seconds": 0.035403552999923704, "degree_bound": 34, "elapsed_seconds": 0.07020569299857016, "improvements": 0, "initial_bound": "260100/664631", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 17, 18 ], "integral_over_2pi_display": 4.251954293932406, "lambda": "5/2", "leaves": 1, "node_limit": 10000000, "nodes": 6550, "normalized_best": "260100/664631", "normalized_minimum": "260100/664631", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], "polynomial_degree": 33, "python_version": "3.12.14", "real_relaxation_minimum": "5444517870735015415413993718908291383296/49954689679663878271884468653501275721677", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 199, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "472342115898312999935577216/2264343061497449700535639025", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ] ], "decomposition_seconds": 0.0370257809991017, "degree_bound": 34, "elapsed_seconds": 0.1507514959994296, "improvements": 0, "initial_bound": "472342115898312999935577216/2264343061497449700535639025", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 8, 9, 17 ], "integral_over_2pi_display": 5.6866081883377735, "lambda": "13/4", "leaves": 1, "node_limit": 10000000, "nodes": 21894, "normalized_best": "472342115898312999935577216/2264343061497449700535639025", "normalized_minimum": "472342115898312999935577216/2264343061497449700535639025", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ], "polynomial_degree": 31, "python_version": "3.12.14", "real_relaxation_minimum": "99954423529308095922054922883728798600368463282176/2059118340412367613819206398269975654285303386541875", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 240, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "22012256064/137052276053", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ] ], "decomposition_seconds": 0.032521060998988105, "degree_bound": 34, "elapsed_seconds": 0.13154036899868515, "improvements": 0, "initial_bound": "22012256064/137052276053", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 8, 9, 17 ], "integral_over_2pi_display": 5.98301834961786, "lambda": "7/2", "leaves": 1, "node_limit": 10000000, "nodes": 20404, "normalized_best": "22012256064/137052276053", "normalized_minimum": "22012256064/137052276053", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ], "polynomial_degree": 31, "python_version": "3.12.14", "real_relaxation_minimum": "21778071482940061661655974875633165533184/587446263654583934381916660995006291152125", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 197, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "19902285164557952968720661632/150243769804249537177524159267", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ] ], "decomposition_seconds": 0.035842024997691624, "degree_bound": 34, "elapsed_seconds": 0.2147003419995599, "improvements": 0, "initial_bound": "19902285164557952968720661632/150243769804249537177524159267", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 8, 9, 17 ], "integral_over_2pi_display": 6.757816741463586, "lambda": "15/4", "leaves": 1, "node_limit": 10000000, "nodes": 34613, "normalized_best": "19902285164557952968720661632/150243769804249537177524159267", "normalized_minimum": "19902285164557952968720661632/150243769804249537177524159267", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 44, 51, 57, 62, 66, 69, 71, 72, 72, 71, 69, 66, 62, 57, 51, 44, 36, 28, 21, 15, 10, 6, 3, 1 ], "polynomial_degree": 31, "python_version": "3.12.14", "real_relaxation_minimum": "25699104363086005063528824872116538821606113280/907200436399077511205674921927145651088895348053", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 240, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "1244343605022927332687987339264/15182420227340400242091459662625", "polynomial": [ 1, 4, 10, 20, 35, 55, 79, 106, 135, 165, 195, 224, 251, 275, 295, 310, 319, 322, 319, 310, 295, 275, 251, 224, 195, 165, 135, 106, 79, 55, 35, 20, 10, 4, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 4, 10, 20, 35, 55, 79, 106, 135, 165, 195, 224, 251, 275, 295, 310, 319, 322, 319, 310, 295, 275, 251, 224, 195, 165, 135, 106, 79, 55, 35, 20, 10, 4, 1 ] ], "decomposition_seconds": 0.03686905999711598, "degree_bound": 34, "elapsed_seconds": 0.28382110099846614, "improvements": 0, "initial_bound": "1244343605022927332687987339264/15182420227340400242091459662625", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 5, 6, 11, 16 ], "integral_over_2pi_display": 7.885704564799357, "lambda": "17/4", "leaves": 1, "node_limit": 10000000, "nodes": 48518, "normalized_best": "1244343605022927332687987339264/15182420227340400242091459662625", "normalized_minimum": "1244343605022927332687987339264/15182420227340400242091459662625", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 4, 10, 20, 35, 55, 79, 106, 135, 165, 195, 224, 251, 275, 295, 310, 319, 322, 319, 310, 295, 275, 251, 224, 195, 165, 135, 106, 79, 55, 35, 20, 10, 4, 1 ], "polynomial_degree": 34, "python_version": "3.12.14", "real_relaxation_minimum": "921801905881396884614506511038832253758953605824512/55596195191133925573118572753289342665703191436630625", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 239, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "601836/9686105", "polynomial": [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ] ], "decomposition_seconds": 0.03291560700017726, "degree_bound": 34, "elapsed_seconds": 0.21706785400238005, "improvements": 0, "initial_bound": "601836/9686105", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 2, 3, 5, 7 ], "integral_over_2pi_display": 8.229595503857196, "lambda": "9/2", "leaves": 1, "node_limit": 10000000, "nodes": 37855, "normalized_best": "601836/9686105", "normalized_minimum": "601836/9686105", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ], "polynomial_degree": 13, "python_version": "3.12.14", "real_relaxation_minimum": "5444517870735015415413993718908291383296/428567601477547452559417236746572203794875", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 194, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "835708169080/17115040517913", "polynomial": [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ] ], "decomposition_seconds": 0.03715394800019567, "degree_bound": 34, "elapsed_seconds": 0.24430536100044264, "improvements": 0, "initial_bound": "835708169080/17115040517913", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 2, 3, 5, 7 ], "integral_over_2pi_display": 8.915217961798785, "lambda": "19/4", "leaves": 1, "node_limit": 10000000, "nodes": 41709, "normalized_best": "835708169080/17115040517913", "normalized_minimum": "835708169080/17115040517913", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ], "polynomial_degree": 13, "python_version": "3.12.14", "real_relaxation_minimum": "149054805305898829368467184258275925165315457024/15295081041745850671379887718806788959586463675069", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 239, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "400467507595222905790905088/13170158622995370707197084125", "polynomial": [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ] ], "decomposition_seconds": 0.03652199899806874, "degree_bound": 34, "elapsed_seconds": 0.29304095299812616, "improvements": 0, "initial_bound": "400467507595222905790905088/13170158622995370707197084125", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 3, 4, 7, 10, 11 ], "integral_over_2pi_display": 10.587947196796257, "lambda": "21/4", "leaves": 1, "node_limit": 10000000, "nodes": 51141, "normalized_best": "400467507595222905790905088/13170158622995370707197084125", "normalized_minimum": "400467507595222905790905088/13170158622995370707197084125", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ], "polynomial_degree": 30, "python_version": "3.12.14", "real_relaxation_minimum": "921801905881396884614506511038832253758953605824512/160128790305584414171843042847430558722603158297870625", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 253, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "25715948378176/1209849943022825", "polynomial": [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ] ], "decomposition_seconds": 0.03320165500190342, "degree_bound": 34, "elapsed_seconds": 0.1171565170006943, "improvements": 0, "initial_bound": "25715948378176/1209849943022825", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 3, 4, 7, 10, 11 ], "integral_over_2pi_display": 10.237356870580617, "lambda": "11/2", "leaves": 1, "node_limit": 10000000, "nodes": 18442, "normalized_best": "25715948378176/1209849943022825", "normalized_minimum": "25715948378176/1209849943022825", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ], "polynomial_degree": 30, "python_version": "3.12.14", "real_relaxation_minimum": "98001321673230277477451886940349244899328/22104879345631187201845644417647579536229875", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 205, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "1974507412739563448778683648/122739189519718729456238271987", "polynomial": [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ] ], "decomposition_seconds": 0.03657476900116308, "degree_bound": 34, "elapsed_seconds": 0.10209602699978859, "improvements": 0, "initial_bound": "1974507412739563448778683648/122739189519718729456238271987", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 3, 4, 7, 10, 11 ], "integral_over_2pi_display": 10.727097226979549, "lambda": "23/4", "leaves": 1, "node_limit": 10000000, "nodes": 13844, "normalized_best": "1974507412739563448778683648/122739189519718729456238271987", "normalized_minimum": "1974507412739563448778683648/122739189519718729456238271987", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 5, 15, 34, 64, 106, 160, 225, 299, 379, 461, 540, 610, 665, 700, 712, 700, 665, 610, 540, 461, 379, 299, 225, 160, 106, 64, 34, 15, 5, 1 ], "polynomial_degree": 30, "python_version": "3.12.14", "real_relaxation_minimum": "250299578721226336109312818848802968673831616512/73201541708154890671386686707734163883505784344561", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 245, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "polynomial": [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 281, 350, 425, 505, 589, 676, 765, 855, 945, 1034, 1121, 1205, 1285, 1360, 1429, 1491, 1545, 1590, 1625, 1649, 1661, 1661, 1649, 1625, 1590, 1545, 1491, 1429, 1360, 1285, 1205, 1121, 1034, 945, 855, 765, 676, 589, 505, 425, 350, 281, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 281, 350, 425, 505, 589, 676, 765, 855, 945, 1034, 1121, 1205, 1285, 1360, 1429, 1491, 1545, 1590, 1625, 1649, 1661, 1661, 1649, 1625, 1590, 1545, 1491, 1429, 1360, 1285, 1205, 1121, 1034, 945, 855, 765, 676, 589, 505, 425, 350, 281, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1 ] ], "decomposition_seconds": 0.23864955700264545, "degree_bound": 61, "elapsed_seconds": 30.146401355003036, "improvements": 0, "initial_bound": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "integral_over_2pi_display": 7.76259340993152, "lambda": "17/4", "leaves": 1, "node_limit": 100000000, "nodes": 3894122, "normalized_best": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "normalized_minimum": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 281, 350, 425, 505, 589, 676, 765, 855, 945, 1034, 1121, 1205, 1285, 1360, 1429, 1491, 1545, 1590, 1625, 1649, 1661, 1661, 1649, 1625, 1590, 1545, 1491, 1429, 1360, 1285, 1205, 1121, 1034, 945, 855, 765, 676, 589, 505, 425, 350, 281, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1 ], "polynomial_degree": 61, "python_version": "3.12.14", "real_relaxation_minimum": "18395086716300764463799105052759763073773809152294446680313547196105596476902906789888/1344481975735638730238370028854834711531954040668947444554292893525506658463127726442275", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 416, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "19683/26243", "polynomial": [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ], "decomposition_seconds": 0.49116205500104115, "degree_bound": 80, "elapsed_seconds": 0.5112816050022957, "improvements": 0, "initial_bound": "19683/26243", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 81 ], "integral_over_2pi_display": 2.546576124073437, "lambda": "3/2", "leaves": 1, "node_limit": 10000000, "nodes": 1398, "normalized_best": "19683/26243", "normalized_minimum": "19683/26243", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], "polynomial_degree": 80, "python_version": "3.12.14", "real_relaxation_minimum": "133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536/441001784559254150297433317615466503730467164400397947427513258920671003650493324179086591964225", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 450, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "67240000/172075351", "polynomial": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] ], "decomposition_seconds": 0.4980138140017516, "degree_bound": 80, "elapsed_seconds": 1.9306741729997157, "improvements": 0, "initial_bound": "67240000/172075351", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 40, 41 ], "integral_over_2pi_display": 4.245588222748232, "lambda": "5/2", "leaves": 1, "node_limit": 10000000, "nodes": 149987, "normalized_best": "67240000/172075351", "normalized_minimum": "67240000/172075351", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ], "polynomial_degree": 79, "python_version": "3.12.14", "real_relaxation_minimum": "133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536/1345240737773187029898893229364826393732433451070121469883926999900870372480076274596709520025325", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 447, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "397421143002128/2488650531906825", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 230, 249, 267, 284, 300, 315, 329, 342, 354, 365, 375, 384, 392, 399, 405, 410, 414, 417, 419, 420, 420, 419, 417, 414, 410, 405, 399, 392, 384, 375, 365, 354, 342, 329, 315, 300, 284, 267, 249, 230, 210, 190, 171, 153, 136, 120, 105, 91, 78, 66, 55, 45, 36, 28, 21, 15, 10, 6, 3, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 230, 249, 267, 284, 300, 315, 329, 342, 354, 365, 375, 384, 392, 399, 405, 410, 414, 417, 419, 420, 420, 419, 417, 414, 410, 405, 399, 392, 384, 375, 365, 354, 342, 329, 315, 300, 284, 267, 249, 230, 210, 190, 171, 153, 136, 120, 105, 91, 78, 66, 55, 45, 36, 28, 21, 15, 10, 6, 3, 1 ] ], "decomposition_seconds": 0.4678508739998506, "degree_bound": 80, "elapsed_seconds": 20.069198550998408, "improvements": 0, "initial_bound": "397421143002128/2488650531906825", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 20, 21, 41 ], "integral_over_2pi_display": 5.948796105764671, "lambda": "7/2", "leaves": 1, "node_limit": 10000000, "nodes": 2226136, "normalized_best": "397421143002128/2488650531906825", "normalized_minimum": "397421143002128/2488650531906825", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 230, 249, 267, 284, 300, 315, 329, 342, 354, 365, 375, 384, 392, 399, 405, 410, 414, 417, 419, 420, 420, 419, 417, 414, 410, 405, 399, 392, 384, 375, 365, 354, 342, 329, 315, 300, 284, 267, 249, 230, 210, 190, 171, 153, 136, 120, 105, 91, 78, 66, 55, 45, 36, 28, 21, 15, 10, 6, 3, 1 ], "polynomial_degree": 79, "python_version": "3.12.14", "real_relaxation_minimum": "133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536/4298020269877009173656802987026651769366919064829260817229103001516253158219366161327486745788325", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 460, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "polynomial": [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 281, 350, 425, 505, 589, 676, 765, 855, 945, 1034, 1121, 1205, 1285, 1360, 1429, 1491, 1545, 1590, 1625, 1649, 1661, 1661, 1649, 1625, 1590, 1545, 1491, 1429, 1360, 1285, 1205, 1121, 1034, 945, 855, 765, 676, 589, 505, 425, 350, 281, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 281, 350, 425, 505, 589, 676, 765, 855, 945, 1034, 1121, 1205, 1285, 1360, 1429, 1491, 1545, 1590, 1625, 1649, 1661, 1661, 1649, 1625, 1590, 1545, 1491, 1429, 1360, 1285, 1205, 1121, 1034, 945, 855, 765, 676, 589, 505, 425, 350, 281, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1 ] ], "decomposition_seconds": 0.6048848699974769, "degree_bound": 80, "elapsed_seconds": 288.96991907399934, "improvements": 0, "initial_bound": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "integral_over_2pi_display": 7.76259340993152, "lambda": "17/4", "leaves": 1, "node_limit": 100000000, "nodes": 34239539, "normalized_best": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "normalized_minimum": "3278824635541247815125114181047484955184155424876416/40639891549624156371693126611609552341028229338209875", "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 219, 281, 350, 425, 505, 589, 676, 765, 855, 945, 1034, 1121, 1205, 1285, 1360, 1429, 1491, 1545, 1590, 1625, 1649, 1661, 1661, 1649, 1625, 1590, 1545, 1491, 1429, 1360, 1285, 1205, 1121, 1034, 945, 855, 765, 676, 589, 505, 425, 350, 281, 219, 165, 120, 84, 56, 35, 20, 10, 4, 1 ], "polynomial_degree": 61, "python_version": "3.12.14", "real_relaxation_minimum": "4056996222254896642985150675988499062694689906234628096159886496051766453182352782360994950013803697950359170318336/315390221562443430674012420464144386331259731356958044114894168427494990618632021200317618724790820867357430896240225", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 552, "status": "complete" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "601836/9686105", "polynomial": [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ] ], "decomposition_seconds": 0.5071104880007624, "degree_bound": 80, "elapsed_seconds": 89.84251230800146, "improvements": 0, "initial_bound": "601836/9686105", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 2, 3, 5, 7 ], "integral_over_2pi_display": 8.229595503857196, "lambda": "9/2", "leaves": 0, "node_limit": 10000000, "nodes": 10000000, "normalized_best": "601836/9686105", "normalized_minimum": null, "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 4, 9, 15, 21, 26, 29, 29, 26, 21, 15, 9, 4, 1 ], "polynomial_degree": 13, "python_version": "3.12.14", "real_relaxation_minimum": "133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536/13932102704341988311067069584890273656212527001542222018032052074260096067631746332274923271644575", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 464, "status": "node_limit" }, { "arithmetic": "rational LDL^T; integer comparisons and exact integer-square-root branch bounds", "best_history": [ { "nodes": 0, "normalized_value": "520034022876812917530880/25278701452008761497932009", "polynomial": [ 1, 5, 15, 35, 70, 126, 210, 330, 494, 709, 981, 1315, 1715, 2184, 2724, 3336, 4020, 4775, 5599, 6489, 7441, 8450, 9510, 10614, 11754, 12921, 14105, 15295, 16479, 17644, 18776, 19860, 20880, 21820, 22665, 23402, 24020, 24510, 24865, 25080, 25152, 25080, 24865, 24510, 24020, 23402, 22665, 21820, 20880, 19860, 18776, 17644, 16479, 15295, 14105, 12921, 11754, 10614, 9510, 8450, 7441, 6489, 5599, 4775, 4020, 3336, 2724, 2184, 1715, 1315, 981, 709, 494, 330, 210, 126, 70, 35, 15, 5, 1 ] } ], "canonical_tie_count": 1, "canonical_ties": [ [ 1, 5, 15, 35, 70, 126, 210, 330, 494, 709, 981, 1315, 1715, 2184, 2724, 3336, 4020, 4775, 5599, 6489, 7441, 8450, 9510, 10614, 11754, 12921, 14105, 15295, 16479, 17644, 18776, 19860, 20880, 21820, 22665, 23402, 24020, 24510, 24865, 25080, 25152, 25080, 24865, 24510, 24020, 23402, 22665, 21820, 20880, 19860, 18776, 17644, 16479, 15295, 14105, 12921, 11754, 10614, 9510, 8450, 7441, 6489, 5599, 4775, 4020, 3336, 2724, 2184, 1715, 1315, 981, 709, 494, 330, 210, 126, 70, 35, 15, 5, 1 ] ], "decomposition_seconds": 0.5074840800007223, "degree_bound": 80, "elapsed_seconds": 84.06282507099968, "improvements": 0, "initial_bound": "520034022876812917530880/25278701452008761497932009", "initial_candidate_kind": "Dirichlet product", "initial_dirichlet_lengths": [ 8, 9, 17, 25, 26 ], "integral_over_2pi_display": 9.90817807064279, "lambda": "11/2", "leaves": 1, "node_limit": 10000000, "nodes": 10000000, "normalized_best": "520034022876812917530880/25278701452008761497932009", "normalized_minimum": null, "normalized_objective": "integral / (2*pi*c0(lambda))", "polynomial": [ 1, 5, 15, 35, 70, 126, 210, 330, 494, 709, 981, 1315, 1715, 2184, 2724, 3336, 4020, 4775, 5599, 6489, 7441, 8450, 9510, 10614, 11754, 12921, 14105, 15295, 16479, 17644, 18776, 19860, 20880, 21820, 22665, 23402, 24020, 24510, 24865, 25080, 25152, 25080, 24865, 24510, 24020, 23402, 22665, 21820, 20880, 19860, 18776, 17644, 16479, 15295, 14105, 12921, 11754, 10614, 9510, 8450, 7441, 6489, 5599, 4775, 4020, 3336, 2724, 2184, 1715, 1315, 981, 709, 494, 330, 210, 126, 70, 35, 15, 5, 1 ], "polynomial_degree": 80, "python_version": "3.12.14", "real_relaxation_minimum": "133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536/45220181504902217804852057024284214894140359868142536799786350838432619504231312521040185524049175", "script_sha256": "586c569e25f769cd87db7bc558942e622576af6f764910f8616523abaed41885", "search_denominator_bits": 463, "status": "node_limit" } ] }