{ "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" }