{"id":"W2902145203","doi":"10.1016/j.jsc.2019.10.015","title":"On the maximal number of real embeddings of minimally rigid graphs in R2, R3 and S2","year":2019,"lang":"lv","type":"article","venue":"Journal of Symbolic Computation","topic":"Structural Analysis and Optimization","field":"Engineering","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Horizon 2020; Agence Nationale de la Recherche; European Commission; Horizon 2020 Framework Programme; Alberta Livestock and Meat Agency; Institut national de recherche en informatique et en automatique (INRIA)","keywords":"Mathematics; Combinatorics; Algebraic number; Vertex (graph theory); Upper and lower bounds; Heuristics; Discrete mathematics; Euclidean space; Graph; Mathematical optimization","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003396087,0.0001384791,0.0004406813,0.0002496371,0.00002083379,0.00002739202,0.0001060515,0.0000805676,0.0001109223],"category_scores_gemma":[0.00003826162,0.0000989283,0.0001449098,0.0003899249,0.00003891096,0.0001572209,0.00002053517,0.0002048146,0.000003454181],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004481751,"about_ca_system_score_gemma":0.00002728115,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007813524,"about_ca_topic_score_gemma":0.000005706749,"domain_scores_codex":[0.9985798,0.00006346645,0.0008194124,0.00009874423,0.0003193194,0.0001192315],"domain_scores_gemma":[0.9987632,0.0002224775,0.0006698147,0.00007747272,0.0002276752,0.00003938379],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"observational","study_design_scores_codex":[0.0003074309,0.00009643337,0.06127612,0.000323943,0.0003567844,0.000009926301,0.004793583,0.8989698,0.009523175,0.01272976,0.0001649731,0.01144806],"study_design_scores_gemma":[0.001125733,0.0002861611,0.523468,0.0005304486,0.0001360021,0.00005433112,0.0006179817,0.4646625,0.000800584,0.008159612,0.000007720679,0.0001509017],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9979125,0.0001427954,0.0005723263,0.0001383664,0.0001931137,0.0001051561,0.000004156594,0.000003251494,0.0009282915],"genre_scores_gemma":[0.9980872,0.0002995796,0.001516762,0.00001589371,0.00004736455,3.436263e-7,0.000003028181,0.00001267008,0.00001710451],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4621919,"threshold_uncertainty_score":0.4034179,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005954589595655223,"score_gpt":0.2329022632428291,"score_spread":0.2269476736471738,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}