{"id":"W100499361","doi":"","title":"Static symmetry breaking in circle packing","year":2010,"lang":"en","type":"article","venue":"Cologne Twente Workshop on Graphs and Combinatorial Optimization","topic":"Optimization and Packing Problems","field":"Engineering","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"HEC Montréal","funders":"","keywords":"Circle packing; Square (algebra); RADIUS; Packing problems; Symmetry breaking; Combinatorics; Unit square; Symmetry (geometry); Unit (ring theory); Mathematics; Unit circle; Work (physics); Physics; Geometry; Computer science; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001610866,0.001187035,0.001162779,0.0009203675,0.0008568522,0.002234546,0.002663003,0.001310102,0.01042598],"category_scores_gemma":[0.007828545,0.0005637723,0.000857229,0.001762537,0.002120449,0.003972176,0.001911895,0.002301038,0.001166291],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002001138,"about_ca_system_score_gemma":0.0009376251,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002123623,"about_ca_topic_score_gemma":0.001250193,"domain_scores_codex":[0.9970408,0.0009004578,0.0001259243,0.0003957556,0.001107339,0.0004297452],"domain_scores_gemma":[0.9948225,0.002523329,0.0008440065,0.0007936954,0.0007085871,0.0003079],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0002722233,0.00008935657,0.0008653029,0.0003327443,0.00003665085,0.000171825,0.0001598142,0.2447183,0.00516699,0.6680594,0.00842876,0.07169855],"study_design_scores_gemma":[0.00002772643,0.0001047251,0.0003548384,0.00005426786,0.00001210156,0.0001153698,0.00006587605,0.6183398,0.003419734,0.3696611,0.007811524,0.00003292111],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07895827,0.00259543,0.841749,0.001469704,0.0003245328,0.0001178136,0.0005102342,0.0003166283,0.07395844],"genre_scores_gemma":[0.8489428,0.001742274,0.135224,0.0004082926,0.0004235857,0.0002173179,0.0006166863,0.0001778545,0.01224726],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01042598,"threshold_uncertainty_score":0.03487837,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006615354732950662,"score_gpt":0.2182841252345507,"score_spread":0.2116687705016001,"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."}}