{"id":"W2075335903","doi":"10.4153/cjm-2011-028-8","title":"Critical Points and Resonance of Hyperplane Arrangements","year":2011,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":29,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Natural Sciences and Engineering Research Council of Canada; National Security Agency; National Science Foundation","keywords":"Hyperplane; Mathematics; Codimension; Rank (graph theory); Dimension (graph theory); Combinatorics; Variety (cybernetics); Resonance (particle physics); Function (biology); Set (abstract data type); Pure mathematics; Statistics; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0005905885,0.0003355625,0.0005355275,0.002333144,0.001437058,0.002051454,0.0005522246,0.0007110898,0.004728456],"category_scores_gemma":[0.002443386,0.0002601237,0.0003341974,0.0005119977,0.002511609,0.001798153,0.00160898,0.0007955093,0.0003642235],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001310809,"about_ca_system_score_gemma":0.0002941843,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007902394,"about_ca_topic_score_gemma":0.000607005,"domain_scores_codex":[0.9995234,0.00007941732,0.00002495955,0.00009365942,0.0001255485,0.000152996],"domain_scores_gemma":[0.9990615,0.0002563025,0.000210967,0.00008367324,0.0001277927,0.0002597454],"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":[0.0001339153,0.00004867969,0.003799828,0.00004626533,0.00001596011,0.0002204961,0.0004898225,0.003870935,0.00930538,0.977241,0.0007519735,0.004075679],"study_design_scores_gemma":[0.0001043666,0.0001836832,0.007334338,0.00007428758,0.00002973824,0.0006691113,0.001274318,0.04986799,0.009956737,0.9260578,0.004377573,0.00007008565],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9716341,0.0001835878,0.01315839,0.0001940384,0.00003125489,0.00001809867,0.00005501802,0.00006950885,0.01465596],"genre_scores_gemma":[0.9968032,0.00005570884,0.001527306,0.00002245288,0.00003167768,0.0000126751,0.00004550537,0.00001886619,0.001482566],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004728456,"threshold_uncertainty_score":0.0158183,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07535042346305441,"score_gpt":0.2973873456833578,"score_spread":0.2220369222203034,"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."}}