{"id":"W2027950769","doi":"10.1515/advgeom.2008.033","title":"Counting the hyperplane sections with fixed invariants of a plane quintic – three approaches to a classical enumerative problem","year":2008,"lang":"en","type":"article","venue":"Advances in Geometry","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Hyperplane; Quintic function; Intersection (aeronautics); Plane (geometry); Pure mathematics; Mathematical analysis; Combinatorics; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003098493,0.0002384536,0.0004875365,0.000203532,0.000172786,0.00001532528,0.000347445,0.00008313504,0.00001424235],"category_scores_gemma":[0.001034453,0.0001597315,0.00004389279,0.001227216,0.0002309404,0.0003103946,0.0001152552,0.0003707549,0.00001089528],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008204105,"about_ca_system_score_gemma":0.00007520155,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001244357,"about_ca_topic_score_gemma":0.0003386998,"domain_scores_codex":[0.9983009,0.00007025721,0.0005068678,0.000316358,0.0004537613,0.0003518257],"domain_scores_gemma":[0.997079,0.002013892,0.0002944172,0.0004638901,0.00008302498,0.00006584088],"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":[0.001185779,0.003865245,0.1058043,0.002721165,0.000552159,0.0002394349,0.02715819,0.01616221,0.001645487,0.8336068,0.0007868927,0.006272361],"study_design_scores_gemma":[0.003196123,0.001409792,0.004474969,0.001207481,0.0001420066,0.0006724039,0.004712902,0.001680954,0.005609536,0.9732806,0.00256154,0.001051686],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9202976,0.0003697716,0.07440234,0.0002520551,0.0002311673,0.001178391,0.00001795099,0.00008920658,0.003161566],"genre_scores_gemma":[0.9030877,0.0000319323,0.09645547,0.00003002188,0.0000804831,0.0001595189,0.000003481364,0.00003609682,0.0001152345],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1396738,"threshold_uncertainty_score":0.6513664,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1034268025673875,"score_gpt":0.285514019565968,"score_spread":0.1820872169985805,"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."}}