{"id":"W2056947633","doi":"10.1016/j.jalgebra.2014.02.013","title":"Star configurations on generic hypersurfaces","year":2014,"lang":"en","type":"preprint","venue":"Journal of Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Lakehead University","funders":"Natural Sciences and Engineering Research Council of Canada; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Hypersurface; Mathematics; Homogeneous; Polynomial; Star (game theory); Combinatorics; Homogeneous polynomial; Matrix (chemical analysis); Rank (graph theory); Algebraic number; Algebraic geometry; Commutative property; Algebra over a field; Pure mathematics; Discrete mathematics; Matrix polynomial; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006391217,0.0003671425,0.0008224808,0.0002666558,0.00009870072,0.00009943927,0.000724058,0.0003399538,0.0003975005],"category_scores_gemma":[0.001146116,0.00030613,0.0003818434,0.0000988,0.00009461476,0.0001101678,0.0002102688,0.001553585,0.00005781766],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001900509,"about_ca_system_score_gemma":0.0002644344,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001474339,"about_ca_topic_score_gemma":0.000002676108,"domain_scores_codex":[0.997452,0.0001703387,0.001094627,0.0002711278,0.0007394894,0.0002724356],"domain_scores_gemma":[0.9959702,0.0007722367,0.00189588,0.0007186731,0.0004733235,0.0001696222],"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":[0.0001784569,0.0006649568,0.00008915982,0.0007764921,0.001186117,0.0001949508,0.001508682,0.004600442,0.003266209,0.9340941,0.0476838,0.005756631],"study_design_scores_gemma":[0.0005203049,0.000295082,0.0001607377,0.0004344595,0.0001972757,0.00008341488,0.0001120112,0.0002119226,0.003639512,0.9801656,0.01381456,0.0003650895],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9617195,0.0005957413,0.0245607,0.001893288,0.003307801,0.0003239589,0.00002792194,0.00006978996,0.007501276],"genre_scores_gemma":[0.7924919,0.0003902979,0.2026125,0.0006745912,0.002474578,0.00001143195,0.00001027395,0.0001367437,0.001197749],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1780518,"threshold_uncertainty_score":0.9999391,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06964939006758782,"score_gpt":0.337399191484093,"score_spread":0.2677498014165052,"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."}}