{"id":"W71831445","doi":"10.1016/j.jalgebra.2012.11.034","title":"Star configurations in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">P</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>","year":2012,"lang":"lv","type":"article","venue":"Journal of Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":102,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada; National Security Agency; Simons Foundation","keywords":"Mathematics; Star (game theory); Hyperplane; Codimension; Algebraic number; Linear subspace; Ideal (ethics); Pure mathematics; Discrete mathematics; Combinatorics; 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","sts","scholarly_communication","research_integrity","insufficient_payload"],"consensus_categories":["research_integrity","insufficient_payload"],"category_scores_codex":[0.002583246,0.0009080223,0.0005257035,0.0007728146,0.001529552,0.001491253,0.002271012,0.001899341,0.3679909],"category_scores_gemma":[0.001784412,0.001566876,0.001853846,0.001367232,0.001240476,0.002582887,0.001367549,0.002515007,0.002934025],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003985756,"about_ca_system_score_gemma":0.002243327,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008533939,"about_ca_topic_score_gemma":0.0008571988,"domain_scores_codex":[0.9905118,0.0005232215,0.002948805,0.001127717,0.00257709,0.002311334],"domain_scores_gemma":[0.9900216,0.002430639,0.003494266,0.002355081,0.0003729996,0.001325437],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.001079096,0.0006798164,0.0000287311,0.0008096534,0.001713408,0.0007333078,0.005441444,0.0004115124,0.002853417,0.8088773,0.1761873,0.001184971],"study_design_scores_gemma":[0.005151563,0.002379402,0.0006686955,0.001897255,0.002958577,0.004760202,0.007251079,0.05498509,0.9047279,0.002505842,0.01054278,0.00217163],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6496451,0.001470114,0.001479995,0.00170542,0.00185941,0.00006687162,0.0002587067,0.0001139496,0.3434004],"genre_scores_gemma":[0.986555,0.001390152,0.006027758,0.001340989,0.002548932,0.0005928961,0.0004405461,0.0006652559,0.000438479],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9018745,"threshold_uncertainty_score":0.9997863,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0271448315256661,"score_gpt":0.2683339258017351,"score_spread":0.241189094276069,"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."}}