{"id":"W1925057626","doi":"10.48550/arxiv.1007.2750","title":"Poset pinball, GKM-compatible subspaces, and Hessenberg varieties","year":2010,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Partially ordered set; Linear subspace; Cohomology; Equivariant cohomology; Algebra over a field; Subspace topology; Group cohomology; Lift (data mining); Pure mathematics; Discrete mathematics; Computer science","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003187906,0.0005887986,0.0008179592,0.0002256232,0.0002246276,0.0001210834,0.000856535,0.0007529757,0.0001029255],"category_scores_gemma":[0.0003824925,0.0006599426,0.0001837725,0.0003046367,0.0003222308,0.0002606655,0.001597075,0.001470836,0.00004491904],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001536064,"about_ca_system_score_gemma":0.0001672771,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008225737,"about_ca_topic_score_gemma":0.0001594347,"domain_scores_codex":[0.9979382,0.0001197523,0.0003596166,0.0009309594,0.0001712811,0.0004802279],"domain_scores_gemma":[0.9968024,0.0006726365,0.0005625509,0.001451825,0.0002618989,0.0002486416],"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":[0.00004813393,0.0002176386,0.000595785,0.0007714994,0.0001535303,0.0001244038,0.0005740257,0.0008904106,0.0001352875,0.995442,0.0009997446,0.00004752416],"study_design_scores_gemma":[0.0006721799,0.0000583142,0.0000767621,0.0001754306,0.0002661598,0.00001231644,0.0002870283,0.007519908,0.0004924808,0.9883434,0.001405684,0.0006903341],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9168275,0.0001215748,0.0737941,0.0001144685,0.001667419,0.0007651024,0.00005994832,0.0005145946,0.006135316],"genre_scores_gemma":[0.9834384,0.0002357311,0.01275558,0.0000276523,0.0001648673,0.000002957729,0.00002316722,0.00009458606,0.003257062],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06661092,"threshold_uncertainty_score":0.9995852,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1054514886635035,"score_gpt":0.2248193237778233,"score_spread":0.1193678351143199,"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."}}