{"id":"W4415735986","doi":"10.5802/alco.447","title":"Combinatorial flats and Schubert varieties of subspace arrangements","year":2025,"lang":"en","type":"article","venue":"Algebraic Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Centre de Recherches Mathématiques; National Science Foundation","keywords":"Hyperplane; Matroid; Subspace topology; Lattice (music); Variety (cybernetics); Schubert variety; Oriented matroid; Schubert calculus","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006172871,0.0004121584,0.0008254148,0.000293228,0.0002033874,0.00005814071,0.0005142814,0.0002615285,0.00003028936],"category_scores_gemma":[0.001813321,0.0004249283,0.0001301299,0.0009599169,0.0002611972,0.0002381233,0.0004707306,0.0003663737,0.000007897055],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001399625,"about_ca_system_score_gemma":0.0001412398,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001616311,"about_ca_topic_score_gemma":0.000003427787,"domain_scores_codex":[0.9975377,0.0001306897,0.0007999007,0.0004607892,0.0006052459,0.0004656333],"domain_scores_gemma":[0.9967082,0.001483497,0.0003980688,0.0008739425,0.0004042411,0.0001320606],"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":[0.00004751015,0.0004676356,0.0013808,0.0006039821,0.000162935,0.000005149989,0.0005188362,5.048292e-7,0.0003529513,0.9935139,0.002436845,0.0005089282],"study_design_scores_gemma":[0.002584326,0.0001691831,0.0003596644,0.000183089,0.0001688653,0.000003972947,0.0002403336,0.00009420771,0.005184815,0.9883995,0.002276567,0.0003354653],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9417877,0.001204246,0.009485405,0.0007055058,0.008986572,0.001449378,0.00001228713,0.0004707658,0.03589814],"genre_scores_gemma":[0.9955994,0.0001056588,0.002746797,0.000055415,0.00005701269,0.00005245908,0.000004011465,0.0000575866,0.001321584],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05381177,"threshold_uncertainty_score":0.9998202,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01826119698740124,"score_gpt":0.3134626299542104,"score_spread":0.2952014329668091,"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."}}