{"id":"W2168074581","doi":"10.1090/surv/239/12","title":"Invariant subspaces of the Dirichlet shift","year":2019,"lang":"en","type":"book-chapter","venue":"Mathematical surveys and monographs","topic":"advanced mathematical theories","field":"Mathematics","cited_by":157,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Linear subspace; Invariant (physics); Mathematics; Pure mathematics; Dirichlet distribution; Mathematical analysis; Mathematical physics","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":[0.002790614,0.0006800251,0.001548883,0.0001463913,0.0001320268,0.00006203837,0.0006140036,0.0005017131,0.0007023754],"category_scores_gemma":[0.001060823,0.0004118181,0.0005475591,0.0001280366,0.0009450359,0.0001006266,0.0005759164,0.0005837231,0.00007082197],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002427,"about_ca_system_score_gemma":0.00006411381,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003269162,"about_ca_topic_score_gemma":0.00002038415,"domain_scores_codex":[0.9970683,0.0003095709,0.001075481,0.0004499274,0.0006619761,0.0004347348],"domain_scores_gemma":[0.9934369,0.004178966,0.0007569419,0.001334443,0.0001238285,0.0001688933],"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":[0.000008453636,0.00008825902,0.0000560478,0.001677283,0.0002013663,0.000002806945,0.0005445191,2.800743e-7,0.00001184328,0.9963393,0.0004341822,0.0006356101],"study_design_scores_gemma":[0.0002710995,0.0000746863,0.0001352109,0.001045416,0.0002573499,0.00001106542,0.00007576799,0.00002387641,0.0001232802,0.9950528,0.002451819,0.0004775908],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.004667052,0.001130875,0.0773897,0.0005361321,0.0003787733,0.00264306,0.0004391006,0.000225114,0.9125902],"genre_scores_gemma":[0.2621821,0.001088776,0.05029596,0.0002573479,0.0003275421,0.0001538444,0.00005694427,0.0009861198,0.6846513],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.2575151,"threshold_uncertainty_score":0.9998333,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04358827560776025,"score_gpt":0.2773655005731183,"score_spread":0.233777224965358,"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."}}