{"id":"W4409231185","doi":"10.1103/physrevd.111.085010","title":"Virasoro completeness relation and the inverse Shapovalov form","year":2025,"lang":"en","type":"article","venue":"Physical review. D/Physical review. D.","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada; U.S. Department of Energy","keywords":"Completeness (order theory); Relation (database); Mathematics; Inverse; Algebra over a field; Calculus (dental); Pure mathematics; Computer science; Mathematical analysis; Geometry; Medicine; Data mining","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":[0.0007329657,0.0004840841,0.001772867,0.00003557231,0.0002686284,0.00005634315,0.0005680864,0.00005836232,0.00002078483],"category_scores_gemma":[0.002120282,0.0002892004,0.0007303815,0.0007012645,0.0003471178,0.0002258698,0.0003641348,0.0005717703,0.00007687417],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007997499,"about_ca_system_score_gemma":0.00007259191,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002067619,"about_ca_topic_score_gemma":0.000005004385,"domain_scores_codex":[0.9971924,0.0004554262,0.0007560378,0.0005850364,0.000592165,0.0004189042],"domain_scores_gemma":[0.9962866,0.002026626,0.0003883379,0.0009533669,0.000192704,0.0001523924],"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":[0.00003271561,0.0001465677,0.00009842831,0.005593211,0.00009404759,0.000001182177,0.00007901401,5.820328e-7,0.0001738986,0.9769588,0.007411408,0.009410152],"study_design_scores_gemma":[0.0009305493,0.00004659657,0.0005566288,0.006827416,0.0009339577,0.000002871096,0.000006885904,0.001995455,0.0001218558,0.967779,0.02049298,0.0003058505],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8682664,0.08979775,0.0007028088,0.01438119,0.0007692256,0.005932305,0.00002112415,0.0002681809,0.01986104],"genre_scores_gemma":[0.908442,0.08121863,0.0002266736,0.008870643,0.0005637154,0.000430859,0.00001912259,0.0000532187,0.0001751042],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04017566,"threshold_uncertainty_score":0.999956,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02719157977344542,"score_gpt":0.4252434311209746,"score_spread":0.3980518513475291,"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."}}