{"id":"W2951389377","doi":"10.48550/arxiv.0804.0251","title":"An Index Theorem for Toeplitz Operators on the Quarter-Plane","year":2008,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Toeplitz matrix; Mathematics; Toeplitz operator; Tensor product; Plane (geometry); Index (typography); Atiyah–Singer index theorem; Quarter (Canadian coin); Pure mathematics; Operator (biology); Algebra over a field; Geometry; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001108457,0.0005697479,0.000652917,0.001791547,0.001272939,0.002160418,0.0007859584,0.0009711554,0.003796471],"category_scores_gemma":[0.002129885,0.0002635291,0.0009191451,0.0009248473,0.002498403,0.004444536,0.001958031,0.001930553,0.0005789354],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009021884,"about_ca_system_score_gemma":0.0004192682,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003972224,"about_ca_topic_score_gemma":0.0002259504,"domain_scores_codex":[0.9993287,0.00008801634,0.0000454836,0.0001132973,0.0003098683,0.0001146094],"domain_scores_gemma":[0.9990214,0.0002412381,0.0001719641,0.0001258242,0.0002504135,0.0001891033],"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":[0.00001648109,0.00001050528,0.0001567539,0.00002149408,0.000004175952,0.00008976237,0.0001055161,0.0006181551,0.002158515,0.9936738,0.0004846347,0.0026601],"study_design_scores_gemma":[0.000009265053,0.00003488151,0.0002512413,0.00001337781,0.000006114558,0.0002229856,0.00007859553,0.0109954,0.002074436,0.9842139,0.002085216,0.00001446402],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4076728,0.001150896,0.4889362,0.001346082,0.0006040144,0.00008401483,0.0002581436,0.0003178261,0.09963001],"genre_scores_gemma":[0.9385146,0.0007894298,0.04610194,0.0004045868,0.0004841535,0.0001006898,0.0001597137,0.0001355765,0.01330931],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003796471,"threshold_uncertainty_score":0.01270044,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07529896403581608,"score_gpt":0.3112240054888639,"score_spread":0.2359250414530478,"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."}}