{"id":"W2952282911","doi":"10.48550/arxiv.math/0411021","title":"The Local Index Formula in Semifinite von Neumann Algebras II: The Even Case","year":2004,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Index (typography); Tomita–Takesaki theory; Affiliated operator; Von Neumann architecture; Pure mathematics; Mathematics; Algebra over a field; Jordan algebra; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008122253,0.0003761282,0.0005340167,0.00106145,0.0009075142,0.002460887,0.0009193548,0.0006737011,0.002745613],"category_scores_gemma":[0.001620844,0.0001947238,0.0004580641,0.0005895739,0.003186693,0.00433983,0.001892573,0.001371572,0.0004667956],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001274064,"about_ca_system_score_gemma":0.0004739835,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007112236,"about_ca_topic_score_gemma":0.0006605453,"domain_scores_codex":[0.9996912,0.00004456668,0.00001721417,0.00005555677,0.00011624,0.00007529085],"domain_scores_gemma":[0.9994346,0.0001667332,0.00008431836,0.00008306585,0.0001047101,0.0001264785],"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":[0.00001785023,0.0000096158,0.0003188023,0.00003176592,0.000003114259,0.0001434044,0.000234466,0.0005115795,0.002035663,0.9936519,0.0003496011,0.002692197],"study_design_scores_gemma":[0.000008012727,0.00001642913,0.0002519627,0.00001620308,0.000007126394,0.0001987673,0.00013702,0.00690821,0.00265723,0.9884614,0.001326049,0.00001161078],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6840431,0.001256417,0.1929582,0.001344304,0.0002544739,0.00005033312,0.000129591,0.000234918,0.1197286],"genre_scores_gemma":[0.9849911,0.0002837714,0.00879667,0.0001506923,0.00009043147,0.00002553258,0.00003718861,0.0000493085,0.005575385],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002745613,"threshold_uncertainty_score":0.009244025,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0773237377983286,"score_gpt":0.3608434461902009,"score_spread":0.2835197083918722,"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."}}