{"id":"W1679931098","doi":"10.1090/fic/061/01","title":"Local index theorem for projective families","year":2011,"lang":"en","type":"preprint","venue":"","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Index (typography); Atiyah–Singer index theorem; Mathematics; Projective test; Dirac (video compression format); Pure mathematics; Algebra over a field; Computer science; Physics; Quantum mechanics; World Wide Web","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":[0.000538408,0.000372003,0.0005366739,0.0001875793,0.00009520041,0.0000530352,0.0006297887,0.0004571564,0.0002969762],"category_scores_gemma":[0.000768097,0.0002825394,0.0002142702,0.0001007731,0.0002971373,0.0000822528,0.001207624,0.0008329173,0.00004721438],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002126971,"about_ca_system_score_gemma":0.0004192402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008496187,"about_ca_topic_score_gemma":0.0001695986,"domain_scores_codex":[0.9980322,0.00009574408,0.0003628454,0.0006583613,0.000368558,0.0004823152],"domain_scores_gemma":[0.9976961,0.000691362,0.0001248867,0.0008798825,0.0005074415,0.0001003117],"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":[0.000224273,0.0001900858,0.0001031857,0.0008882068,0.0002090474,0.000004900366,0.002137776,0.00004166023,0.00002770447,0.9827636,0.002697668,0.01071192],"study_design_scores_gemma":[0.0003815654,0.0001038206,0.00003549496,0.00009032938,0.00002919533,0.000002526799,0.00209457,0.002254826,0.007562934,0.9865811,0.0004994713,0.0003641633],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01005087,0.00005969599,0.9171079,0.00005507125,0.0002290346,0.003423507,0.00006618535,0.0002869318,0.06872075],"genre_scores_gemma":[0.8374914,0.00004638014,0.1510467,0.0000826409,0.0002051038,0.002328363,0.00002920768,0.0001873404,0.008582878],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8274406,"threshold_uncertainty_score":0.9999627,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09824987524335284,"score_gpt":0.3873686031190265,"score_spread":0.2891187278756737,"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."}}