{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008850346,0.0004483643,0.0005345754,0.001939898,0.002003179,0.00212011,0.0007716769,0.0006075485,0.01024277],"category_scores_gemma":[0.002018786,0.0002760302,0.0006558729,0.0008868893,0.002035949,0.004608271,0.003777282,0.001967173,0.0009363382],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001085226,"about_ca_system_score_gemma":0.0003282045,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005530089,"about_ca_topic_score_gemma":0.0003732734,"domain_scores_codex":[0.9993238,0.0001172143,0.0000361822,0.0001267742,0.0002392676,0.0001567647],"domain_scores_gemma":[0.9990513,0.0002210338,0.0001027182,0.0001601174,0.0002300208,0.0002349612],"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":[0.00001371711,0.000008610595,0.0003021393,0.00001808122,0.000004515294,0.00010738,0.0001817412,0.0002080246,0.001248185,0.9953023,0.0004673854,0.002137835],"study_design_scores_gemma":[0.00002307657,0.00003643155,0.001238647,0.00001916891,0.0000193316,0.0004281032,0.0002584321,0.0065731,0.002708299,0.9834794,0.005191988,0.00002397355],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.6153459,0.0005522564,0.1295224,0.001504768,0.0002688215,0.00007536269,0.0003655278,0.0003354342,0.2520294],"genre_scores_gemma":[0.9807506,0.0002325011,0.006485899,0.0002012621,0.000217983,0.00005729785,0.0001969123,0.00007423582,0.01178332],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.01024277,"threshold_uncertainty_score":0.03426546,"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."}}