{"id":"W2609790057","doi":"10.1090/amsip/050/15","title":"Representations of the Ptolemy groupoid, Johnson homomorphisms, and finite type invariants","year":2011,"lang":"en","type":"book-chapter","venue":"AMS/IP studies in advanced mathematics","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Ptolemy's table of chords; Homomorphism; Type (biology); Pure mathematics; Mathematics; Algebra over a field; Geology; Geometry","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":[0.0004278551,0.0004264812,0.0004763268,0.001207301,0.001417866,0.003374542,0.0006964885,0.0007172819,0.006010172],"category_scores_gemma":[0.001068805,0.0002674244,0.0004631887,0.00127008,0.003616233,0.00535891,0.001169489,0.0025793,0.0009143131],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0014309,"about_ca_system_score_gemma":0.0005777739,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009262396,"about_ca_topic_score_gemma":0.001053094,"domain_scores_codex":[0.9997773,0.00005522052,0.00001163385,0.00003823354,0.00008002146,0.00003759074],"domain_scores_gemma":[0.999724,0.0001045511,0.00003488931,0.00005898016,0.00003397032,0.00004364472],"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":[0.000005615775,0.000006332305,0.00002701254,0.00001058566,0.000001287325,0.00001118118,0.000131082,0.0001058978,0.0001413314,0.9948394,0.001087041,0.003633301],"study_design_scores_gemma":[0.000003792851,0.000004911193,0.00006368495,0.000006573245,0.000001897599,0.0000316638,0.00006563652,0.0002317962,0.00009230508,0.9929826,0.006511766,0.000003507616],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1579753,0.01198875,0.06818534,0.004500575,0.00163294,0.00003750003,0.0002915853,0.0004417705,0.7549462],"genre_scores_gemma":[0.8657278,0.004849301,0.01319656,0.0006155496,0.001635258,0.0000580822,0.0002691583,0.0001528927,0.1134954],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006010172,"threshold_uncertainty_score":0.02010602,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1477464233158832,"score_gpt":0.3666137998039895,"score_spread":0.2188673764881063,"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."}}