{"id":"W4392569964","doi":"10.2298/fil2312755r","title":"New proofs of some Dedekind η-function identities of level 6","year":2023,"lang":"en","type":"article","venue":"Filomat","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Mathematical proof; Dedekind cut; Dedekind sum; Pure mathematics; Function (biology); Dedekind eta function; Algebra over a field; Modular form; Geometry; Evolutionary biology","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":[],"consensus_categories":[],"category_scores_codex":[0.0001990704,0.0001270905,0.0003476864,0.0001836749,0.00003713529,0.00001497,0.000172067,0.00007032701,0.0005638299],"category_scores_gemma":[0.0006325403,0.00011739,0.0001103683,0.0002773109,0.00007909723,0.0003498764,0.0001243101,0.00006784813,0.0001954296],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002281955,"about_ca_system_score_gemma":0.00004670116,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001528116,"about_ca_topic_score_gemma":0.00001274712,"domain_scores_codex":[0.9987609,0.00002280578,0.000486621,0.0001412466,0.0003899296,0.0001984766],"domain_scores_gemma":[0.9988837,0.0003875385,0.0002541508,0.0003320052,0.00009278752,0.00004985671],"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":[0.00003095946,0.00008632513,0.0001517468,0.002201692,0.0001036606,0.000006150131,0.001184423,0.00001893263,0.01019663,0.9313349,0.05379067,0.0008939579],"study_design_scores_gemma":[0.0002617958,0.00006005412,0.0009186603,0.0001654863,0.00005170852,0.000003957485,0.0004255241,0.00006810648,0.03849757,0.9592501,0.0001939308,0.0001030997],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8939005,0.0002763827,0.07715928,0.0002748852,0.001207022,0.001104036,0.0001851266,0.0008525233,0.02504026],"genre_scores_gemma":[0.7490853,0.00007600115,0.06921264,0.00002978109,0.0003369875,0.00006716832,0.00003495413,0.0001366932,0.1810205],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1559802,"threshold_uncertainty_score":0.6173542,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.14505296809029,"score_gpt":0.3528824654239284,"score_spread":0.2078294973336385,"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."}}