{"id":"W4384152037","doi":"10.1007/978-3-031-32629-5_4","title":"Application: Eta Quotients","year":2023,"lang":"en","type":"book-chapter","venue":"Synthesis lectures on mathematics and statistics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Carleton University; Northwestern Polytechnic","funders":"","keywords":"Quotient; Mathematics; Dedekind sum; Modular form; Eisenstein series; Pure mathematics; Multiplicative function; Normalization (sociology); Dedekind eta function; Dedekind cut; Algebra over a field; Mathematical analysis","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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004225665,0.0008494061,0.001298472,0.0003222772,0.0002731869,0.0001654583,0.0004456711,0.0005139324,0.0004491558],"category_scores_gemma":[0.00313189,0.0007398362,0.0001871591,0.00006547468,0.0003397541,0.00005119522,0.0002163904,0.0006101907,0.0008054924],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001043975,"about_ca_system_score_gemma":0.00006011309,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002224502,"about_ca_topic_score_gemma":0.00003032458,"domain_scores_codex":[0.9967303,0.00002672262,0.001056843,0.0007060064,0.0009999643,0.0004801553],"domain_scores_gemma":[0.9893538,0.008377455,0.0007473647,0.001094035,0.0002082297,0.0002191665],"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":[0.000009695082,0.00008182454,3.156088e-7,0.002038434,0.0002218983,0.00003106299,0.0002507613,0.000005804661,0.000009399601,0.9742857,0.0180659,0.004999267],"study_design_scores_gemma":[0.0001275509,0.00007423093,0.000001746974,0.0009606465,0.0004672101,0.00001939842,0.00004966033,0.001378747,0.00009776109,0.9868099,0.009301294,0.0007118691],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.00001712006,0.0002409565,0.4621288,0.0002350244,0.0003779303,0.001627457,0.002346466,0.0007385943,0.5322877],"genre_scores_gemma":[0.0002884513,0.0008412176,0.3479036,0.0001092975,0.0002774315,0.0002320437,0.00007822033,0.0006403357,0.6496294],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.1173417,"threshold_uncertainty_score":0.9999725,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05003632339424931,"score_gpt":0.3074431471064208,"score_spread":0.2574068237121715,"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."}}