{"id":"W4360992383","doi":"10.1007/978-3-031-13017-5_2","title":"Polygons and Modular Arithmetic","year":2023,"lang":"en","type":"book-chapter","venue":"Undergraduate texts in mathematics","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Fredericton","funders":"","keywords":"Mathematics; Field (mathematics); Algebra over a field; Modular form; Modular arithmetic; Function (biology); Modular design; Algebraic number theory; Algebraic geometry; Elementary algebra; Graph; Abstract algebra; Algebraic number; Pure mathematics; Arithmetic; Discrete mathematics; Computer science; 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":[0.001439485,0.0009692664,0.001561402,0.0008245884,0.0002082762,0.00009272528,0.0005740639,0.0007592316,0.0002005816],"category_scores_gemma":[0.00082628,0.0009521387,0.0002964642,0.0001408381,0.0005047827,0.0001160739,0.0003416824,0.001074988,0.0008184285],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002271673,"about_ca_system_score_gemma":0.0001109095,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003124667,"about_ca_topic_score_gemma":0.00009014818,"domain_scores_codex":[0.9962984,0.00007185112,0.001440993,0.000744559,0.0007999141,0.0006442281],"domain_scores_gemma":[0.9953058,0.002308193,0.0007349376,0.001322902,0.00009542071,0.0002327942],"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":[0.000006384971,0.0001611527,8.560463e-7,0.002280181,0.0001627336,0.0002017744,0.001414717,0.000006376622,0.00001484728,0.9909079,0.003905839,0.000937249],"study_design_scores_gemma":[0.0004970567,0.00006766967,8.889541e-7,0.002066032,0.0002901083,0.0001578941,0.0001258607,0.001267512,0.00001386441,0.9818352,0.01275924,0.0009186275],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0008894408,0.0006550459,0.004411948,0.0007896757,0.0006166201,0.001562207,0.0001095829,0.000961518,0.9900039],"genre_scores_gemma":[0.001854741,0.0007059028,0.04106582,0.00005227231,0.0001429884,0.0000446222,0.00002409092,0.0005592281,0.9555503],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.03665387,"threshold_uncertainty_score":0.9999595,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05173901222145938,"score_gpt":0.2791625956520443,"score_spread":0.2274235834305849,"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."}}