{"id":"W1029952621","doi":"10.1007/978-3-662-04524-4_9","title":"Homeomorphisms of the Unit Circle","year":2001,"lang":"en","type":"book-chapter","venue":"","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Fields Institute for Research in Mathematical Sciences","funders":"","keywords":"Endomorphism; Unit circle; Encyclopedia; Unit (ring theory); Subject (documents); Dynamics (music); Mathematics; Pure mathematics; Mathematical analysis; Computer science; Physics; Mathematics education; Library science","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0001094298,0.0001440086,0.000279562,0.0000375545,0.00005366864,0.0000088648,0.000358618,0.0001488804,0.004788757],"category_scores_gemma":[0.00002803375,0.00009906876,0.0001700215,0.00003251705,0.00008854715,0.000009250378,0.0001085274,0.0001591051,0.0001387027],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001143428,"about_ca_system_score_gemma":0.00003529188,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004756596,"about_ca_topic_score_gemma":0.00001999602,"domain_scores_codex":[0.9992011,0.000004312923,0.00034006,0.0001282205,0.0002337787,0.00009258071],"domain_scores_gemma":[0.9985301,0.0001776817,0.0003105054,0.0008634357,0.00008604321,0.00003220495],"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":[2.971825e-7,0.00002404354,8.529669e-7,0.00008901921,0.00002772962,3.261483e-7,0.00003178798,9.97377e-8,0.00001673114,0.9591021,0.04019522,0.00051178],"study_design_scores_gemma":[0.00004813975,0.000004729399,0.000002845498,0.00009430719,0.00005546063,0.000005234496,0.000006979496,0.00001172008,0.0001076533,0.6898122,0.3097631,0.00008761105],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.00008775354,0.00002830576,0.001711481,0.0003048132,0.00003829869,0.000353718,0.00003395827,0.00003587387,0.9974058],"genre_scores_gemma":[0.002051922,0.00004940809,0.003820303,0.00005986352,0.00005339172,0.00001328589,0.000004578907,0.00004942935,0.9938978],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.2695679,"threshold_uncertainty_score":0.996121,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09251478769662798,"score_gpt":0.2945083011276403,"score_spread":0.2019935134310124,"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."}}