{"id":"W4389261049","doi":"10.48550/arxiv.2311.18381","title":"On the dynamics of endomorphisms of affine surfaces","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Agence Nationale de la Recherche; Centre Henri Lebesgue; Centre de Recherches Mathématiques","keywords":"Endomorphism; Mathematics; Automorphism; Affine transformation; Pure mathematics; Affine plane (incidence geometry); Degree (music); Algebraic number; Mathematical analysis; Plane curve; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000551982,0.0005002614,0.0004260907,0.001585126,0.001059089,0.001709559,0.0004588821,0.0005308669,0.002229268],"category_scores_gemma":[0.001577798,0.0002896283,0.0006665289,0.0005023499,0.002577465,0.003303422,0.001549291,0.00121792,0.0002739655],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001442468,"about_ca_system_score_gemma":0.0002858325,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009901527,"about_ca_topic_score_gemma":0.0004802661,"domain_scores_codex":[0.9995958,0.00006340052,0.00001734785,0.00009190002,0.0001264405,0.0001050514],"domain_scores_gemma":[0.9992943,0.0002113959,0.0001295821,0.00008969667,0.0001012563,0.0001737461],"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":[0.0000303135,0.00001577702,0.0008359389,0.00002379044,0.000007185374,0.0001115913,0.0006070118,0.00379776,0.005667366,0.9841989,0.0002324832,0.004471975],"study_design_scores_gemma":[0.00001782164,0.00006694806,0.001974355,0.00002408432,0.000006484952,0.0003105552,0.0002595603,0.0183298,0.003210349,0.9692904,0.006478336,0.00003140127],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8877376,0.001654175,0.07074685,0.0009616808,0.0001145516,0.00003778072,0.000177285,0.0001263051,0.03844379],"genre_scores_gemma":[0.98706,0.0005002497,0.00626492,0.00006109589,0.00007901373,0.00002097243,0.00007997014,0.00003654278,0.005897228],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002229268,"threshold_uncertainty_score":0.01046586,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1642082427298368,"score_gpt":0.2257476669946102,"score_spread":0.06153942426477343,"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."}}