{"id":"W2951906953","doi":"10.48550/arxiv.0808.3263","title":"Proof of a dynamical Bogomolov conjecture for lines under polynomial actions","year":2008,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Lethbridge","funders":"","keywords":"Conjecture; Polynomial; Mathematics; Affine transformation; Space (punctuation); Pure mathematics; Action (physics); Degree (music); Line (geometry); Dynamical systems theory; Combinatorics; Mathematical analysis; Physics; Computer science; Geometry; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007377157,0.0004830311,0.0006126043,0.0008548281,0.001204399,0.001266959,0.0008101728,0.001094655,0.008404807],"category_scores_gemma":[0.002674855,0.000300941,0.0008160644,0.0004863045,0.002482483,0.002826119,0.00296443,0.002109798,0.0006502948],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008458924,"about_ca_system_score_gemma":0.0004032637,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001011732,"about_ca_topic_score_gemma":0.0006164851,"domain_scores_codex":[0.9996217,0.00007545597,0.00002082285,0.00008147897,0.0001168491,0.00008357569],"domain_scores_gemma":[0.9990163,0.0003442563,0.000181894,0.00014662,0.0001457255,0.0001652291],"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":[0.00002269645,0.0000210042,0.0004283657,0.00004662742,0.000008533488,0.000219883,0.0002063181,0.001997157,0.001527224,0.9915994,0.001530462,0.002392377],"study_design_scores_gemma":[0.00004873057,0.00003632224,0.0006529008,0.00002255746,0.00001027726,0.0002388357,0.000109439,0.01709375,0.0009667275,0.97604,0.00476155,0.00001888114],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.5311984,0.001382071,0.3185422,0.01010628,0.001252836,0.0001120246,0.0007151136,0.0007747479,0.1359164],"genre_scores_gemma":[0.9783787,0.0004982381,0.01225423,0.000578402,0.0004687451,0.00006482878,0.0002639653,0.00007050532,0.007422494],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.008404807,"threshold_uncertainty_score":0.02811694,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1277050999365249,"score_gpt":0.364824841663868,"score_spread":0.2371197417273431,"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."}}