{"id":"W3014383176","doi":"10.2969/jmsj/80868086","title":"Newton polyhedra and order of contact on real hypersurfaces","year":2020,"lang":"en","type":"preprint","venue":"Journal of the Mathematical Society of Japan","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Polyhedron; Hypersurface; Mathematics; Regular polygon; Order (exchange); Equivalence (formal languages); Singularity; Type (biology); Function (biology); Gravitational singularity; Pseudoconvex function; Simple (philosophy); Pure mathematics; Convex function; Mathematical analysis; Combinatorics; Geometry; Subderivative; Convex optimization","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":[0.0004786181,0.0003580956,0.0004477655,0.001919131,0.001075722,0.002055986,0.000515907,0.0005303645,0.005207033],"category_scores_gemma":[0.002193598,0.0002189674,0.0004447255,0.000589977,0.003062099,0.002780179,0.001271196,0.001355739,0.0004825332],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009990585,"about_ca_system_score_gemma":0.0003703612,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001252052,"about_ca_topic_score_gemma":0.0008821704,"domain_scores_codex":[0.9993162,0.0001096162,0.00003498061,0.0001030297,0.0003019858,0.0001341476],"domain_scores_gemma":[0.9987862,0.0003791437,0.0002732273,0.00009003226,0.0002283045,0.0002431462],"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":[0.00005017321,0.00002570493,0.001139903,0.00004280996,0.00000505588,0.000185341,0.0004875107,0.004364116,0.003346821,0.9830057,0.0003474401,0.006999384],"study_design_scores_gemma":[0.00002262461,0.0001180894,0.002915641,0.00003877722,0.000007438277,0.0005179781,0.0009926877,0.0455536,0.004989508,0.9375523,0.007251378,0.00003976916],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8304379,0.0004478212,0.1177255,0.0003111976,0.00007499683,0.00006779419,0.0001611735,0.00008588553,0.05068763],"genre_scores_gemma":[0.9817901,0.0002362978,0.009463395,0.00002825881,0.00005263434,0.00001814415,0.000115273,0.00003831114,0.00825758],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005207033,"threshold_uncertainty_score":0.01741928,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02603153760369918,"score_gpt":0.2605852100663348,"score_spread":0.2345536724626356,"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."}}