{"id":"W3100813850","doi":"10.1007/jhep11%282017%29039","title":"Positive geometries and canonical forms","year":2023,"lang":"en","type":"article","venue":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":152,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Goddard Space Flight Center; Princeton University; U.S. Department of Energy; National Science Foundation","keywords":"Canonical form; Grassmannian; Mathematics; Connection (principal bundle); Pure mathematics; Triangulation; Polytope; Gravitational singularity; Simplex; Differential form; Boundary (topology); Tree (set theory); Combinatorics; Geometry; Mathematical analysis","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":[0.0008643994,0.0006219228,0.0003278911,0.001698618,0.001414368,0.003077345,0.000661694,0.000644121,0.008250951],"category_scores_gemma":[0.003086278,0.000360784,0.0005133834,0.0008573058,0.005818534,0.004921642,0.002606115,0.001472969,0.001312811],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008334686,"about_ca_system_score_gemma":0.0004564044,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005699483,"about_ca_topic_score_gemma":0.0005111736,"domain_scores_codex":[0.9985304,0.0004596657,0.00006842297,0.0003484547,0.0004206825,0.0001723135],"domain_scores_gemma":[0.9990848,0.0002504642,0.0001218839,0.0001404321,0.0002399671,0.0001624729],"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":[0.000002786382,0.000002525659,0.0001369145,0.00001134179,9.670672e-7,0.00002426515,0.0002164648,0.0002490889,0.0002219297,0.9954834,0.0005192087,0.003131178],"study_design_scores_gemma":[0.000003091016,0.00001451426,0.0002740213,0.00001309103,0.000002237207,0.0001838939,0.0002932849,0.001876616,0.000597226,0.9852405,0.0114882,0.00001327402],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.461888,0.001712518,0.3018759,0.002294217,0.0007503476,0.0001283917,0.0006746607,0.0005911669,0.2300849],"genre_scores_gemma":[0.9218882,0.000960023,0.05887305,0.0002795799,0.0003838216,0.0000690501,0.0004213821,0.000204135,0.01692085],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008250951,"threshold_uncertainty_score":0.0276022,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01663875193497328,"score_gpt":0.2548114733508728,"score_spread":0.2381727214158995,"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."}}