{"id":"W2066625570","doi":"10.1090/s0002-9939-2012-11531-x","title":"Polyhedral surfaces and determinant of Laplacian","year":2012,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"Hausdorff Research Institute for Mathematics; Natural Sciences and Engineering Research Council of Canada","keywords":"Laplace operator; Semantics (computer science); Holonomy; Genus; Surface (topology); Algorithm; Computer science; Annotation; Mathematics; Artificial intelligence; Geometry; Pure mathematics; Mathematical analysis; Biology; Programming language","routes":{"ca_aff":true,"ca_fund":true,"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":[],"consensus_categories":[],"category_scores_codex":[0.0005618858,0.0001520123,0.0004784846,0.0000185642,0.00008189779,0.00001455519,0.0003083506,0.00004057029,0.00003313123],"category_scores_gemma":[0.0003305442,0.00009571447,0.0002349319,0.0003327752,0.0006574183,0.0001359804,0.0002706141,0.0001200679,0.000002514156],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001508271,"about_ca_system_score_gemma":0.000008786403,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001023154,"about_ca_topic_score_gemma":2.108847e-7,"domain_scores_codex":[0.9988822,0.000009334102,0.0003606902,0.0001232167,0.0003100103,0.0003145367],"domain_scores_gemma":[0.9988521,0.0002922869,0.0005387058,0.0001321563,0.00008974326,0.0000950206],"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":[0.00005850126,0.001183515,0.1688717,0.003891626,0.0003400031,1.117365e-7,0.01533167,2.381872e-7,0.0811519,0.7230631,0.003783693,0.002323904],"study_design_scores_gemma":[0.0006172992,0.0004070363,0.1178404,0.0004609062,0.0004930063,0.00009316563,0.02009282,0.001210977,0.09693889,0.7608342,0.000351819,0.0006594803],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9966459,0.0000508542,0.0001332489,0.0002382053,0.00002178136,0.0001628472,0.00000435532,0.00002729281,0.002715472],"genre_scores_gemma":[0.9615605,0.00001173031,0.03812708,0.00005927905,0.00003541758,0.000007108953,7.097992e-8,0.00001649885,0.0001823555],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05103131,"threshold_uncertainty_score":0.3903123,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02862085582303745,"score_gpt":0.2870594943483094,"score_spread":0.2584386385252719,"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."}}