{"id":"W3127718424","doi":"10.1063/5.0062138","title":"Discrete and zeta-regularized determinants of the Laplacian on polygonal domains with Dirichlet boundary conditions","year":2023,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Ministero dell’Istruzione, dell’Università e della Ricerca; Banff International Research Station for Mathematical Innovation and Discovery; H2020 European Research Council; Università degli Studi Roma Tre; Università degli Studi di Roma Tor Vergata; European Commission","keywords":"Dirichlet distribution; Laplace operator; Boundary (topology); Mathematics; Dirichlet boundary condition; Boundary value problem; Mathematical analysis; Dirichlet problem; Applied mathematics; Pure mathematics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008212287,0.0003060347,0.0008918148,0.00008570232,0.0002013247,0.00005953447,0.000467843,0.00009033018,0.00004739731],"category_scores_gemma":[0.0008054798,0.0001664015,0.0003440655,0.0005409193,0.0007730321,0.0002081174,0.0001360065,0.0004801751,0.0000196854],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004987816,"about_ca_system_score_gemma":0.00008948871,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":3.415609e-7,"about_ca_topic_score_gemma":0.000001234679,"domain_scores_codex":[0.9973599,0.0001852062,0.0008993379,0.0001794766,0.001022252,0.0003538252],"domain_scores_gemma":[0.9955202,0.002720869,0.0008830941,0.0005360408,0.0001742293,0.0001655318],"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":[0.0001821581,0.0006186448,0.0002108295,0.0005929695,0.000264857,0.00004037168,0.0009237156,0.00002795294,0.002891957,0.9930326,0.0008918113,0.0003220839],"study_design_scores_gemma":[0.0009535275,0.0003523096,0.001033813,0.0008530125,0.0003028209,0.0001351024,0.0002255213,0.0008751326,0.005755041,0.9892855,0.00002648217,0.0002017191],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9909668,0.000009044173,0.005521661,0.000560224,0.00009761337,0.0003603915,0.00005669675,0.00004406457,0.002383522],"genre_scores_gemma":[0.9907984,0.000006731842,0.008564773,0.00009975617,0.000204805,0.0000098467,0.000001454347,0.00006626168,0.0002479619],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003747131,"threshold_uncertainty_score":0.6785657,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03083581831222702,"score_gpt":0.3241254219312497,"score_spread":0.2932896036190227,"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."}}