{"id":"W2607708259","doi":"10.1090/crmp/055/01","title":"A self-contained proof of the strong-type capacitary inequality for the Dirichlet space","year":2012,"lang":"en","type":"book-chapter","venue":"CRM proceedings & lecture notes","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Space (punctuation); Type (biology); Dirichlet distribution; Dirichlet boundary condition; Pure mathematics; Unit (ring theory); Point (geometry); Boundary (topology); Inequality; Mathematical analysis; Boundary value problem; Geometry; Computer science","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004704434,0.0004880834,0.0005245933,0.00007168728,0.0001916467,0.0000744108,0.001495975,0.0003325124,0.00000698587],"category_scores_gemma":[0.00129783,0.0002796773,0.0002459433,0.000145609,0.0001079993,0.0002577756,0.000404802,0.0006847784,0.000002244709],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001186346,"about_ca_system_score_gemma":0.0001113371,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002434864,"about_ca_topic_score_gemma":0.000001920258,"domain_scores_codex":[0.9981406,0.000005174075,0.0004542136,0.0004750337,0.0004647622,0.0004601713],"domain_scores_gemma":[0.9974182,0.0008283401,0.0004506925,0.0006033679,0.0005962473,0.0001031453],"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":[0.00001369096,0.00002462499,0.00000905356,0.0008554583,0.0001172218,1.907602e-7,0.001652971,0.001760018,0.0004681375,0.9923244,0.000027184,0.002747063],"study_design_scores_gemma":[0.0002299482,0.0001410915,0.00001238833,0.0004557976,0.0002343966,0.00001706481,0.00001289651,0.07956438,0.008911629,0.9024091,0.007458352,0.0005529046],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0001184335,0.002271401,0.9823157,0.001676332,0.0004789529,0.001438918,0.00001185529,0.0002540032,0.01143445],"genre_scores_gemma":[0.9432675,0.00003025276,0.05533456,0.000254435,0.0006369562,0.0001041804,0.000002895694,0.0001105677,0.0002586615],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.943149,"threshold_uncertainty_score":0.9999655,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02729200339992427,"score_gpt":0.247752603611253,"score_spread":0.2204606002113287,"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."}}