{"id":"W4292703475","doi":"10.48550/arxiv.1306.3104","title":"The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian","year":2013,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Japan Society for the Promotion of Science; Natural Sciences and Engineering Research Council of Canada; Seoul National University","keywords":"Conformal map; Laplace operator; Gravitational singularity; Mathematics; Logarithm; Pure mathematics; Extremal length; Conformal geometry; Einstein; Metric (unit); Function (biology); Mathematical analysis; Conformal symmetry; Mathematical physics","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":[0.000465405,0.0002289444,0.0004214333,0.0001212302,0.0003784148,0.00002808765,0.001845292,0.0002669903,0.0001015741],"category_scores_gemma":[0.0002961967,0.0001096443,0.0008764003,0.00104945,0.0008377663,0.00007662805,0.001409272,0.0006827309,0.000004061451],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006868788,"about_ca_system_score_gemma":0.0002220382,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001088537,"about_ca_topic_score_gemma":0.0009082941,"domain_scores_codex":[0.9986189,0.0002426161,0.0004116588,0.000247038,0.0002563077,0.0002234588],"domain_scores_gemma":[0.9964069,0.0003670943,0.001066959,0.001680946,0.0004422658,0.00003580279],"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":[0.0001021438,0.000442777,0.05593404,0.0008418091,0.003004327,0.000003098554,0.003348297,0.02440808,0.0001944229,0.9042556,0.006856931,0.0006085082],"study_design_scores_gemma":[0.003356986,0.0002697846,0.1900454,0.001961652,0.01070807,0.00002154306,0.05099788,0.04697386,0.003493479,0.6632637,0.02700588,0.001901687],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9846524,0.0001168861,0.001542707,0.0004591308,0.0007654693,0.0006489379,0.0001005328,0.00001674776,0.01169719],"genre_scores_gemma":[0.9816555,0.00004131137,0.00002571973,0.00003367676,0.00003232488,0.000001018939,0.000002536062,0.00001356002,0.01819436],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2409918,"threshold_uncertainty_score":0.4471163,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05504985412599127,"score_gpt":0.1820033991263383,"score_spread":0.126953545000347,"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."}}