{"id":"W3036701764","doi":"10.1093/imrn/rnaa167","title":"Restriction of Laplace–Beltrami Eigenfunctions to Arbitrary Sets on Manifolds","year":2020,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; Dalhousie University","funders":"","keywords":"Mathematics; Pure mathematics; Riemannian manifold; Eigenfunction; Lebesgue integration; Ball (mathematics); Hausdorff dimension; Hausdorff measure; Borel measure; Mathematical analysis; Uniqueness; Lebesgue measure; Probability measure; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001805575,0.0008955244,0.0006837242,0.001949301,0.0005695085,0.001411045,0.0008202896,0.0006158184,0.001100051],"category_scores_gemma":[0.008514965,0.0002825742,0.0004827006,0.000523059,0.00264142,0.00205855,0.001836558,0.001297304,0.0001137426],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001064255,"about_ca_system_score_gemma":0.0003008428,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007783322,"about_ca_topic_score_gemma":0.0005273736,"domain_scores_codex":[0.9993559,0.0002167751,0.0000355579,0.0001236683,0.0001761727,0.00009196447],"domain_scores_gemma":[0.995901,0.002289838,0.0005969334,0.0003581276,0.0004421973,0.0004118239],"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":[0.0002828396,0.0001516462,0.01900212,0.0002401548,0.0001053691,0.0009692317,0.000687799,0.08615812,0.05363995,0.8225054,0.00124231,0.01501491],"study_design_scores_gemma":[0.0000224223,0.0001890286,0.01571591,0.00008698621,0.00003774034,0.0006503796,0.0005436927,0.5810891,0.02039166,0.3793547,0.001827484,0.00009090389],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8755594,0.0005144122,0.1173155,0.0005191865,0.00004899522,0.00001964451,0.00008726,0.00007457533,0.005861092],"genre_scores_gemma":[0.9911892,0.0002480158,0.007395074,0.00004375348,0.0000579703,0.00002667617,0.00007752454,0.00001885744,0.0009427766],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001949301,"threshold_uncertainty_score":0.009548903,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.317677137042576,"score_gpt":0.4871540697921228,"score_spread":0.1694769327495468,"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."}}