{"id":"W2949798177","doi":"10.48550/arxiv.1005.1636","title":"Quantum ergodic restriction theorems, I: interior hypersurfaces in domains with ergodic billiards","year":2010,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Ergodic theory; Hypersurface; Mathematics; Geodesic; Pure mathematics; Eigenfunction; Dirichlet distribution; Mathematical physics; Mathematical analysis; Boundary value problem; Physics; Eigenvalues and eigenvectors; Quantum mechanics","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":[0.00153973,0.0005312632,0.0006439387,0.001288529,0.001085883,0.001704781,0.0009052154,0.0007173222,0.002792116],"category_scores_gemma":[0.005036539,0.0004232276,0.001046524,0.0004935024,0.003402629,0.004087813,0.003054626,0.001808621,0.0003289739],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001000543,"about_ca_system_score_gemma":0.0006196246,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009590879,"about_ca_topic_score_gemma":0.0004999771,"domain_scores_codex":[0.999379,0.0001752191,0.00005178502,0.0001251066,0.0001795196,0.00008919177],"domain_scores_gemma":[0.9976875,0.001193847,0.00028045,0.0003102499,0.0002980684,0.0002299354],"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":[0.00002517758,0.00001317147,0.0005438921,0.00004613234,0.000009348876,0.0001039501,0.0001694579,0.003213756,0.002417473,0.9892825,0.0007220898,0.003453088],"study_design_scores_gemma":[0.00003499091,0.00006901855,0.001641483,0.00004237996,0.00002204039,0.0003132301,0.0002277072,0.05096741,0.00449065,0.9355504,0.006604146,0.0000364731],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5663736,0.001857412,0.3714565,0.002538157,0.0001989062,0.000103756,0.0005565745,0.0003219105,0.05659316],"genre_scores_gemma":[0.9491149,0.0007844181,0.03916401,0.0003212048,0.0003615521,0.0001779049,0.0005645107,0.000106917,0.00940447],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002792116,"threshold_uncertainty_score":0.009340584,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07306191475822203,"score_gpt":0.2223179768784518,"score_spread":0.1492560621202297,"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."}}