{"id":"W2009870930","doi":"10.1007/s00023-011-0154-8","title":"Quantum Ergodic Restriction Theorems. I: Interior Hypersurfaces in Domains with Ergodic Billiards","year":2011,"lang":"en","type":"article","venue":"Annales Henri Poincaré","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":33,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Ergodic theory; Mathematics; Hypersurface; Pure mathematics; Geodesic; Mathematical analysis; Eigenfunction; Orthogonality; Mathematical physics; Physics; Quantum mechanics; Eigenvalues and eigenvectors; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[],"consensus_categories":[],"category_scores_codex":[0.0006903667,0.0003262077,0.0005066783,0.0002556186,0.0001044247,0.00005121189,0.0003307019,0.0001725696,0.0002820394],"category_scores_gemma":[0.0002747342,0.0002313678,0.0001339639,0.0004130801,0.0002320692,0.0002211107,0.00009587654,0.0003247551,0.0001045893],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007304491,"about_ca_system_score_gemma":0.00007396084,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001703621,"about_ca_topic_score_gemma":0.0003943775,"domain_scores_codex":[0.9979676,0.0001463448,0.0005893256,0.0004088798,0.0003911919,0.0004966571],"domain_scores_gemma":[0.9986095,0.0003553823,0.0002214902,0.0005555502,0.00009757826,0.0001604663],"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":[0.0004738983,0.0007700602,0.01317094,0.0004307017,0.0001535779,0.0002346405,0.005356287,0.000004046072,0.00102819,0.9756554,0.001282768,0.00143954],"study_design_scores_gemma":[0.001454818,0.0009066697,0.01779991,0.0006886101,0.0001238237,0.0001150249,0.002272733,0.004978075,0.0007176507,0.9683045,0.001801336,0.000836849],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.971534,0.0001971461,0.005318269,0.000185643,0.0001235296,0.0004028407,0.0000222776,0.0001418154,0.02207446],"genre_scores_gemma":[0.9920139,0.0002921138,0.007039601,0.0001063147,0.00004902515,0.00004603811,0.000009030886,0.00006458241,0.000379435],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02169503,"threshold_uncertainty_score":0.9434906,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05664017338956954,"score_gpt":0.2835624765121453,"score_spread":0.2269223031225757,"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."}}