{"id":"W2234665215","doi":"10.1007/s00020-015-2263-0","title":"Dilating Covariant Representations of a Semigroup Dynamical System Arising from Number Theory","year":2015,"lang":"en","type":"article","venue":"Integral Equations and Operator Theory","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Semigroup; Homomorphism; Injective function; Ring (chemistry); Isomorphism (crystallography); Covariant transformation; Combinatorics; Crossed product; Algebra over a field; Pure mathematics; Discrete mathematics; Mathematical 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":[0.001011575,0.0006992269,0.0008279797,0.00161298,0.001477384,0.002283897,0.001209206,0.001249613,0.004432118],"category_scores_gemma":[0.001579992,0.0003392735,0.0007713075,0.0008609938,0.003101871,0.002979916,0.001672847,0.001684662,0.0005593006],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001207409,"about_ca_system_score_gemma":0.0007668885,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009620824,"about_ca_topic_score_gemma":0.000828224,"domain_scores_codex":[0.9995477,0.000117874,0.00002535469,0.00006301482,0.000163791,0.00008222539],"domain_scores_gemma":[0.9991492,0.0002228337,0.00012301,0.000102916,0.0001649248,0.0002369992],"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":[0.00001494397,0.00001889311,0.00006762399,0.000007608926,0.000003232831,0.00007731466,0.0001745033,0.0007717491,0.001314822,0.9960669,0.0002132752,0.001269323],"study_design_scores_gemma":[0.00001589524,0.00002134704,0.000111081,0.000003562627,0.00000401257,0.0001098552,0.0000513462,0.01705002,0.0003445157,0.9813012,0.0009741618,0.00001315547],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6198698,0.0006877155,0.294662,0.001691257,0.0006962114,0.00007928624,0.0001864712,0.0004148897,0.08171234],"genre_scores_gemma":[0.9444397,0.0002866669,0.02612692,0.0002893357,0.0004691459,0.00004719804,0.000128063,0.0001591822,0.02805386],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004432118,"threshold_uncertainty_score":0.01482689,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01668413671906975,"score_gpt":0.2753829182384483,"score_spread":0.2586987815193785,"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."}}