{"id":"W3022426023","doi":"10.48550/arxiv.2005.04471","title":"$C^*$-Envelope and Dilation Theory of Semigroup Dynamical Systems","year":2020,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Semigroup; Commutative property; Operator algebra; Pure mathematics; Operator (biology); Self-adjoint operator; Envelope (radar); Dilation (metric space); Dynamical systems theory; Algebra over a field; Discrete mathematics; Hilbert space; Combinatorics; Physics; Computer science; 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":[0.001031287,0.0002635982,0.0003689217,0.000468508,0.0008167108,0.001520993,0.0004275306,0.0005130398,0.002750129],"category_scores_gemma":[0.001864845,0.0001702379,0.0005780168,0.000266669,0.002123685,0.003480889,0.001386492,0.001057849,0.0002888333],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006323888,"about_ca_system_score_gemma":0.0004693276,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003013268,"about_ca_topic_score_gemma":0.0001539364,"domain_scores_codex":[0.9994043,0.0001448769,0.00003280479,0.0001464937,0.0001732515,0.00009834923],"domain_scores_gemma":[0.9990816,0.0003491892,0.0001466187,0.0001226531,0.0001505678,0.0001493869],"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":[0.000007504058,0.000006451775,0.000147792,0.00001095129,0.000002662088,0.00003879428,0.00009611325,0.0005701013,0.001154003,0.9959926,0.0001128585,0.001860237],"study_design_scores_gemma":[0.000009672334,0.00002840935,0.0005296508,0.000009114236,0.000004863212,0.0002014705,0.00008931855,0.01546528,0.001625247,0.9781401,0.003884638,0.0000121987],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4413937,0.0011137,0.493475,0.001620379,0.0002617812,0.00005353371,0.0001655688,0.0002166241,0.06169956],"genre_scores_gemma":[0.9713888,0.0002977752,0.02348565,0.0001586003,0.0001735607,0.00003251418,0.00008163189,0.00003206521,0.004349325],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002750129,"threshold_uncertainty_score":0.009200096,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1456498224125986,"score_gpt":0.246820206141724,"score_spread":0.1011703837291253,"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."}}