{"paper":{"title":"Crossed product C*-algebras by finite group actions with the projection free tracial Rokhlin property","arxiv_id":"0902.3324","primary_cat":"math.OA","submitted_at":"2009-02-19T08:51:42+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":1.0,"id":"s0","own":true,"role":"contribution","text":"In this paper we introduce an analog of the tracial Rokhlin property, called the {\\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.94,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":1,"p":0.78,"id":"s1","own":true,"role":"result","text":"Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^*$-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if $\\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^*(G, A, \\alpha)$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven)","hedge":{"p":0.95,"label":"asserted"},"own_p":0.83,"main_claim_p":0.79,"quantitative":false,"quantitative_p":0.48,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.78,"background":0.0,"limitation":0.2,"future_work":0.0,"contribution":0.02,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.98,"text":"Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^*$-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if $\\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^*(G, A, \\alpha)$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven)","location":"abstract s1","hedge_strength":{"p":0.95,"label":"asserted"}},"provenance":{"route":{"via":"OpenRouter","model":"classifier-1.13","endpoint":"https://openrouter.ai/api/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":2527,"cost_usd_reported":0.000106},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.08,"states_limitation":0.97,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.06,"compares_with_prior_results":0.19,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.99,"value":"proof or derivation","probabilities":{"argument":0.01,"literature":0.0,"proof_or_derivation":0.99,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.6,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.4,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.6,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.99,"text":"In this paper we introduce an analog of the tracial Rokhlin property, called the {\\emph {projection free tracial Rokhlin property}}, for $C^*$-algebras which may not have any nontrivial projections.","location":"abstract s0"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v2"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":2,"sentences_in_abstract":2},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}