{"id":"W1719284971","doi":"10.1090/s0002-9939-02-06742-4","title":"Invariant complementation and projectivity in the Fourier algebra","year":2002,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Annotation; Invariant (physics); Semantics (computer science); Algorithm; Bounded function; Computer science; Algebra over a field; Mathematics; Artificial intelligence; Pure mathematics; Programming language","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001208932,0.0001524265,0.0003310466,0.00002401667,0.0001626395,0.00006322446,0.0004601467,0.00003045569,0.00006384191],"category_scores_gemma":[0.001092796,0.00008353587,0.0001259648,0.0006596571,0.0007032633,0.0001882025,0.0002438792,0.000324739,0.000004653471],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006782712,"about_ca_system_score_gemma":0.00001193233,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001506794,"about_ca_topic_score_gemma":0.000003104651,"domain_scores_codex":[0.998459,0.00004371838,0.0003457753,0.0002262184,0.0006227925,0.0003024928],"domain_scores_gemma":[0.9986067,0.0007722307,0.0002780172,0.0001894421,0.0001081385,0.0000454119],"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":[0.00003474232,0.001201097,0.01546142,0.001184088,0.0001429476,9.697316e-7,0.04999995,8.022674e-7,0.008925729,0.9053398,0.0128687,0.004839723],"study_design_scores_gemma":[0.0006693852,0.0001904494,0.007290259,0.000129005,0.00006254845,0.00003648412,0.02258441,0.01353411,0.002500719,0.9526252,0.0001196538,0.0002578545],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9924832,0.00001691182,0.0005621687,0.00347971,0.000006626807,0.0008302429,0.000003858973,0.00002598504,0.002591268],"genre_scores_gemma":[0.9459305,0.00002386458,0.05345964,0.0003546976,0.00002847707,0.0001052723,1.459728e-7,0.00002117097,0.00007621298],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05289747,"threshold_uncertainty_score":0.3406494,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0646998091605427,"score_gpt":0.3411681899287576,"score_spread":0.2764683807682149,"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."}}