{"id":"W1541774427","doi":"10.1016/j.jfa.2012.10.018","title":"Closure of the cone of sums of 2d-powers in commutative real topological algebras","year":2012,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Mathematics; Hausdorff space; Closure (psychology); Topology (electrical circuits); Commutative property; Commutative ring; Combinatorics; Topological ring; Polynomial ring; Polynomial; Product (mathematics); Unitary state; Ring (chemistry); Borel measure; Discrete mathematics; Pure mathematics; Topological space; Probability measure; Mathematical analysis; Geometry","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":[0.0009613456,0.0001052667,0.0006712357,0.0002899627,0.00002923859,0.000002059902,0.0002223135,0.00009011203,0.0003713939],"category_scores_gemma":[0.0008145383,0.00006524326,0.0005586027,0.0008759672,0.0002881273,0.0001320259,0.0000671002,0.0003130667,6.147882e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007426294,"about_ca_system_score_gemma":0.00007008776,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003475714,"about_ca_topic_score_gemma":0.00003682786,"domain_scores_codex":[0.9979693,0.0002250361,0.001009396,0.00006929725,0.0005902584,0.0001367173],"domain_scores_gemma":[0.9965993,0.001138314,0.001526418,0.000214694,0.0004692058,0.00005210621],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.0003348992,0.0007754138,0.6930853,0.00007017177,0.003153599,0.000003495656,0.001527444,0.001508395,0.004209436,0.2947756,0.0003695487,0.0001867093],"study_design_scores_gemma":[0.001090325,0.0002751777,0.5493299,0.00007588417,0.002175309,0.00003155352,0.002962128,0.00009135234,0.01117845,0.4325718,0.00007928604,0.0001388536],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.991825,0.0001978747,0.006201207,0.0002986034,0.0001727252,0.00005360033,0.00001730613,0.000002013615,0.001231635],"genre_scores_gemma":[0.9939526,0.0000396459,0.00574632,0.00002627549,0.00008467087,9.291113e-7,0.000001976757,0.000005985558,0.0001416377],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1437554,"threshold_uncertainty_score":0.4066503,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05450000955134664,"score_gpt":0.3360256946251413,"score_spread":0.2815256850737947,"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."}}