{"id":"W4391212022","doi":"10.48550/arxiv.2401.12352","title":"Completely Bounded Norms of $k$-positive Maps","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Agence Nationale de la Recherche; Norges Forskningsråd; European Commission","keywords":"Bounded function; Mathematics; Combinatorics; Sequence (biology); Operator (biology); Norm (philosophy); Bounded operator; Matrix (chemical analysis); Discrete mathematics; Mathematical analysis; Chemistry","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001869767,0.0003987082,0.0006421894,0.0002787893,0.00008079351,0.00003708249,0.0007861389,0.0003789248,0.0001441276],"category_scores_gemma":[0.0001305337,0.0004403261,0.0003609296,0.000380768,0.0003184779,0.00007966011,0.002210692,0.001071624,0.0001474701],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003465562,"about_ca_system_score_gemma":0.0001705478,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005530824,"about_ca_topic_score_gemma":0.0000636246,"domain_scores_codex":[0.9982341,0.00008953884,0.0003645117,0.0008423735,0.0001361135,0.0003333493],"domain_scores_gemma":[0.9977865,0.0004188578,0.0003846927,0.001071707,0.0002218575,0.0001164221],"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":[0.00004669791,0.0001067848,0.0001385072,0.0008176379,0.0003146324,0.000330188,0.0003268372,0.0007186455,0.00005406448,0.9962293,0.0007987717,0.0001179704],"study_design_scores_gemma":[0.0003276241,0.00006610492,0.00007144125,0.0004558452,0.000307183,0.000006764308,0.0001625819,0.00222441,0.0009991385,0.9945666,0.0003974936,0.0004148252],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8972571,0.0001488407,0.06059635,0.00008692598,0.001118561,0.0007064836,0.0004782359,0.0003643797,0.0392431],"genre_scores_gemma":[0.9868937,0.00006385068,0.007030904,0.00003133914,0.0001176399,0.000001961196,0.00004789063,0.00007008781,0.005742655],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08963654,"threshold_uncertainty_score":0.9998049,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1417421586200535,"score_gpt":0.2462898799304752,"score_spread":0.1045477213104217,"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."}}