{"id":"W2124343650","doi":"10.1090/s0002-9939-07-09068-5","title":"An elementary and constructive solution to Hilbert’s 17th Problem for matrices","year":2007,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":29,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Banff International Research Station for Mathematical Innovation and Discovery; National Science Foundation","keywords":"Constructive; Mathematics; Pure mathematics; Algebra over a field; Computer science; Process (computing); Programming language","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001065692,0.000125916,0.00023672,0.00002608382,0.0001811765,0.00007092817,0.0006229223,0.00002574179,0.000003213919],"category_scores_gemma":[0.00005525328,0.00008660334,0.0001205799,0.0004158015,0.0003217102,0.0003188649,0.0002534563,0.0000823568,0.000001345358],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003908415,"about_ca_system_score_gemma":0.00001600926,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001151269,"about_ca_topic_score_gemma":5.582266e-7,"domain_scores_codex":[0.9989148,0.000006365657,0.0002705589,0.0002777694,0.0002352092,0.0002952965],"domain_scores_gemma":[0.9991361,0.000185366,0.0002798903,0.0001255775,0.000146279,0.00012676],"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":[0.00005751127,0.0002242351,0.001691031,0.0004218331,0.00008875371,9.464979e-8,0.007044589,0.000001939376,0.03163701,0.9076902,0.001169716,0.04997313],"study_design_scores_gemma":[0.0006014879,0.0009608013,0.003025371,0.000145605,0.00008819047,0.00004327326,0.007204476,0.03230856,0.04351739,0.9110276,0.0005847563,0.0004925267],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.5414879,0.00001482467,0.4553593,0.001588768,0.00003038599,0.0006815726,0.000006376104,0.00007177667,0.0007590973],"genre_scores_gemma":[0.3976346,0.000003800009,0.6018493,0.0004188642,0.00004229336,0.00002198415,1.936769e-7,0.000006918286,0.00002201707],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.14649,"threshold_uncertainty_score":0.3531581,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008320411574523567,"score_gpt":0.2616575047403066,"score_spread":0.2533370931657831,"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."}}