{"id":"W2321930835","doi":"10.4153/cmb-2001-022-2","title":"Extending the Archimedean Positivstellensatz to the Non-Compact Case","year":2001,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Generalization; Extension (predicate logic); Pure mathematics; Set (abstract data type); Compact space; Algebra over a field; Discrete mathematics; Mathematical analysis; Computer science; Programming language","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00169716,0.0005073072,0.0004912913,0.001153254,0.001117311,0.001314818,0.0009286657,0.0009410908,0.005764437],"category_scores_gemma":[0.003446163,0.0002735505,0.0008683884,0.0006473069,0.005812011,0.005282231,0.003410511,0.003014137,0.0005200947],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001333852,"about_ca_system_score_gemma":0.0008620207,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001833562,"about_ca_topic_score_gemma":0.001532484,"domain_scores_codex":[0.9993095,0.000170525,0.00003221222,0.0001510064,0.0002172744,0.0001195038],"domain_scores_gemma":[0.9982027,0.0007577777,0.0001715667,0.0003275528,0.0003338062,0.0002066297],"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":[0.00002168089,0.00002220007,0.0002200783,0.00003346611,0.000006754883,0.0002654877,0.000192303,0.001257754,0.001220954,0.9922947,0.0007449537,0.003719703],"study_design_scores_gemma":[0.00002018554,0.00002354978,0.0003620698,0.00001199829,0.000003939804,0.0001715416,0.00006985074,0.006072646,0.0005889244,0.989175,0.003490298,0.000009940312],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6365458,0.001334281,0.1710314,0.008812986,0.000518546,0.0001126449,0.0003667412,0.0003782973,0.1808992],"genre_scores_gemma":[0.9847296,0.0003486664,0.009351754,0.0003989402,0.000242143,0.00003377964,0.00009946017,0.00001738572,0.004778306],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005764437,"threshold_uncertainty_score":0.01928395,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03303593891198246,"score_gpt":0.2867556904862159,"score_spread":0.2537197515742334,"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."}}