{"id":"W4388321717","doi":"10.1093/oso/9780198501657.003.0006","title":"Functional analytic basis","year":2000,"lang":"en","type":"book-chapter","venue":"","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Mathematics; Baire category theorem; Section (typography); Open mapping theorem (functional analysis); Banach space; Metric space; Mathematical proof; Basis (linear algebra); Pure mathematics; Topological space; Fréchet space; Interpolation space; Eberlein–Šmulian theorem; Discrete mathematics; Algebra over a field; Functional analysis; Lp space; Computer science","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.00007198354,0.0001753694,0.0001980837,0.0002979622,0.00008598928,0.0001281734,0.000364219,0.0001337315,0.04948103],"category_scores_gemma":[0.000004450145,0.0001550123,0.0002290474,0.0001043752,0.00001758645,0.0001932174,0.00007128651,0.0001167763,0.003848343],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004767968,"about_ca_system_score_gemma":0.000105014,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008145298,"about_ca_topic_score_gemma":0.000008297579,"domain_scores_codex":[0.9988504,0.000007208781,0.0002404546,0.0003923958,0.0004041482,0.0001053753],"domain_scores_gemma":[0.999258,0.00004568575,0.00008910624,0.0004010932,0.0001240782,0.00008207377],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.000001061291,0.000006956897,0.000002295373,0.000001341588,0.0000981526,0.000002437662,0.000004551234,0.003073396,1.252804e-7,0.9709961,0.01945802,0.006355538],"study_design_scores_gemma":[0.0001551985,0.00001789614,0.0001636584,0.00001279915,0.00009631889,0.00000943903,4.383853e-7,0.2374263,0.00000275189,0.1733866,0.5883229,0.000405654],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[3.461981e-8,0.00002834489,0.3718273,0.001196646,0.00007551425,0.00002632372,0.000003958554,0.00008798902,0.6267539],"genre_scores_gemma":[0.0001968791,0.0001094455,0.01797631,0.00158654,0.0001387432,0.000002097512,0.00007953022,0.00001142854,0.979899],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.7976096,"threshold_uncertainty_score":0.9969273,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02086590770552969,"score_gpt":0.2040801340135772,"score_spread":0.1832142263080475,"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."}}