{"id":"W2127640939","doi":"10.70930/tac/ej5u1k5p","title":"An embedding theorem for Hilbert categories","year":2009,"lang":"en","type":"article","venue":"Theory and applications of categories","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":38,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Embedding; Axiom; Pure mathematics; Morphism; Functor; Hilbert space; Hilbert manifold; Symmetric monoidal category; Enriched category; Hilbert R-tree; Monoidal category; Closed monoidal category; Hilbert's basis theorem; Algebra over a field; Rigged Hilbert space; Reproducing kernel Hilbert space; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.0007594792,0.0001409915,0.00026944,0.00006722614,0.0002635166,0.00001801461,0.0002402399,0.0001237982,0.00005552585],"category_scores_gemma":[0.000141468,0.0001217555,0.0000502709,0.0001107325,0.0005607486,0.000127594,0.00001836178,0.00008530448,0.000002411751],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007297324,"about_ca_system_score_gemma":0.00003306071,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002997861,"about_ca_topic_score_gemma":0.000004952708,"domain_scores_codex":[0.9991412,0.0001124567,0.0002743047,0.0002181671,0.0000598283,0.0001940646],"domain_scores_gemma":[0.9982925,0.001001237,0.000132839,0.0004173378,0.00009829752,0.00005775848],"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":[0.000120677,0.0001168891,0.00003959261,0.00003666799,0.00002424814,2.242952e-7,0.00139706,0.000001561339,0.001054591,0.9786375,0.00007642026,0.01849453],"study_design_scores_gemma":[0.000213213,0.0002103065,0.00009617488,0.000003922095,0.00006544594,0.00001842665,0.001656965,0.00001889345,0.01538103,0.9800863,0.002117962,0.0001313875],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3721355,0.0006268328,0.614418,0.0009824432,0.00007948083,0.001142424,0.0000411191,0.0002300328,0.01034416],"genre_scores_gemma":[0.9938096,0.00002571139,0.005036885,0.000140108,0.0001268389,0.0002519768,0.00002324954,0.00001282352,0.0005727651],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6216741,"threshold_uncertainty_score":0.4965044,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01556039060464528,"score_gpt":0.3193703177223238,"score_spread":0.3038099271176785,"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."}}