{"id":"W4390078244","doi":"10.4153/s0008414x23000901","title":"Symmetric and antisymmetric tensor products for the function-theoretic operator theorist","year":2023,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"Engineering and Physical Sciences Research Council; National Science Foundation","keywords":"Antisymmetric tensor; Antisymmetric relation; Mathematics; Symmetric tensor; Hilbert space; Operator (biology); Tensor (intrinsic definition); Pure mathematics; Space (punctuation); Function (biology); Tensor product; Field (mathematics); Algebra over a field; Mathematical physics; Mathematical analysis; Gauge theory; Exact solutions in general relativity; 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":[],"consensus_categories":[],"category_scores_codex":[0.002017475,0.0001176323,0.0002038365,0.0006725625,0.0003602967,0.000292518,0.0006935598,0.00004266817,0.000009950832],"category_scores_gemma":[0.001813586,0.00007314995,0.00007002479,0.002024293,0.000113044,0.0002027513,0.0000347108,0.0001455842,0.00002552028],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000031871,"about_ca_system_score_gemma":0.0004190748,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002089886,"about_ca_topic_score_gemma":0.0000339173,"domain_scores_codex":[0.9990065,0.0000515933,0.0003340661,0.0001364487,0.0001778682,0.0002935041],"domain_scores_gemma":[0.9978254,0.001077268,0.0001967201,0.0003316346,0.0003255565,0.0002433708],"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":[0.000002655765,0.00001441245,0.00007858622,0.0001395057,0.00006034935,0.00003787927,0.0007868646,0.0000373639,0.00003009549,0.9761575,0.00563684,0.01701793],"study_design_scores_gemma":[0.001843897,0.001023301,0.003186098,0.0003059446,0.0003588509,0.001946413,0.003119194,0.1230034,0.001672249,0.7902365,0.07247903,0.0008251186],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09178789,0.006028861,0.8828322,0.01246306,0.004341245,0.001175968,0.00005114226,0.00009784028,0.001221775],"genre_scores_gemma":[0.969308,0.0001732285,0.02868485,0.0003207749,0.0004902103,0.00001293244,9.093565e-7,0.00002802087,0.0009810465],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8775201,"threshold_uncertainty_score":0.2982968,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01832636511007984,"score_gpt":0.225874399243781,"score_spread":0.2075480341337012,"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."}}