{"id":"W2750233391","doi":"10.5817/am2017-3-141","title":"Isometry invariant Finsler metrics on Hilbert spaces","year":2017,"lang":"en","type":"article","venue":"Archivum Mathematicum","topic":"Advanced Differential Geometry Research","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"","keywords":"Isometry (Riemannian geometry); Mathematics; Invariant (physics); Pure mathematics; Hilbert space; Metric (unit); Scalar (mathematics); Product metric; Metric space; Mathematical analysis; Geometry; Mathematical physics","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":[0.000247633,0.0002402587,0.0003409211,0.0003198866,0.0005651889,0.0003950782,0.0008550992,0.00003435242,0.001595965],"category_scores_gemma":[0.0002998277,0.0001912707,0.0001587992,0.0002046996,0.0001497176,0.0002490064,0.0004465129,0.0003302534,0.001197171],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001888424,"about_ca_system_score_gemma":0.00003577138,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007849406,"about_ca_topic_score_gemma":0.00000249083,"domain_scores_codex":[0.9983393,0.00004765521,0.0002614993,0.0003581227,0.0004823804,0.0005110743],"domain_scores_gemma":[0.9977278,0.0004920243,0.0002434265,0.001301943,0.00004709835,0.0001877662],"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":[0.00007376771,0.001387222,0.0395651,0.0001949131,0.0004062775,0.00002188024,0.0007472137,0.00004479964,0.002756183,0.8808424,0.00488816,0.06907205],"study_design_scores_gemma":[0.002289741,0.0003662031,0.0379788,0.000327765,0.00009919539,0.000005317429,0.0005766096,0.005482556,0.02560932,0.9149469,0.01118141,0.00113626],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5325647,0.00002880804,0.07470264,0.001205518,0.00037479,0.0005867445,0.00008128843,0.00007572336,0.3903798],"genre_scores_gemma":[0.9848289,0.000003650391,0.005837132,0.00004196528,0.0002962021,0.00004362474,0.00001742824,0.00004071424,0.00889036],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4522642,"threshold_uncertainty_score":0.9995805,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03717434664143106,"score_gpt":0.3247332914092383,"score_spread":0.2875589447678072,"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."}}