{"id":"W2959466226","doi":"10.48550/arxiv.1907.06815","title":"Isometries of combinatorial Banach spaces","year":2019,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"MacEwan University","funders":"","keywords":"Isometry (Riemannian geometry); Basis (linear algebra); Mathematics; Banach space; Pure mathematics; Permutation (music); Unit (ring theory); Physics; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008434806,0.0006478081,0.0003681419,0.001349552,0.0007368192,0.001801887,0.0006128536,0.0005364287,0.005025712],"category_scores_gemma":[0.003107113,0.0002641484,0.0006534552,0.0005578304,0.0024823,0.003242257,0.002169032,0.002021018,0.0008681774],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005888933,"about_ca_system_score_gemma":0.0003290686,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002429855,"about_ca_topic_score_gemma":0.0001900752,"domain_scores_codex":[0.9987154,0.0003373317,0.00008223829,0.0003036241,0.0004198437,0.0001416361],"domain_scores_gemma":[0.9989285,0.0002872077,0.0002146555,0.0002253596,0.000208455,0.0001357106],"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":[0.00001450022,0.00002001208,0.0001753999,0.0000168598,0.000004334867,0.00008887774,0.000181531,0.0004772954,0.0024581,0.9906647,0.0003297894,0.005568551],"study_design_scores_gemma":[0.00001329736,0.0000514098,0.0003875471,0.00001240614,0.000006793096,0.0003144562,0.0001954541,0.007152784,0.003155619,0.9822271,0.006470466,0.00001258292],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5449138,0.0007599158,0.3250076,0.0009985771,0.000597799,0.00008461589,0.0001566797,0.0002379493,0.1272429],"genre_scores_gemma":[0.9384511,0.0005599962,0.0387778,0.000245173,0.0003852495,0.0001201225,0.0001849567,0.000136671,0.02113876],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005025712,"threshold_uncertainty_score":0.01681268,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07822273027954545,"score_gpt":0.2296145334159537,"score_spread":0.1513918031364083,"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."}}