{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004180498,0.0004139846,0.0008723457,0.0005035274,0.00006913619,0.00002437857,0.0009453656,0.0004738612,0.0001639352],"category_scores_gemma":[0.0005284705,0.0004711804,0.0003291633,0.0006143291,0.0003217828,0.0001882484,0.001237285,0.000703116,0.0000779232],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002471606,"about_ca_system_score_gemma":0.0002015473,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007298683,"about_ca_topic_score_gemma":0.00001978715,"domain_scores_codex":[0.9982409,0.0001890122,0.0003022899,0.0007372521,0.0001633592,0.0003671785],"domain_scores_gemma":[0.9965678,0.0008950082,0.0007194373,0.001439149,0.0002671773,0.0001113796],"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":[0.0001949801,0.0002096089,0.003071304,0.0007416219,0.0002586611,0.00004787486,0.0002896588,0.01476368,0.00007016931,0.9794543,0.0008662834,0.00003189415],"study_design_scores_gemma":[0.001061614,0.0001101109,0.00008842446,0.0002199534,0.0002944006,0.000001681034,0.0007922379,0.002530052,0.00128326,0.9925109,0.0005960477,0.000511387],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9228122,0.00016145,0.06253436,0.00004324297,0.001891896,0.000676875,0.00009129593,0.0002240271,0.01156467],"genre_scores_gemma":[0.9930341,0.0001458269,0.001497547,0.000009830046,0.0001174594,6.381019e-7,0.00001558288,0.00006219794,0.00511679],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07022194,"threshold_uncertainty_score":0.999774,"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."}}