{"id":"W4385839037","doi":"10.4153/s0008439523000620","title":"Block perturbation of symplectic matrices in Williamson’s theorem","year":2023,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Science Foundation","keywords":"Symplectic geometry; Mathematics; Symplectic matrix; Eigenvalues and eigenvectors; Block matrix; Diagonal matrix; Symplectic vector space; Matrix (chemical analysis); Diagonal; Symplectic group; Block (permutation group theory); Combinatorics; Moment map; Symplectic representation; Pure mathematics; Physics; Geometry; Quantum mechanics","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0007293307,0.0001127837,0.0002025892,0.0003877609,0.00006012493,0.00005535921,0.0005638783,0.00007235811,0.0009969714],"category_scores_gemma":[0.0003783602,0.0001005995,0.00005590152,0.0009030913,0.00005437841,0.0000590469,0.00006264637,0.0001115213,0.003798175],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007641176,"about_ca_system_score_gemma":0.0001272747,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001963983,"about_ca_topic_score_gemma":0.0002136066,"domain_scores_codex":[0.9988204,0.00009347636,0.0002982397,0.0002305279,0.0001881139,0.0003692363],"domain_scores_gemma":[0.9988891,0.0004422134,0.00006056745,0.0003497282,0.00004057563,0.0002177552],"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":[0.000001645481,0.00002082515,0.00004629167,0.0001047918,0.00000592273,0.00004882123,0.0007486194,0.00006159718,0.00003902231,0.9934473,0.003284071,0.002191059],"study_design_scores_gemma":[0.0002617249,0.000054514,0.0004859577,0.0001588827,0.000006991568,0.00003469495,0.0001503709,0.04555647,0.0004055598,0.9415114,0.01112145,0.0002520013],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.777351,0.0004754522,0.05456276,0.04566929,0.0007390768,0.001568084,0.00004809356,0.0008065294,0.1187797],"genre_scores_gemma":[0.9940244,0.00001189956,0.003096724,0.0002573585,0.00003964174,0.00002355528,0.000002703865,0.00001298122,0.002530752],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2166733,"threshold_uncertainty_score":0.9999163,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01041943465066462,"score_gpt":0.2204540121932465,"score_spread":0.2100345775425819,"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."}}