{"id":"W2019396321","doi":"10.1112/s0024609399006426","title":"Non-Linear Spectrum-Preserving Maps","year":2000,"lang":"en","type":"article","venue":"Bulletin of the London Mathematical Society","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":53,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"","keywords":"Mathematics; Holomorphic function; Automorphism; Eigenvalues and eigenvectors; Mathematics Subject Classification; Spectrum (functional analysis); Unit sphere; Pure mathematics; Combinatorics; Unit (ring theory)","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":[0.001088694,0.0002513291,0.0004978236,0.00001017624,0.0002134293,0.00002493218,0.0008745324,0.0001927693,0.02744471],"category_scores_gemma":[0.0003039416,0.0001609448,0.0006317861,0.0001623506,0.0003264676,0.00002183969,0.0002520737,0.0003878466,0.001136796],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004314498,"about_ca_system_score_gemma":0.00002992721,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001662693,"about_ca_topic_score_gemma":8.869602e-7,"domain_scores_codex":[0.9980989,0.0001185728,0.0005840351,0.0002725068,0.0005147518,0.0004112046],"domain_scores_gemma":[0.9981113,0.0006316839,0.000149115,0.0009490516,0.00004765539,0.0001111791],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000107399,0.001183814,0.0002783962,0.00161891,0.0003371373,0.000009495085,0.003977714,0.00008673977,0.001168905,0.2621909,0.7280758,0.0009647304],"study_design_scores_gemma":[0.001294313,0.0000745463,0.0001229663,0.0004731127,0.0001602014,0.00004554072,0.0005059406,0.002243633,0.00955513,0.8792172,0.1058472,0.0004602681],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8343736,0.0001355873,0.002440557,0.0155105,0.0001595468,0.001086401,0.00003919207,0.0002143758,0.1460402],"genre_scores_gemma":[0.7024682,0.0002091151,0.1435149,0.003571727,0.0007316141,0.0001026993,0.000007284025,0.0002595034,0.1491349],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6222287,"threshold_uncertainty_score":0.9996409,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02103549597714654,"score_gpt":0.2623535742620292,"score_spread":0.2413180782848827,"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."}}