{"id":"W2952263812","doi":"10.48550/arxiv.1506.06283","title":"Rank one perturbations of diagonal operators without eigenvalues","year":2015,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"","keywords":"Diagonal; Eigenvalues and eigenvectors; Mathematics; Multiplicity (mathematics); Hilbert space; Perturbation (astronomy); Rank (graph theory); Diagonal matrix; Operator (biology); Pure mathematics; Spectrum (functional analysis); Mathematical analysis; Combinatorics; Physics; Geometry; Quantum mechanics","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":[0.0006407824,0.0003398857,0.0006714353,0.0002044853,0.0001195621,0.00002841168,0.0006835075,0.0004105893,0.0003928003],"category_scores_gemma":[0.0003562436,0.000358299,0.0002374103,0.0002677597,0.0003207361,0.000130251,0.0006163494,0.0005608891,0.00008227143],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001845043,"about_ca_system_score_gemma":0.0005239185,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007396674,"about_ca_topic_score_gemma":0.00003551918,"domain_scores_codex":[0.998319,0.0003000518,0.0003416789,0.0006024347,0.0001614331,0.0002753686],"domain_scores_gemma":[0.997834,0.0002410561,0.000287169,0.0009088062,0.0005044751,0.0002245045],"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":[0.0002108303,0.0006779719,0.01120318,0.0004057045,0.0006762942,0.0000982834,0.002383926,0.01078768,0.0002514832,0.9703254,0.002894878,0.00008443165],"study_design_scores_gemma":[0.002141716,0.0001688366,0.0007708276,0.0005180414,0.001105801,0.000007440633,0.001739111,0.0198412,0.001499831,0.9703122,0.0007240814,0.001170959],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9743407,0.000145066,0.01445804,0.00004348627,0.0002969661,0.0004437331,0.0001649763,0.0001316525,0.009975357],"genre_scores_gemma":[0.9938848,0.0001278148,0.001141402,0.00004183432,0.0001259988,0.000002174109,0.00004755152,0.00005044136,0.004577977],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01954408,"threshold_uncertainty_score":0.9998869,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1813244947323931,"score_gpt":0.2427917256306522,"score_spread":0.06146723089825906,"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."}}