{"id":"W2170720872","doi":"10.1103/physrevlett.101.090401","title":"Special Comparison Theorem for the Dirac Equation","year":2008,"lang":"en","type":"article","venue":"Physical Review Letters","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Eigenvalues and eigenvectors; Monotonic function; Dirac equation; Dirac (video compression format); Dirac comb; Dirac algebra; Mathematical physics; Mathematics; Pure mathematics; Applied mathematics; Mathematical analysis; Physics; Dirac spinor; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002152751,0.0003407038,0.0006249222,0.001539533,0.0007936297,0.001446113,0.001077491,0.0007975335,0.01057775],"category_scores_gemma":[0.00471037,0.0001511396,0.0007208755,0.0006645838,0.00118788,0.00331512,0.001270308,0.001340864,0.0006304333],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001006691,"about_ca_system_score_gemma":0.0004585825,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004614178,"about_ca_topic_score_gemma":0.0003703511,"domain_scores_codex":[0.9993355,0.0001628233,0.00003089685,0.0001509681,0.0002421049,0.00007781851],"domain_scores_gemma":[0.9983485,0.0008195646,0.0001799867,0.0001251452,0.0003805032,0.0001463918],"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":[0.00001152152,0.000005873145,0.0001010471,0.00001866307,0.000005563733,0.00004228652,0.00002674157,0.0005555521,0.0005807914,0.9951823,0.0008024818,0.00266718],"study_design_scores_gemma":[0.00001590276,0.00002083767,0.0003124484,0.00001102152,0.000004760749,0.0001804956,0.00002246175,0.01744988,0.0005060122,0.9769416,0.004524942,0.000009600353],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2847224,0.003090122,0.4401109,0.003696771,0.001191053,0.0001313565,0.0009187168,0.0003977661,0.265741],"genre_scores_gemma":[0.9199883,0.0007809071,0.05138814,0.0008960832,0.0009631329,0.0001899924,0.0004676793,0.0002033073,0.02512246],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01057775,"threshold_uncertainty_score":0.03538609,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1371076933938744,"score_gpt":0.3895045470569946,"score_spread":0.2523968536631201,"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."}}