{"id":"W2095187878","doi":"10.1063/1.1644902","title":"An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics","year":2004,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":39,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; University of Waterloo","funders":"","keywords":"Mathematics; Minkowski space; Pure mathematics; Lie group; Tensor field; Mathematical physics; Mathematical analysis; Exact solutions in general relativity","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":[],"consensus_categories":[],"category_scores_codex":[0.0007084089,0.0002163884,0.0006132819,0.00006347838,0.00008005148,0.00002955723,0.0004305294,0.00006838016,0.00004372757],"category_scores_gemma":[0.00006097277,0.000145057,0.0002781513,0.0003443592,0.0000994279,0.0002263437,0.0001415245,0.0003525434,0.000007456068],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002421649,"about_ca_system_score_gemma":0.00015603,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002011371,"about_ca_topic_score_gemma":3.363656e-7,"domain_scores_codex":[0.9982138,0.0001135514,0.000734564,0.0001810075,0.0005171501,0.0002399059],"domain_scores_gemma":[0.9981761,0.0001855968,0.0006496221,0.0004850672,0.000273999,0.0002296344],"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":[0.00005446276,0.0008544009,0.00003394057,0.00007653367,0.00009805826,0.00000250662,0.0006519261,0.0001801416,0.04163418,0.949813,0.00004209467,0.00655875],"study_design_scores_gemma":[0.0006523831,0.0004320869,0.0005378245,0.0003888732,0.0001236243,0.00001289507,0.0003722271,0.00143683,0.0385779,0.9573002,0.00001328311,0.000151879],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7572664,0.00001829673,0.2418087,0.000296046,0.0001308184,0.0001744133,0.00002834214,0.000004418145,0.0002725367],"genre_scores_gemma":[0.9943545,0.000002976016,0.005213095,0.0001138763,0.0002616498,0.000001785018,8.865874e-7,0.00003367965,0.0000175107],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2370882,"threshold_uncertainty_score":0.5915253,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01570032839539171,"score_gpt":0.2552547481023726,"score_spread":0.2395544197069809,"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."}}