{"id":"W2161568247","doi":"10.1007/s10440-011-9638-2","title":"On the Cohomology of the Invariant Euler–Lagrange Complex","year":2011,"lang":"en","type":"article","venue":"Acta Applicandae Mathematicae","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Equivariant cohomology; Cohomology; Lie group; Equivariant map; Invariant (physics); Group cohomology; Pure mathematics; Lie algebra; Algebra over a field; Mathematical physics","routes":{"ca_aff":true,"ca_fund":true,"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":[],"category_scores_codex":[0.0001917298,0.0001301482,0.0002207581,0.00001418582,0.0001312536,0.00001184875,0.0004763756,0.0000304188,0.002818267],"category_scores_gemma":[0.00001388133,0.00006313259,0.0001329486,0.0001107836,0.0002167285,0.00001689055,0.0001265805,0.0001500036,0.00007846778],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005801884,"about_ca_system_score_gemma":0.00002535772,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001511832,"about_ca_topic_score_gemma":0.000006007308,"domain_scores_codex":[0.9992337,0.00005958454,0.0002328826,0.000142768,0.0001339663,0.0001970816],"domain_scores_gemma":[0.9987781,0.0003710934,0.0001524259,0.0006267648,0.00002834796,0.00004323775],"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":[0.000009739957,0.0002294713,0.0005475244,0.00001285924,0.00006592899,2.580435e-7,0.001036164,2.111019e-7,0.001375668,0.993161,0.003232209,0.000328923],"study_design_scores_gemma":[0.0007454592,0.0001276133,0.01486328,0.0000801119,0.0001450029,0.000006563726,0.001397682,0.0008061941,0.01137033,0.9549303,0.01517657,0.0003509042],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7263227,0.000004311597,0.001838721,0.001278151,0.00007173295,0.0006950546,0.0001174704,0.0000204407,0.2696515],"genre_scores_gemma":[0.998686,4.585106e-7,0.0006730829,0.000221189,0.00009215408,0.00005778142,0.000004709465,0.0000159384,0.0002487416],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2723633,"threshold_uncertainty_score":0.9980933,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04586249094618765,"score_gpt":0.2460095981834198,"score_spread":0.2001471072372322,"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."}}