{"id":"W4405031120","doi":"10.1007/978-3-031-72936-2_1","title":"The Clebsch-Mayer Theory of the Second Variation in the Calculus of Variations: A Case Study in the Influence of Dynamical Analysis on Pure Mathematics","year":2024,"lang":"en","type":"book-chapter","venue":"Annals of the Canadian Society for History and Philosophy of Mathematics","topic":"Mathematical and Theoretical Analysis","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Calculus (dental); Variation (astronomy); Mathematics; Pure mathematics; Algebra over a field; Physics","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":[0.00589874,0.0004107223,0.001263357,0.0002304976,0.0002436985,0.00002084816,0.001333385,0.0003745123,0.00006560532],"category_scores_gemma":[0.001109769,0.0001899139,0.001804122,0.0005490858,0.001482152,0.00005026479,0.0001322203,0.0006883569,6.913627e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001395738,"about_ca_system_score_gemma":0.0003072665,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007532166,"about_ca_topic_score_gemma":0.01801056,"domain_scores_codex":[0.9962558,0.0003312,0.001929491,0.0002999152,0.0009096585,0.0002739154],"domain_scores_gemma":[0.9888816,0.007338073,0.00173864,0.001566717,0.0004029907,0.00007201769],"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":[0.00001736038,0.000490269,0.000008387682,0.003063936,0.001810471,0.000004564197,0.0400732,0.0000726784,0.000006502927,0.9541419,0.0002815984,0.00002917195],"study_design_scores_gemma":[0.0002141761,0.0001520498,0.00004382673,0.0007332328,0.003146345,0.00001725856,0.003884593,0.003271864,0.00001511449,0.9880656,0.0002752636,0.0001807024],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8385463,0.005013544,0.001852501,0.01893175,0.0004678395,0.01525673,0.005189097,0.00003790553,0.1147043],"genre_scores_gemma":[0.9961548,0.00004875419,0.000586617,0.0002896501,0.00003658574,0.00007915344,0.000004419459,0.00004385901,0.00275618],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1576084,"threshold_uncertainty_score":0.9999082,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05654755259537667,"score_gpt":0.2850040185514529,"score_spread":0.2284564659560762,"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."}}