{"id":"W1528819562","doi":"10.4310/jdg/1090351123","title":"Gauge-Fixing Constant Scalar Curvature Equations on Ruled Manifolds and the Futaki Invariants","year":2002,"lang":"en","type":"article","venue":"Journal of Differential Geometry","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Scalar curvature; Mathematics; Constant (computer programming); Scalar (mathematics); Curvature; Holomorphic function; Manifold (fluid mechanics); Mathematical physics; Mathematical analysis; Geometry","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0007504353,0.0002711902,0.0006131982,0.0004780191,0.00032033,0.0002110603,0.0004148575,0.0001671684,0.002075286],"category_scores_gemma":[0.001083524,0.0001676008,0.0002842348,0.0005662733,0.0001593083,0.000187714,0.0001247829,0.0007096027,0.00003507122],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004060379,"about_ca_system_score_gemma":0.00002008524,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005312085,"about_ca_topic_score_gemma":0.00000542759,"domain_scores_codex":[0.997686,0.000259454,0.0007986012,0.0001939941,0.0007200896,0.0003418979],"domain_scores_gemma":[0.9971334,0.001442878,0.000712083,0.0003474172,0.0001955014,0.0001687584],"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":[0.0007531684,0.001562126,0.001904301,0.0002239125,0.001328167,0.0001906872,0.001487218,0.00001939966,0.00252427,0.9704115,0.0127136,0.006881637],"study_design_scores_gemma":[0.03216473,0.002181258,0.03185117,0.001573214,0.002996089,0.002025593,0.002459838,0.009908986,0.00246048,0.9062209,0.004301167,0.001856559],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9783711,0.0008305748,0.01303091,0.001838182,0.000888889,0.0002767357,0.00002818025,0.00003112077,0.004704333],"genre_scores_gemma":[0.9976788,0.0001253022,0.0007073402,0.0002266462,0.0005037419,0.000003001788,0.000002080605,0.00002697851,0.0007261682],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0641906,"threshold_uncertainty_score":0.9988369,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05145429501960356,"score_gpt":0.2700917882426019,"score_spread":0.2186374932229984,"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."}}