{"id":"W2950891929","doi":"10.48550/arxiv.1210.0256","title":"On the stability of the $p$-affine isoperimetric inequality","year":2012,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Isoperimetric inequality; Affine transformation; Ellipse; Mathematics; Regular polygon; Combinatorics; Hausdorff space; Pure mathematics; Affine hull; Transformation (genetics); Convex body; Mathematical analysis; Geometry; Convex hull; Affine space; Chemistry","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":[0.00271972,0.0009686868,0.0009560448,0.002312184,0.001682582,0.002313082,0.001523922,0.001096843,0.005517588],"category_scores_gemma":[0.01396222,0.0003843699,0.00151386,0.001127205,0.003778223,0.005068001,0.003811511,0.003332505,0.0007791452],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001486127,"about_ca_system_score_gemma":0.0005721164,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001298819,"about_ca_topic_score_gemma":0.0004859155,"domain_scores_codex":[0.9987864,0.0003323533,0.00004686908,0.0003287868,0.0003441843,0.0001613226],"domain_scores_gemma":[0.992875,0.004463405,0.0008217766,0.0003124492,0.00103561,0.0004918085],"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":[0.000157679,0.00003356628,0.002375949,0.0001712691,0.00005354345,0.0003327837,0.0004179885,0.01984562,0.009841862,0.9485996,0.002056589,0.01611342],"study_design_scores_gemma":[0.00002860231,0.0002190666,0.003513396,0.00005216734,0.00004301592,0.000457646,0.0002104289,0.3343132,0.005915637,0.6506178,0.004563952,0.00006502921],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2241471,0.002269076,0.7092571,0.003539114,0.0003583732,0.0001035407,0.000431801,0.0002279388,0.05966593],"genre_scores_gemma":[0.9399858,0.001642365,0.04677938,0.0005284034,0.0006014901,0.0002008675,0.0003523919,0.000122884,0.00978637],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005517588,"threshold_uncertainty_score":0.01845825,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2656039374463015,"score_gpt":0.2447158292294046,"score_spread":0.02088810821689688,"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."}}