{"id":"W2469323228","doi":"10.5802/aif.3085","title":"Polynomial Bound on the Local Betti Numbers of a Real Analytic Germ","year":2017,"lang":"en","type":"preprint","venue":"Annales de l’institut Fourier","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"University of Toronto","keywords":"Betti number; Mathematics; Germ; Isolated singularity; Tangent cone; Upper and lower bounds; Polynomial; Algebraic variety; Algebraic number; Combinatorics; Pure mathematics; Discrete mathematics; Tangent; Mathematical analysis; Singularity; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001169984,0.000904923,0.001064664,0.003094716,0.000965031,0.00163225,0.001216611,0.0004931533,0.005184088],"category_scores_gemma":[0.004720421,0.0003240423,0.0006035744,0.0009660296,0.003490133,0.004579217,0.00254377,0.002925864,0.0006666073],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001161022,"about_ca_system_score_gemma":0.0003239105,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003248816,"about_ca_topic_score_gemma":0.0002994039,"domain_scores_codex":[0.9991844,0.0001275238,0.00003005295,0.0002079972,0.0002752618,0.0001747944],"domain_scores_gemma":[0.9976988,0.001177015,0.0002894159,0.0001806595,0.0002149214,0.0004392416],"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":[0.0001099814,0.00003734535,0.001794038,0.0001385623,0.00003237499,0.0002542321,0.0003971976,0.007314969,0.007151091,0.9687482,0.0008002922,0.01322184],"study_design_scores_gemma":[0.00001855477,0.00007892994,0.002772012,0.00004659226,0.00004192382,0.000441565,0.0001262582,0.05518358,0.005969545,0.9311529,0.004114338,0.00005379086],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7143897,0.002786392,0.2270258,0.001438407,0.0002698703,0.00002984159,0.0001960367,0.0003212655,0.05354268],"genre_scores_gemma":[0.9868307,0.0005796773,0.006158569,0.00006305399,0.0002730933,0.00002452487,0.00007714015,0.00006952317,0.005923773],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005184088,"threshold_uncertainty_score":0.01734251,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08350668920969449,"score_gpt":0.3591026715081749,"score_spread":0.2755959822984804,"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."}}