{"id":"W2731346518","doi":"10.1017/s0963548318000342","title":"Bounding the Number of Common Zeros of Multivariate Polynomials and Their Consecutive Derivatives","year":2018,"lang":"en","type":"preprint","venue":"Combinatorics Probability Computing","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Canada Research Chairs; University of Toronto","funders":"","keywords":"Mathematics; Upper and lower bounds; Bounding overwatch; Combinatorics; Hermite polynomials; Uniqueness; Polynomial; Context (archaeology); Grid; Orthogonal polynomials; Discrete mathematics; Pure mathematics; Computer science","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.003395704,0.0004511034,0.0009579817,0.0001237976,0.0004343555,0.000178818,0.002040731,0.0002654837,0.000003010319],"category_scores_gemma":[0.0005907389,0.00034107,0.0002861068,0.0006121189,0.00140094,0.0001432517,0.005928988,0.0007122649,8.25048e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008323867,"about_ca_system_score_gemma":0.0002134137,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009572018,"about_ca_topic_score_gemma":0.000001762847,"domain_scores_codex":[0.9962729,0.001190135,0.001002444,0.0008458577,0.0002931395,0.0003955377],"domain_scores_gemma":[0.9935279,0.002879853,0.001351906,0.001563048,0.0005861666,0.00009104869],"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":[0.00003673658,0.0004728794,0.0588283,0.0006623022,0.0002340651,8.847692e-7,0.01757339,0.00007616388,0.0007766591,0.9166136,0.00001549482,0.004709478],"study_design_scores_gemma":[0.000403062,0.0001111774,0.02108371,0.0005137997,0.00002777391,0.000008683751,0.0001632166,0.01188628,0.009403174,0.9560233,0.00003109236,0.0003447542],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8664152,0.0002613118,0.1307729,0.0001435102,0.001036099,0.0007330406,0.00001561411,0.0001116267,0.0005107275],"genre_scores_gemma":[0.9918423,0.00001318745,0.008030131,0.00002958151,0.00004756312,0.00001200608,0.000003548041,0.00001882706,0.000002827076],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1254272,"threshold_uncertainty_score":0.9999042,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03031485595492576,"score_gpt":0.2887224744568492,"score_spread":0.2584076185019234,"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."}}