{"id":"W1864140179","doi":"10.19086/da.613","title":"Monochromatic sums and products","year":2016,"lang":"en","type":"article","venue":"Discrete Analysis","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Monochromatic color; Mathematics; Combinatorics; Set (abstract data type); Field (mathematics); Ramsey theory; Multiplication (music); Fraction (chemistry); Finite set; Discrete mathematics; Number theory; Arithmetic; Pure mathematics; Computer science; Physics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006876463,0.0006911547,0.0006692468,0.001327821,0.001335148,0.003020672,0.0006083098,0.0007150655,0.02712772],"category_scores_gemma":[0.003009542,0.0005467164,0.0007022996,0.002314557,0.001924791,0.006415597,0.00180756,0.002237243,0.006131114],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00175748,"about_ca_system_score_gemma":0.0005754201,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001469649,"about_ca_topic_score_gemma":0.001616689,"domain_scores_codex":[0.9990331,0.0002200485,0.0000379116,0.0002696466,0.0003441272,0.00009522562],"domain_scores_gemma":[0.9993426,0.0002512438,0.00008221425,0.0001465478,0.0001121257,0.00006525209],"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":[0.00004873669,0.00001422641,0.0002516582,0.000121237,0.00001705004,0.00005194409,0.0001997943,0.0007606514,0.0006848162,0.9372803,0.0280554,0.03251414],"study_design_scores_gemma":[0.00000425716,0.00001045358,0.0005044248,0.00004701897,0.00001121293,0.0001760537,0.00008471176,0.001674906,0.0003629144,0.9365817,0.06052978,0.00001251171],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.09107636,0.1305591,0.2733601,0.01836991,0.006481348,0.0000772889,0.002818078,0.001346123,0.4759117],"genre_scores_gemma":[0.7010167,0.03707936,0.05714376,0.004977812,0.006408632,0.0001402884,0.002240994,0.001024243,0.1899682],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02712772,"threshold_uncertainty_score":0.09075123,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02151046206878525,"score_gpt":0.2886173432028429,"score_spread":0.2671068811340577,"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."}}