{"id":"W4413005256","doi":"10.4171/jems/1697","title":"Quartic polynomials in two variables do not represent all non-negative integers","year":2025,"lang":"en","type":"article","venue":"Journal of the European Mathematical Society","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Northern British Columbia","funders":"","keywords":"Mathematics; Quartic function; Quartic surface; Pure mathematics; Combinatorics","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":[0.001104496,0.000554183,0.0006972646,0.0006856077,0.001587221,0.002346409,0.0009592058,0.0008614418,0.006228484],"category_scores_gemma":[0.006651684,0.0003153085,0.0007185874,0.001087204,0.00300773,0.004710122,0.001578641,0.002992971,0.001050944],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004989076,"about_ca_system_score_gemma":0.0005225211,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005454082,"about_ca_topic_score_gemma":0.0008445933,"domain_scores_codex":[0.9991305,0.0001427282,0.00004289222,0.0002107686,0.0001779955,0.0002950936],"domain_scores_gemma":[0.9971824,0.001229728,0.0004845785,0.0005266302,0.0003832928,0.0001934661],"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":[0.0001224041,0.000039032,0.001019346,0.0001166965,0.0000127412,0.0004136403,0.0004369596,0.000979609,0.002150768,0.9827669,0.002471781,0.009470123],"study_design_scores_gemma":[0.00003766725,0.00005000599,0.0003922802,0.00002902674,0.00001603081,0.0004620783,0.0002160798,0.006048992,0.001400618,0.9832977,0.008031562,0.00001796575],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6186388,0.001829983,0.2420006,0.00525103,0.001590723,0.00007173891,0.0002840223,0.0002664507,0.1300666],"genre_scores_gemma":[0.9665326,0.000581327,0.01962904,0.0005880984,0.0001790578,0.0000392882,0.0001516988,0.00006405654,0.01223489],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006228484,"threshold_uncertainty_score":0.02083635,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03203338880037045,"score_gpt":0.3434033218789416,"score_spread":0.3113699330785712,"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."}}