{"id":"W3030426705","doi":"10.1090/proc/15608","title":"A tight structure theorem for sumsets","year":2021,"lang":"lv","type":"preprint","venue":"Proceedings of the American Mathematical Society","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"European Research Council; Natural Sciences and Engineering Research Council of Canada; Centre de Recherches Mathématiques","keywords":"Combinatorics; Set (abstract data type); Mathematics; Structured program theorem; Discrete mathematics; Computer science","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.001498857,0.001254513,0.003020108,0.00006683377,0.0009127999,0.0003458753,0.003074042,0.0007171721,0.0003586629],"category_scores_gemma":[0.002722423,0.0008012577,0.00424869,0.0008457478,0.00367422,0.0001682188,0.00408561,0.001837753,0.00000283841],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002429167,"about_ca_system_score_gemma":0.0002341699,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001389078,"about_ca_topic_score_gemma":0.000001348385,"domain_scores_codex":[0.9942103,0.00007651473,0.001833944,0.00132714,0.001396453,0.001155625],"domain_scores_gemma":[0.9913107,0.001951113,0.0038636,0.00117173,0.001400789,0.0003020726],"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":[0.0001968397,0.000579562,0.0007342569,0.01875371,0.002899683,6.516181e-7,0.03086141,0.000008472804,0.01168765,0.9209589,0.01179725,0.001521628],"study_design_scores_gemma":[0.0006118757,0.0001644171,0.0005513726,0.001848948,0.00157847,0.00004914612,0.01221707,0.002138907,0.01634214,0.9630012,0.000550214,0.0009462429],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9875972,0.0003209978,0.002503647,0.001481685,0.0006752386,0.002987995,0.00058985,0.0001416536,0.003701753],"genre_scores_gemma":[0.8215437,0.0002189057,0.1756028,0.0007801774,0.0005853273,0.0001870881,0.0000167619,0.0002509774,0.0008142857],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1730991,"threshold_uncertainty_score":0.9994438,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01710756410346344,"score_gpt":0.2793284129661938,"score_spread":0.2622208488627303,"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."}}