{"id":"W1549301089","doi":"10.4153/cjm-2014-016-0","title":"On a Sumset Conjecture of Erdős","year":2014,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"York University; American Institute of Mathematics; National Science Foundation","keywords":"Mathematics; Conjecture; Countable set; Natural density; Set (abstract data type); Discrete mathematics; Pseudorandom number generator; Combinatorics; Statistics","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":[],"consensus_categories":[],"category_scores_codex":[0.0008653436,0.0001546249,0.0004640362,0.0002893456,0.0001058414,0.00002057531,0.0003861852,0.0001189391,0.000231952],"category_scores_gemma":[0.002126794,0.0001107488,0.0001903932,0.0001211498,0.0001471544,0.00004336475,0.00001341407,0.0002809482,0.000003904298],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004567371,"about_ca_system_score_gemma":0.0002316643,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000044537,"about_ca_topic_score_gemma":0.0008952387,"domain_scores_codex":[0.9987531,0.00007750744,0.0006041099,0.00007501909,0.0002552417,0.0002350397],"domain_scores_gemma":[0.9975807,0.0009456269,0.0005909859,0.0003526269,0.0001859385,0.000344113],"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":[0.000006076958,0.00002857741,0.0001581571,0.0002025095,0.00007415619,0.00002036762,0.002763533,0.00002625933,0.00004351098,0.9872906,0.008916762,0.0004694617],"study_design_scores_gemma":[0.0003837356,0.000249644,0.0001131379,0.0002888302,0.00007288377,0.0002028247,0.0002766213,0.0000921988,0.0008211614,0.9943546,0.003020779,0.0001235637],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9832762,0.0001002899,0.004065163,0.0002143196,0.0005511917,0.000115042,0.00002908791,0.000007353927,0.01164137],"genre_scores_gemma":[0.9833678,0.000003352572,0.01616676,0.0001628891,0.0001349757,5.243814e-7,5.267277e-7,0.00002808312,0.0001350866],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0121016,"threshold_uncertainty_score":0.4516205,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0200986379732112,"score_gpt":0.2545995363139453,"score_spread":0.2345008983407341,"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."}}