{"id":"W4400887743","doi":"10.1016/j.jctb.2024.07.001","title":"The Erdős-Gyárfás function <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.svg\"><mml:mi>f</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>5</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mfrac><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:mfrac><mml:mi>n</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mi>o</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> — So Gyárfás was right","year":2024,"lang":"lv","type":"article","venue":"Journal of Combinatorial Theory Series B","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University","funders":"Natural Sciences and Engineering Research Council of Canada; Simons Foundation","keywords":"Mathematics; Combinatorics","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":["metaresearch","metaepi_narrow","metaepi_broad","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"consensus_categories":["metaepi_narrow","sts","open_science","research_integrity","insufficient_payload"],"category_scores_codex":[0.01806888,0.007436129,0.003448924,0.005243888,0.01091328,0.01377414,0.01611409,0.01573247,0.2971346],"category_scores_gemma":[0.01396582,0.01319808,0.01398163,0.009357156,0.01294615,0.01019992,0.01339077,0.01570477,0.01051423],"about_ca_system_candidate":true,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003744824,"about_ca_system_score_gemma":0.01182366,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.007232042,"about_ca_topic_score_gemma":0.006656017,"domain_scores_codex":[0.9379306,0.006031148,0.01404146,0.01063443,0.01658257,0.01477979],"domain_scores_gemma":[0.9477408,0.01462982,0.01495408,0.01077946,0.002926704,0.008969132],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.01508936,0.00271453,0.00004931185,0.005167642,0.01322392,0.007855199,0.005882822,0.003277587,0.003209582,0.5406607,0.3948252,0.008044076],"study_design_scores_gemma":[0.01231056,0.01145649,0.00008278163,0.008855195,0.01447706,0.01381875,0.01278179,0.01165357,0.8043448,0.06238557,0.03621778,0.01161559],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6740311,0.01667161,0.00413753,0.005365105,0.02949927,0.0009086025,0.00826335,0.003385838,0.2577376],"genre_scores_gemma":[0.9381143,0.01036789,0.005203759,0.004692671,0.01875569,0.00733733,0.006858152,0.007189659,0.001480585],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8011353,"threshold_uncertainty_score":0.9993789,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01501190542327529,"score_gpt":0.2532564712360743,"score_spread":0.238244565812799,"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."}}