{"id":"W2053523467","doi":"10.4153/cmb-2011-165-0","title":"Structure in Sets with Logarithmic Doubling","year":2011,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council","keywords":"Abelian group; Logarithm; Structured program theorem; Set (abstract data type); Finite set","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003051294,0.0002556086,0.000358102,0.0002895459,0.0001515165,0.0000331058,0.0003648209,0.0002002865,0.02056161],"category_scores_gemma":[0.0002925774,0.0001866051,0.00005937228,0.0002221043,0.0001864326,0.00003701958,0.00004931572,0.0004000228,0.0002843505],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000113841,"about_ca_system_score_gemma":0.0001191579,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000871275,"about_ca_topic_score_gemma":0.007803129,"domain_scores_codex":[0.9984633,0.00006929797,0.0003521118,0.0003092655,0.0002070714,0.0005989984],"domain_scores_gemma":[0.9987496,0.0002152929,0.00007427038,0.0004766406,0.00005363243,0.0004305263],"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":[0.00003471053,0.00003610125,0.0006950625,0.0001507742,0.00003413897,0.0002769319,0.003509123,0.000001301989,0.000008737276,0.9926009,0.00210891,0.0005433161],"study_design_scores_gemma":[0.000495263,0.00005356847,0.0008109077,0.0001487907,0.0000266558,0.0001467208,0.0003557516,0.0000530797,0.0001738764,0.9944179,0.002997183,0.0003202719],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9080026,0.00004357759,0.0005748799,0.0005352973,0.00009956463,0.0004965893,0.00003530625,0.00007810874,0.09013412],"genre_scores_gemma":[0.9679772,0.000001613928,0.03098784,0.0004652509,0.00003794531,0.00001737109,0.000003422556,0.0000511411,0.0004582586],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08967586,"threshold_uncertainty_score":0.9803337,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04215964605312174,"score_gpt":0.2455009255603718,"score_spread":0.20334127950725,"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."}}