{"id":"W2020987782","doi":"10.1088/1742-6596/42/1/018","title":"Enumeration Bounds via an Isoperimetric-Type Inequality","year":2006,"lang":"en","type":"article","venue":"Journal of Physics Conference Series","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Isoperimetric inequality; Mathematics; Combinatorics; Enumeration; Upper and lower bounds; Hyperplane; Cardinality (data modeling); Lattice (music); Exponent; Inequality; Discrete mathematics; Mathematical analysis; Physics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005101321,0.001752552,0.002027899,0.004593966,0.002413641,0.004054952,0.004279042,0.002999391,0.01120598],"category_scores_gemma":[0.05148889,0.001264579,0.001915594,0.003940502,0.005383388,0.02125129,0.006703774,0.01220891,0.002661539],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003478875,"about_ca_system_score_gemma":0.0009658737,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001052114,"about_ca_topic_score_gemma":0.0008751946,"domain_scores_codex":[0.9930368,0.001606291,0.0002732611,0.001617724,0.002530085,0.0009357875],"domain_scores_gemma":[0.9519854,0.03779278,0.001736123,0.003919688,0.003227213,0.001338819],"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":[0.0001154586,0.00005930334,0.001583157,0.000186173,0.00002363472,0.000148543,0.0002470068,0.007158658,0.003439714,0.9612014,0.006786752,0.01905014],"study_design_scores_gemma":[0.00002038732,0.0000464617,0.0008383648,0.00008413792,0.0000214785,0.0002962946,0.00004812343,0.06542442,0.00253596,0.9203113,0.01032551,0.00004756817],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09218446,0.008399136,0.689153,0.01264508,0.001114205,0.0001407553,0.001618203,0.0008682091,0.193877],"genre_scores_gemma":[0.7600965,0.006907308,0.1889102,0.005385215,0.003427222,0.0009061691,0.002576396,0.0009842876,0.0308067],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01120598,"threshold_uncertainty_score":0.03748769,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06457364647168899,"score_gpt":0.3228770561090172,"score_spread":0.2583034096373282,"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."}}