{"id":"W2950159272","doi":"10.48550/arxiv.1006.4400","title":"Percolation in an ultrametric space","year":2010,"lang":"en","type":"preprint","venue":"","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Ultrametric space; Percolation threshold; Mathematics; Continuum percolation theory; Percolation critical exponents; Combinatorics; Percolation theory; Percolation (cognitive psychology); Euclidean space; Directed percolation; Statistical physics; Renormalization group; Random graph; Lattice (music); Discrete mathematics; Physics; Mathematical physics; Topology (electrical circuits); Metric space; Quantum mechanics; Graph","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001092758,0.000723499,0.0006155915,0.001866096,0.00111598,0.001422464,0.001323172,0.001011996,0.001303586],"category_scores_gemma":[0.005204504,0.0003495482,0.000673512,0.00128853,0.003778259,0.002618338,0.001858896,0.001349606,0.0002012919],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001493402,"about_ca_system_score_gemma":0.0004298765,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001817048,"about_ca_topic_score_gemma":0.001509687,"domain_scores_codex":[0.9987312,0.0006560713,0.00003917302,0.0001709771,0.0002605374,0.0001421079],"domain_scores_gemma":[0.9959942,0.002320025,0.0009181746,0.0002034628,0.0001903421,0.0003737652],"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":[0.00002812352,0.00004506306,0.001060606,0.0000715378,0.00002945247,0.0002130799,0.0002464381,0.03593725,0.00141719,0.9577593,0.0004550405,0.002737019],"study_design_scores_gemma":[0.00002300776,0.00006476812,0.0008644239,0.00002049562,0.00001620228,0.0002029163,0.000124987,0.2638154,0.0006009758,0.7319067,0.002336064,0.00002407326],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7635925,0.002991227,0.2077094,0.002791672,0.0001587967,0.0000504812,0.0001650563,0.000179717,0.02236107],"genre_scores_gemma":[0.9745215,0.0007907498,0.02168881,0.0001379864,0.0001285333,0.0000371216,0.00006127712,0.0000231953,0.002610897],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001866096,"threshold_uncertainty_score":0.01083541,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07791443209547796,"score_gpt":0.3768174008385032,"score_spread":0.2989029687430252,"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."}}