{"id":"W2001442481","doi":"10.1112/s002460930601842x","title":"A SHORT PROOF OF THE HARRIS–KESTEN THEOREM","year":2006,"lang":"en","type":"article","venue":"Bulletin of the London Mathematical Society","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":37,"is_retracted":false,"has_abstract":true,"ca_institutions":"Trinity College","funders":"","keywords":"Percolation (cognitive psychology); Mathematics Subject Classification; Square lattice; Lattice (music); Upper and lower bounds; Planar; Percolation threshold","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007418417,0.0002287919,0.0005129653,0.000008385217,0.0001473376,0.00001857526,0.0008543759,0.0001601564,0.000418235],"category_scores_gemma":[0.00175583,0.0001143679,0.0006430658,0.000209966,0.000429507,0.00001101122,0.000387696,0.0002797525,0.00001239187],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003708133,"about_ca_system_score_gemma":0.00004349374,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001214959,"about_ca_topic_score_gemma":0.000001677951,"domain_scores_codex":[0.997851,0.00009373001,0.0007619024,0.0002297784,0.0007418336,0.0003217563],"domain_scores_gemma":[0.9971253,0.001554591,0.0003213145,0.0007682552,0.0001784548,0.00005203706],"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":[0.0000166338,0.0003993748,0.00003093048,0.0009939029,0.00005804468,3.514701e-7,0.0002409745,0.00001536882,0.0004138096,0.9680192,0.02938252,0.0004288429],"study_design_scores_gemma":[0.0003008903,0.00004226906,0.0001333147,0.0003392722,0.0001781548,0.0000135231,0.000149925,0.002514907,0.01209779,0.9823434,0.001737451,0.0001490568],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06890079,0.0003496653,0.8835418,0.0138162,0.0004274051,0.003015946,0.0001878546,0.0001406339,0.02961971],"genre_scores_gemma":[0.9275331,0.000003694331,0.06831642,0.0002273028,0.0000957141,0.00006189918,0.000001049808,0.00005384392,0.0037069],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8586324,"threshold_uncertainty_score":0.4663787,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01906523960240041,"score_gpt":0.2601634717513361,"score_spread":0.2410982321489357,"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."}}