{"id":"W2141576341","doi":"10.1214/aop/1055425778","title":"The lowest crossing in two-dimensional critical percolation","year":2003,"lang":"en","type":"article","venue":"The Annals of Probability","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Division of Mathematical Sciences; Natural Sciences and Engineering Research Council of Canada; Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Combinatorics; Percolation (cognitive psychology); Line (geometry); Geometry; Plane (geometry); Hexagonal lattice; Lattice (music); Condensed matter physics; Physics","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"],"consensus_categories":[],"category_scores_codex":[0.002711147,0.00009268534,0.0001622824,0.00001268955,0.0002960699,0.00005472423,0.0001616503,0.00003435534,0.00004466857],"category_scores_gemma":[0.02164275,0.00005089151,0.00005363439,0.0001483675,0.000400934,0.00006070849,0.00004199486,0.0001692803,0.000005386968],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001686354,"about_ca_system_score_gemma":0.0001181424,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002005103,"about_ca_topic_score_gemma":0.00009743634,"domain_scores_codex":[0.9987159,0.000218613,0.0003907352,0.0001594555,0.0002674171,0.0002478778],"domain_scores_gemma":[0.9943011,0.004966222,0.00007120375,0.0003302592,0.0002867916,0.00004438878],"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":[0.0000487307,0.0001477883,0.0001029069,0.00007103061,0.000004614877,7.182842e-7,0.0002393572,0.00007703522,0.0001360118,0.9980244,0.00009665062,0.001050779],"study_design_scores_gemma":[0.0001300434,0.00004620933,0.000812099,0.00003979167,0.000008308586,0.000004499364,0.00005696735,0.005268424,0.0008615647,0.9926525,0.00005811006,0.00006143546],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8970101,0.0003479834,0.09439354,0.005530476,0.0002273421,0.000650105,0.00002144197,0.00003335571,0.001785606],"genre_scores_gemma":[0.9884328,0.000001600965,0.01138792,0.0001125883,0.00001808712,0.00001821217,3.856923e-7,0.000007124141,0.00002131546],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09142261,"threshold_uncertainty_score":0.9865984,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.186007290178646,"score_gpt":0.4431558697526825,"score_spread":0.2571485795740365,"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."}}