{"id":"W1533252206","doi":"10.1007/s00023-015-0433-x","title":"The Divisible Sandpile at Critical Density","year":2015,"lang":"en","type":"article","venue":"Annales Henri Poincaré","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":false,"ca_institutions":"Pacific Institute for the Mathematical Sciences; University of British Columbia","funders":"National Science Foundation","keywords":"Abelian sandpile model; Finite graph; Mathematics; Vertex (graph theory); Combinatorics; Laplace operator; Graph; Transitive relation; Gaussian; Discrete mathematics; Statistical physics; Physics; Mathematical analysis; Quantum mechanics","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":[0.001062707,0.0007510125,0.001846165,0.003860773,0.002534019,0.003745511,0.001767122,0.002592266,0.008183849],"category_scores_gemma":[0.009667723,0.0006983815,0.0006895186,0.00125398,0.004333639,0.005295057,0.003041213,0.002987308,0.0006158935],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002001951,"about_ca_system_score_gemma":0.0009973291,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001873697,"about_ca_topic_score_gemma":0.001203448,"domain_scores_codex":[0.9995655,0.0001038953,0.00001661885,0.00007728463,0.0001325947,0.000104071],"domain_scores_gemma":[0.9961106,0.00161504,0.0004494635,0.0002909392,0.0004182169,0.001115757],"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":[0.00004625004,0.00001578516,0.0002726584,0.00003212488,0.000009385947,0.0001130505,0.00008647569,0.002019911,0.0006772925,0.9941226,0.001223531,0.001380994],"study_design_scores_gemma":[0.00002098912,0.00001369285,0.0003927911,0.00002084754,0.000007153711,0.0001455645,0.00004727487,0.02482262,0.0002838411,0.973116,0.001113476,0.00001579899],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7701188,0.003143217,0.1159132,0.009404544,0.0006871918,0.00009146501,0.0005131958,0.0008220354,0.09930633],"genre_scores_gemma":[0.9717862,0.0007542482,0.006151787,0.0006947986,0.0006809559,0.00006904566,0.0001968236,0.0001658467,0.01950037],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008183849,"threshold_uncertainty_score":0.02737767,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.104085421596314,"score_gpt":0.3671692113200901,"score_spread":0.2630837897237761,"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."}}