{"id":"W2080233228","doi":"10.1007/s11511-010-0051-x","title":"The Fourier spectrum of critical percolation","year":2010,"lang":"en","type":"article","venue":"Acta Mathematica","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":88,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche; Microsoft Research","keywords":"Percolation (cognitive psychology); Mathematics; Square tiling; Square (algebra); Fourier transform; Dimension (graph theory); Plane (geometry); Combinatorics; Function (biology); Spectrum (functional analysis); Percolation critical exponents; Order (exchange); Grid; Mathematical analysis; Critical exponent; Geometry; Physics; Quantum mechanics","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":[0.0004140449,0.000123563,0.0002273865,0.0000195414,0.000156614,0.00004725167,0.0002907725,0.00008106963,0.0003248875],"category_scores_gemma":[0.01736768,0.00007831569,0.00006711017,0.0001115691,0.0001748813,0.00007283062,0.00006921776,0.0002667452,0.00004660069],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006556301,"about_ca_system_score_gemma":0.00004349578,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":9.281111e-7,"about_ca_topic_score_gemma":0.000007994118,"domain_scores_codex":[0.9988449,0.00002139728,0.0003917312,0.0001484793,0.0003536612,0.0002398225],"domain_scores_gemma":[0.9943025,0.004962478,0.000109284,0.0004158154,0.0001025782,0.0001073427],"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":[0.00001133368,0.0000841561,0.000001397475,0.0001929737,0.00001179018,0.00000152184,0.0003182732,1.420098e-8,0.001971877,0.9955907,0.0009496298,0.000866266],"study_design_scores_gemma":[0.0001060674,0.00007141432,0.0000175061,0.00002394938,0.00005528988,0.00002011062,0.0001432139,0.0150792,0.001436976,0.9821348,0.0008151466,0.0000963034],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03528464,0.0000221765,0.9334494,0.0144044,0.0005711698,0.0005107409,0.00002930378,0.0001254371,0.01560268],"genre_scores_gemma":[0.8739697,0.000002243189,0.1257423,0.00004327706,0.0000951616,0.0000194203,5.846525e-7,0.00002196941,0.0001053937],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.838685,"threshold_uncertainty_score":0.9909095,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02935086578457686,"score_gpt":0.3385690419525245,"score_spread":0.3092181761679477,"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."}}