{"id":"W1551475051","doi":"10.1007/s00222-016-0653-9","title":"Unimodular hyperbolic triangulations: circle packing and random walk","year":2016,"lang":"en","type":"article","venue":"Inventiones mathematicae","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":28,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Engineering and Physical Sciences Research Council","keywords":"Unimodular matrix; Random walk; Mathematics; Circle packing; Unit circle; Triangulation; Boundary (topology); Combinatorics; Metric (unit); Degree (music); Mathematical analysis; Geometry; Physics; Statistics","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":[0.0006516404,0.0001600516,0.0003874488,0.0002465061,0.0001496899,0.00003453551,0.0001414299,0.0001038067,0.0006775981],"category_scores_gemma":[0.001995153,0.0001128033,0.0001242954,0.0003178194,0.0001665683,0.0001711601,0.00007856206,0.00006367364,0.0001812003],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002645058,"about_ca_system_score_gemma":0.00001941351,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004404887,"about_ca_topic_score_gemma":0.00000430984,"domain_scores_codex":[0.9986385,0.0001120561,0.0004891073,0.00026018,0.0002223704,0.0002778355],"domain_scores_gemma":[0.998037,0.001208243,0.000198105,0.0003833191,0.00007193939,0.0001013289],"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":[0.00002321723,0.0002153093,0.0006284289,0.0002416495,0.0001172681,0.000008875279,0.000511296,2.127175e-7,0.00222218,0.9527257,0.0006959192,0.04260995],"study_design_scores_gemma":[0.002432192,0.00003288427,0.001794534,0.0001904606,0.00008089474,0.0000687001,0.0001753601,0.0000774248,0.0007280188,0.9930273,0.001210512,0.0001817457],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.876203,0.0005342747,0.1162455,0.00291255,0.0002072634,0.0005342522,0.000008589785,0.0002461646,0.003108396],"genre_scores_gemma":[0.9883921,0.00006026729,0.008944778,0.00005935926,0.0001069807,0.0000539335,0.000001794402,0.00003238291,0.002348475],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.112189,"threshold_uncertainty_score":0.7419224,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04982202684616513,"score_gpt":0.2999668640749159,"score_spread":0.2501448372287508,"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."}}