{"id":"W4293334318","doi":"10.48550/arxiv.0905.1932","title":"C*-algebras of Penrose's hyperbolic tilings","year":2009,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Digital Image Processing Techniques","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Pacific Institute for the Mathematical Sciences","funders":"","keywords":"Invariant (physics); Mathematics; Affine transformation; Hyperbolic geometry; Substitution tiling; Pure mathematics; Order (exchange); Hyperbolic triangle; Harmonic; Combinatorics; Physics; Mathematical physics; Algebraic geometry; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002308624,0.0003322376,0.0004401326,0.0003721617,0.00006645484,0.0002301899,0.003357993,0.0002786586,0.000008269118],"category_scores_gemma":[0.00006314661,0.0003933867,0.0002329437,0.0007005946,0.0001907416,0.0008945827,0.002537471,0.0004724491,0.00004217015],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001068952,"about_ca_system_score_gemma":0.0002675274,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005187532,"about_ca_topic_score_gemma":0.000004097468,"domain_scores_codex":[0.998184,0.00005946174,0.0002674201,0.001018564,0.0001336468,0.0003368666],"domain_scores_gemma":[0.9976354,0.000053959,0.0003912645,0.001499532,0.0002829374,0.0001368767],"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":[0.00004893724,0.0007234424,0.00218184,0.0005565532,0.0001433357,0.0007585972,0.0005678137,0.006193102,0.00171709,0.9351313,0.002146251,0.04983171],"study_design_scores_gemma":[0.0003213641,0.0001430664,0.001432492,0.0004047109,0.00006324468,0.00001590135,0.0000167116,0.09920408,0.01681069,0.879993,0.0007615245,0.0008332633],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1881694,0.0001829074,0.7826098,0.0001092518,0.0001916129,0.0002447467,0.000008665151,0.001054312,0.02742935],"genre_scores_gemma":[0.966399,0.000105864,0.03224294,0.0001408832,0.0000313094,4.9728e-7,0.000006155094,0.0000188204,0.001054512],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7782297,"threshold_uncertainty_score":0.9998518,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06197507930926001,"score_gpt":0.1947955263674835,"score_spread":0.1328204470582235,"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."}}