{"id":"W2012995549","doi":"10.4153/cmb-2006-010-9","title":"A Dynamical Proof of Pisot's Theorem","year":2006,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"semigroups and automata theory","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Algebraic number; Dual (grammatical number); Discrete mathematics; Pure mathematics; Combinatorics; Algebra over a field; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0003528576,0.0001295351,0.0002239235,0.0001160123,0.00005688753,0.00006195128,0.0007197444,0.00008158219,0.002204595],"category_scores_gemma":[0.0001049154,0.0001087297,0.00008416246,0.0001917826,0.000140063,0.00004244529,0.00007224988,0.0001043821,0.001245483],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000676271,"about_ca_system_score_gemma":0.0001296252,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009690625,"about_ca_topic_score_gemma":0.0004112816,"domain_scores_codex":[0.9988181,0.00005444175,0.000305951,0.0002422383,0.0001971216,0.0003821418],"domain_scores_gemma":[0.9989443,0.0001883143,0.0000624747,0.000515055,0.00004506788,0.0002447175],"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":[9.558155e-7,0.00004591934,0.00001469695,0.00003559409,0.00000455083,0.00002586381,0.00005157302,0.0000081245,0.000109917,0.9906132,0.00665746,0.002432139],"study_design_scores_gemma":[0.0002078417,0.00004666081,0.0002675304,0.00008304798,0.000007339171,0.00005904584,0.00002569453,0.0278614,0.00174378,0.9502238,0.01923632,0.0002375237],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08892467,0.000187184,0.7124332,0.01514311,0.000149042,0.0005107353,0.0000278894,0.0002252513,0.1823989],"genre_scores_gemma":[0.9778579,3.2285e-7,0.02040421,0.0004205997,0.00004451718,0.00001446264,0.000003270562,0.00001361099,0.001241088],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8889332,"threshold_uncertainty_score":0.9995322,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.004660020410612174,"score_gpt":0.1855592684707434,"score_spread":0.1808992480601313,"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."}}