{"id":"W4390604910","doi":"10.1007/s00283-023-10316-z","title":"On the Three-Distance Theorem","year":2024,"lang":"en","type":"article","venue":"The Mathematical Intelligencer","topic":"semigroups and automata theory","field":"Computer Science","cited_by":25,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"Agence Nationale de la Recherche","keywords":"Mathematics","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001264308,0.0001697551,0.0001334336,0.0000334477,0.0001941107,0.0005266597,0.001996371,0.00004407612,0.001204929],"category_scores_gemma":[0.0001890979,0.00006622849,0.0001318526,0.0004234936,0.0002985006,0.0001419989,0.0002626299,0.0003129306,0.004483776],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000287549,"about_ca_system_score_gemma":0.0000272016,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002419531,"about_ca_topic_score_gemma":0.000001748275,"domain_scores_codex":[0.9986996,0.00009665244,0.000241173,0.0003010793,0.0003726735,0.0002888075],"domain_scores_gemma":[0.9954809,0.00332763,0.00003050514,0.001087551,0.00002493733,0.00004850589],"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":[0.000002763649,0.00002419317,2.239553e-7,0.00002042001,0.00001910743,0.000009069796,0.001078432,0.00001753466,0.00003422207,0.9685313,0.004098817,0.02616393],"study_design_scores_gemma":[0.0000067379,0.00002537749,0.000002123915,0.0001278362,0.000005659023,0.00001701595,0.00006817198,0.2529011,0.001719588,0.7421796,0.002865082,0.00008166958],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.002690546,0.0007007225,0.9501919,0.01110915,0.0003664765,0.0002222905,0.000001998398,0.0003788543,0.03433805],"genre_scores_gemma":[0.9946194,0.00002328953,0.001748774,0.001821617,0.000117222,0.00006083653,2.501095e-7,0.00001889625,0.001589753],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9919288,"threshold_uncertainty_score":0.9997081,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03363884972925238,"score_gpt":0.2801526812953224,"score_spread":0.24651383156607,"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."}}