{"id":"W4400596853","doi":"10.55016/ojs/cdm.v16i1.69831","title":"Lengths of extremal square-free ternary words","year":2021,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"semigroups and automata theory","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Winnipeg","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Square-free integer; Ternary operation; Word (group theory); Mathematics; Square (algebra); Alphabet; Combinatorics; Sigma; Discrete mathematics; Geometry; Computer science; Linguistics; Physics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"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":[0.0003873643,0.0001709808,0.0003400452,0.00009734092,0.0001269795,0.0001207179,0.001168344,0.0000736333,0.00009617811],"category_scores_gemma":[0.001082287,0.0001552606,0.0001626274,0.0006150185,0.00006123522,0.0002568603,0.0009327498,0.0001166223,0.000084387],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006082156,"about_ca_system_score_gemma":0.0001378535,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004373244,"about_ca_topic_score_gemma":0.000005381612,"domain_scores_codex":[0.9984782,0.0000702661,0.0004671855,0.0003073864,0.0003361798,0.0003407194],"domain_scores_gemma":[0.9974066,0.000337947,0.0001411111,0.001638663,0.0003201856,0.0001554799],"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":[0.000002965144,0.0001975877,0.00005863146,0.00007427412,0.00004438922,0.00004818134,0.001218447,0.00005129011,0.005277687,0.9869715,0.002728729,0.00332634],"study_design_scores_gemma":[0.002094261,0.000260424,0.001533457,0.0009222784,0.0001289249,0.0003194098,0.001582876,0.1616206,0.09252585,0.7250692,0.01285186,0.001090858],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0198644,0.0004129529,0.9720138,0.003274035,0.0002337062,0.000198373,0.0002597377,0.0001793309,0.003563716],"genre_scores_gemma":[0.8145308,0.00001988637,0.1841587,0.0002601221,0.0001000111,0.00003939824,0.00002583598,0.00001939523,0.0008459134],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7946664,"threshold_uncertainty_score":0.6331344,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01078679322922826,"score_gpt":0.2717872130663739,"score_spread":0.2610004198371457,"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."}}