{"id":"W4404988981","doi":"10.48550/arxiv.2411.17619","title":"A universal characterization of the shifted plactic monoid","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; University of Waterloo","keywords":"Characterization (materials science); Monoid; Free monoid; Syntactic monoid; Computer science; Algebra over a field; Mathematics; Pure mathematics; Materials science; Nanotechnology","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001553064,0.0002745569,0.000344636,0.0001972691,0.00008681697,0.0000408925,0.0006740295,0.0002783607,0.00007961661],"category_scores_gemma":[0.000075634,0.0002481931,0.0002931241,0.0004308685,0.0001425963,0.000106297,0.001182879,0.0006503144,0.00004607248],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001926332,"about_ca_system_score_gemma":0.0002049206,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006885085,"about_ca_topic_score_gemma":0.00003146186,"domain_scores_codex":[0.9987765,0.0001178979,0.0002323277,0.000554251,0.0001047311,0.0002142771],"domain_scores_gemma":[0.9985114,0.0001118174,0.0003727801,0.0008329465,0.0001033752,0.00006772781],"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":[0.0001409205,0.0002685768,0.002193229,0.001751433,0.0005220663,0.0001625059,0.001805439,0.00133474,0.004889686,0.986366,0.0003776815,0.0001877138],"study_design_scores_gemma":[0.0006462018,0.00004576063,0.00595047,0.0009696322,0.0009996194,0.000006715857,0.000406834,0.03180752,0.005316108,0.9527092,0.0004825162,0.0006593949],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9928625,0.00001659273,0.003117992,0.0001118245,0.0007143344,0.000374246,0.00006930438,0.000151567,0.002581635],"genre_scores_gemma":[0.9942644,0.00006183633,0.00009157843,0.00002200287,0.0001002749,6.191846e-7,0.00002138491,0.0000441333,0.005393765],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03365679,"threshold_uncertainty_score":0.999997,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0681705417341943,"score_gpt":0.1973577538931216,"score_spread":0.1291872121589273,"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."}}