{"id":"W1966299418","doi":"10.4153/cmb-2010-068-3","title":"Elements in a Numerical Semigroup with Factorizations of the Same Length","year":2010,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Element (criminal law); Embedding; Numerical semigroup; Dimension (graph theory); Monoid; Semigroup; Algebra over a field; Pure mathematics; Discrete mathematics; Combinatorics; Computer science; Law","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001165094,0.0003176705,0.0003532498,0.0008601189,0.00121413,0.002065334,0.0003532988,0.0004831923,0.003209804],"category_scores_gemma":[0.002409728,0.0002790321,0.0006652615,0.0005597664,0.002677142,0.003284063,0.001423586,0.0008807007,0.0004258336],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001085819,"about_ca_system_score_gemma":0.0004053143,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004496563,"about_ca_topic_score_gemma":0.0005487747,"domain_scores_codex":[0.9989279,0.0002053776,0.0001321208,0.0002392569,0.0002870719,0.0002082738],"domain_scores_gemma":[0.9967506,0.001136719,0.0007797495,0.0003547295,0.0005154056,0.0004628687],"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":[0.0003100471,0.00005364753,0.00383027,0.00007610569,0.00002345037,0.0004663653,0.001526433,0.001843774,0.01607092,0.964808,0.0004638112,0.01052717],"study_design_scores_gemma":[0.00005483111,0.0001863466,0.003225477,0.00006178943,0.00004984637,0.0007636502,0.0007647988,0.00797737,0.01667148,0.9610763,0.009085342,0.00008291846],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9240403,0.0001925061,0.05945941,0.0002299062,0.00006813314,0.0000239826,0.0001529923,0.000161318,0.0156714],"genre_scores_gemma":[0.978911,0.00005524494,0.01800862,0.00003839943,0.00004137521,0.00002658823,0.0001159248,0.00002576568,0.002776963],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003209804,"threshold_uncertainty_score":0.01073784,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01595126906622914,"score_gpt":0.2375587553418221,"score_spread":0.221607486275593,"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."}}