{"id":"W4413470578","doi":"10.1007/978-3-031-84869-8_1","title":"The Study of the Transformation Semigroup of the Abelian and Directed Non-Abelian Sandpiles","year":2025,"lang":"en","type":"book-chapter","venue":"Springer proceedings in mathematics & statistics","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Abelian group; Semigroup; Transformation (genetics); Mathematics; Pure mathematics; Chemistry","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":[],"consensus_categories":[],"category_scores_codex":[0.0006217628,0.0003680009,0.0005509093,0.0001370691,0.0002161019,0.00009598013,0.001485361,0.0001505233,0.000001163616],"category_scores_gemma":[0.0004865131,0.0002114693,0.00007924667,0.0002313486,0.0002094372,0.0001319177,0.0005900885,0.0005743172,6.742714e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007391074,"about_ca_system_score_gemma":0.00007320337,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006814192,"about_ca_topic_score_gemma":0.00003381204,"domain_scores_codex":[0.9975973,0.000009822784,0.001128802,0.0003123606,0.0006830746,0.0002686843],"domain_scores_gemma":[0.9976219,0.0006585381,0.0007189819,0.00063135,0.0003287424,0.00004049873],"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":[0.000004001382,0.0001210498,0.00004630831,0.002522191,0.00008188163,6.632303e-7,0.01371737,0.0004291696,0.0001755376,0.9779604,0.0001102891,0.004831149],"study_design_scores_gemma":[0.0005262372,0.0001021968,0.0003235385,0.003906565,0.0001775787,0.000005772033,0.0007596827,0.3182212,0.000658182,0.6742705,0.0006291909,0.0004193865],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.006732191,0.0003930728,0.9467078,0.0002470144,0.0006961228,0.003907317,0.00008902032,0.0001669246,0.04106051],"genre_scores_gemma":[0.2520775,0.0009204887,0.727885,0.00005295595,0.00008099198,0.0002078128,0.000002379639,0.0001889398,0.01858393],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3177921,"threshold_uncertainty_score":0.862347,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009538009042287542,"score_gpt":0.2305057103601423,"score_spread":0.2209677013178547,"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."}}