{"id":"W2756299746","doi":"10.1142/s1793042118500446","title":"A unifying look at zero-sum invariants","year":2017,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brock University","funders":"Natural Sciences and Engineering Research Council of Canada; Science and Technology Development Fund; National Science Foundation","keywords":"Mathematics; Zero (linguistics); Subsequence; Combinatorics; Integer (computer science); Abelian group; Sequence (biology); Discrete mathematics; Computer science","routes":{"ca_aff":true,"ca_fund":true,"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":[],"category_scores_codex":[0.0009736868,0.0001345536,0.0002272871,0.00008699943,0.0002042654,0.0002130785,0.001168517,0.00006774478,0.003202765],"category_scores_gemma":[0.001607398,0.0001120366,0.0001886519,0.00001541002,0.0001311748,0.0005356089,0.0002831215,0.0002423237,0.000263124],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001512931,"about_ca_system_score_gemma":0.00006976498,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007620822,"about_ca_topic_score_gemma":0.000009620404,"domain_scores_codex":[0.9985848,0.00008621844,0.000471689,0.0001230733,0.0005665826,0.0001676375],"domain_scores_gemma":[0.9977186,0.0004675342,0.0009992513,0.0003276067,0.0003875003,0.00009950107],"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":[0.0006071707,0.000371652,0.01942471,0.00003860456,0.00109892,0.00106213,0.001671382,0.00000665792,0.002111331,0.8995178,0.06112522,0.01296447],"study_design_scores_gemma":[0.0009749671,0.00002186469,0.005441388,0.0003240782,0.00004239483,0.001106068,0.0001124388,0.00001916864,0.001837503,0.9766161,0.01335239,0.000151578],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9232908,0.00006068867,0.005905865,0.001042349,0.002659983,0.00006944832,0.00003657636,0.00002278868,0.06691148],"genre_scores_gemma":[0.9871196,0.00004431039,0.003734913,0.0002792995,0.0009346948,0.000001586372,0.000002557759,0.00002909141,0.007853914],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07709841,"threshold_uncertainty_score":0.9977084,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04968884413966303,"score_gpt":0.335747157454206,"score_spread":0.286058313314543,"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."}}