{"id":"W2593370264","doi":"10.1080/00927872.2012.695834","title":"Resolutions of 2 and 3 Dimensional Rings of Invariants for Cyclic Groups","year":2013,"lang":"en","type":"article","venue":"Communications in Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Royal Military College of Canada","funders":"","keywords":"Mathematics; Ring (chemistry); Combinatorics; Group ring; Resolution (logic); Order (exchange); Simple (philosophy); Betti number; Cyclic group; Pure mathematics; Group (periodic table)","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":[0.0002874553,0.00008818221,0.0002244923,0.0001566083,0.0001281157,0.000009240767,0.000542804,0.00005455511,0.00005120369],"category_scores_gemma":[0.0005543716,0.00008769824,0.00004815156,0.0003024432,0.0003610079,0.0001390285,0.0004203489,0.0001214026,0.000005537414],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002141626,"about_ca_system_score_gemma":0.00003465117,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001215521,"about_ca_topic_score_gemma":0.0001430364,"domain_scores_codex":[0.9990898,0.00008886385,0.0004923755,0.0001219473,0.00008563591,0.0001213718],"domain_scores_gemma":[0.9962153,0.002086633,0.0002148131,0.001234779,0.0002100078,0.00003844505],"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":[0.000004167871,0.0002952077,0.002934437,0.00005143951,0.00002467353,1.455021e-8,0.0007531194,0.000001528361,0.003989952,0.9888509,0.001225109,0.001869434],"study_design_scores_gemma":[0.0005138878,0.00004223795,0.05938937,0.00009028331,0.00002815991,0.000002315968,0.0002861626,0.002877463,0.000931541,0.9351063,0.0006280353,0.0001042829],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9892967,0.000686045,0.003977215,0.00233908,0.00001302775,0.0009786482,0.00004688899,0.00002464119,0.002637785],"genre_scores_gemma":[0.913691,0.0001107826,0.08562155,0.00003625348,0.000004671625,0.0004264676,0.00002208622,0.00001312795,0.00007405272],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08164434,"threshold_uncertainty_score":0.357623,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09016338491533821,"score_gpt":0.3614138142949578,"score_spread":0.2712504293796196,"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."}}