{"id":"W2950685733","doi":"10.48550/arxiv.1110.5067","title":"Resolutions of 2 and 3 dimensional rings of invariants for cyclic groups","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Royal Military College of Canada","funders":"","keywords":"Mathematics; Ring (chemistry); Combinatorics; Group ring; Betti number; Order (exchange); Resolution (logic); Cyclic group; Simple (philosophy); Field (mathematics); Quadratic equation; Group (periodic table); Pure mathematics; Physics; Geometry; Computer science","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":[0.000165003,0.0001446983,0.0003254644,0.0001510658,0.00008247821,0.000003999402,0.0002808867,0.0001418788,0.00004124546],"category_scores_gemma":[0.0001246994,0.0001603377,0.0001279154,0.0001518455,0.0002193115,0.00006059949,0.000610696,0.0001675399,0.000002214027],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002992016,"about_ca_system_score_gemma":0.0000677002,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001182635,"about_ca_topic_score_gemma":0.00006203334,"domain_scores_codex":[0.9992269,0.00004558924,0.0002361579,0.000325047,0.00004116085,0.0001251723],"domain_scores_gemma":[0.9983707,0.0004840437,0.0003736551,0.00050181,0.0002091797,0.00006061306],"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":[0.00005248226,0.0001786806,0.001196884,0.0002674987,0.0001313938,0.000001293395,0.0004170978,0.0001819031,0.000487554,0.9966723,0.0003693938,0.00004354697],"study_design_scores_gemma":[0.0004674311,0.00005559478,0.005435066,0.0001272542,0.0002561886,0.000001289891,0.0001120819,0.004930692,0.0007851787,0.9875942,0.00007494396,0.000160023],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9458381,0.0000467793,0.05134101,0.00002616087,0.00003476015,0.0004721026,0.0001639343,0.00002410889,0.002053044],"genre_scores_gemma":[0.995164,0.00005127682,0.004272476,0.000007464011,0.00001277209,0.000003855672,0.00001892925,0.00001570524,0.0004534873],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04932594,"threshold_uncertainty_score":0.6538382,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.204229931295055,"score_gpt":0.248136865548415,"score_spread":0.04390693425336004,"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."}}