{"id":"W4285684160","doi":"10.1016/j.jalgebra.2023.03.005","title":"Lefschetz properties of some codimension three Artinian Gorenstein algebras","year":2023,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"Division of Mathematical Sciences; California Institute for Regenerative Medicine; National Science Foundation","keywords":"Codimension; Mathematics; Pure mathematics; Zero (linguistics); Degree (music); Spectrum (functional analysis)","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":[0.0008305169,0.0001743097,0.0004842728,0.000312212,0.0001118348,0.00002860289,0.00034973,0.00008295554,0.0000944213],"category_scores_gemma":[0.0005344999,0.0001279139,0.0002301008,0.000499672,0.0001547258,0.0003152221,0.000131284,0.0002977557,0.0001046354],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003581842,"about_ca_system_score_gemma":0.0001320241,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006376158,"about_ca_topic_score_gemma":0.00001434735,"domain_scores_codex":[0.9980658,0.00008496659,0.0009521979,0.0001341095,0.0005130604,0.0002499019],"domain_scores_gemma":[0.9979621,0.0003086599,0.0008155611,0.0003826464,0.0004116618,0.000119358],"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":[0.0002253526,0.0005822732,0.002028296,0.000398969,0.000546005,0.00005380949,0.005024425,0.0000325425,0.4116895,0.5348228,0.03235205,0.01224397],"study_design_scores_gemma":[0.001205669,0.0005135605,0.008946003,0.0005149894,0.0001836285,0.00009997517,0.0009694448,0.0003746704,0.2042211,0.7804838,0.002186154,0.0003009853],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9961463,0.000446453,0.0003842163,0.002232912,0.0001531541,0.0002082842,0.000005631326,0.00005613125,0.000366908],"genre_scores_gemma":[0.996907,0.00007934166,0.002454139,0.00009155904,0.000176278,0.000007388082,0.000001743115,0.00003696026,0.000245579],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.245661,"threshold_uncertainty_score":0.5216179,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08676636170936847,"score_gpt":0.3117587561717772,"score_spread":0.2249923944624088,"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."}}