{"id":"W3029417687","doi":"10.1017/fms.2021.53","title":"Geometric vertex decomposition and liaison","year":2021,"lang":"en","type":"preprint","venue":"Forum of Mathematics Sigma","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada; Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Mathematics; Vertex (graph theory); Ideal (ethics); Combinatorics; Decomposition; Algebraic number; Pure mathematics; Connection (principal bundle); Geometry; Graph","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005820012,0.0002795468,0.0004978378,0.001411932,0.001727605,0.002395348,0.0006488297,0.000513082,0.005236052],"category_scores_gemma":[0.0009579531,0.0001921947,0.00051626,0.0006539585,0.004877898,0.002845375,0.002822267,0.001466748,0.0004627244],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001372224,"about_ca_system_score_gemma":0.0004266347,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008052978,"about_ca_topic_score_gemma":0.0006114807,"domain_scores_codex":[0.9994408,0.0001050176,0.00001753908,0.000148188,0.0001278665,0.0001606037],"domain_scores_gemma":[0.99945,0.00009418152,0.00008559206,0.00007838273,0.0001179715,0.000173933],"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":[0.00001642846,0.00000686708,0.0004015264,0.00001167866,0.000002395936,0.00007142271,0.0002658331,0.0004196063,0.0009012654,0.9962814,0.000215153,0.001406399],"study_design_scores_gemma":[0.0000089818,0.00003172739,0.0006426906,0.00001652359,0.000008239672,0.0002854837,0.0006672697,0.002936024,0.002352123,0.9863852,0.006651454,0.00001425587],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7310351,0.001236356,0.1243946,0.001500222,0.0002231702,0.00004731661,0.0001363309,0.0003626452,0.1410643],"genre_scores_gemma":[0.9888521,0.0001323619,0.005128386,0.0001010361,0.00007531561,0.00001181486,0.00007002226,0.00002709157,0.005601939],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005236052,"threshold_uncertainty_score":0.01751637,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04243428916305172,"score_gpt":0.3394019666423986,"score_spread":0.2969676774793469,"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."}}