{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003597723,0.0003229179,0.0007749086,0.0003266172,0.0001054251,0.00009621054,0.0003638297,0.0002785134,0.0001887922],"category_scores_gemma":[0.0006032313,0.0003157134,0.0002108284,0.0003510173,0.00009729986,0.00008090833,0.0009557543,0.0004099828,0.000009214355],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005788901,"about_ca_system_score_gemma":0.00008607475,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002090171,"about_ca_topic_score_gemma":0.00002708437,"domain_scores_codex":[0.9981757,0.00005937742,0.0007584223,0.0003747389,0.0003742146,0.0002575674],"domain_scores_gemma":[0.9967021,0.00133715,0.0006518099,0.0009347513,0.0002782355,0.00009596395],"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":[0.00002824341,0.004490703,0.001251234,0.01820401,0.001324634,0.00002047822,0.01315198,0.00008601266,0.006035134,0.9094793,0.02438313,0.02154515],"study_design_scores_gemma":[0.0004107576,0.00009910011,0.0005375629,0.001083903,0.0003391099,0.00002955653,0.002312814,0.005050886,0.01008124,0.9793671,0.0002304189,0.0004575486],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8209919,0.001727276,0.1712503,0.000690185,0.000170614,0.0008944831,0.00009627415,0.0001087765,0.004070159],"genre_scores_gemma":[0.8511988,0.0002098377,0.1480479,0.00003566333,0.00002856034,0.0001162664,0.00008745091,0.00006343173,0.0002120666],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06988782,"threshold_uncertainty_score":0.9999295,"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."}}