{"id":"W6979229722","doi":"","title":"When are Morse resolutions polyhedral?","year":2025,"lang":"en","type":"article","venue":"ArXiv.org","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"","keywords":"Discrete Morse theory; Simplex; Morse code; Betti number; Monomial; Matching (statistics); Ideal (ethics); Chain (unit)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009512591,0.0004543541,0.0006556313,0.0009785608,0.002411508,0.005925306,0.001140447,0.001343593,0.02472354],"category_scores_gemma":[0.008165802,0.0007168056,0.0006109084,0.000991991,0.005129483,0.009518043,0.003814911,0.003293895,0.003927682],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001015824,"about_ca_system_score_gemma":0.0004748272,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008082115,"about_ca_topic_score_gemma":0.0008804774,"domain_scores_codex":[0.9976417,0.0003137921,0.0001081219,0.0005846755,0.0007482244,0.000603641],"domain_scores_gemma":[0.9972837,0.0008870696,0.0004190534,0.0006917953,0.0003253607,0.0003930255],"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":[0.00004656978,0.00002056101,0.000601122,0.00004448396,0.00001249376,0.0002134731,0.0005475586,0.0005374328,0.0008564836,0.9753161,0.002479719,0.01932397],"study_design_scores_gemma":[0.00002068142,0.0000271449,0.0007502253,0.0000694606,0.00001152745,0.000535048,0.001343209,0.001474304,0.00310806,0.9377805,0.05485186,0.00002793594],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3218536,0.006075633,0.2375298,0.0106127,0.001571587,0.0002332228,0.0007582033,0.0009499136,0.4204153],"genre_scores_gemma":[0.9184663,0.002349096,0.03884456,0.001387992,0.0005455184,0.0001271337,0.0007274147,0.0004270016,0.03712497],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02472354,"threshold_uncertainty_score":0.08270842,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09021341979398013,"score_gpt":0.3543794518298675,"score_spread":0.2641660320358873,"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."}}