{"id":"W4409766258","doi":"10.37236/13236","title":"Simplicial Complexes and Matroids with Vanishing $T^2$","year":2025,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni; National Board for Higher Mathematics; Istituto Nazionale di Alta Matematica \"Francesco Severi\"; National Foundation for Science and Technology Development; Banff International Research Station for Mathematical Innovation and Discovery; Vietnam Institute for Advanced Study in Mathematics; National Science Foundation","keywords":"Matroid; Simplicial complex; Abstract simplicial complex; h-vector; Simplicial approximation theorem; Mathematics; Combinatorics; Computer science; Simplicial set; Pure mathematics","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":[0.0003996737,0.0008418314,0.0004482325,0.002563679,0.001685324,0.002633509,0.0008243725,0.0005406909,0.006581069],"category_scores_gemma":[0.001353976,0.000335771,0.0005519373,0.001215415,0.002081277,0.003092719,0.002619119,0.001032134,0.0006767685],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007459522,"about_ca_system_score_gemma":0.0002941657,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007732276,"about_ca_topic_score_gemma":0.000975173,"domain_scores_codex":[0.9996257,0.00004406037,0.00002566847,0.0000881946,0.0000905615,0.0001258303],"domain_scores_gemma":[0.9990017,0.0002212454,0.0002511544,0.00009248501,0.000126616,0.0003068704],"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":[0.00007387813,0.00008125231,0.007412698,0.0001591793,0.0000261765,0.000826392,0.001275683,0.001614905,0.01272619,0.9610428,0.001227856,0.01353314],"study_design_scores_gemma":[0.00002989633,0.0001591543,0.009098705,0.00009779287,0.00007426462,0.002347529,0.002141095,0.01752692,0.0199238,0.9252842,0.02323569,0.00008088246],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9349396,0.0009229527,0.02598139,0.0004821126,0.00009474896,0.00004734375,0.0002100843,0.0001123304,0.03720956],"genre_scores_gemma":[0.9866675,0.0004367048,0.006414146,0.00004841505,0.00007839825,0.0000254954,0.0002567564,0.00003596453,0.00603663],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006581069,"threshold_uncertainty_score":0.02201587,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01135401232864087,"score_gpt":0.2974321554897087,"score_spread":0.2860781431610678,"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."}}