{"id":"W4409870993","doi":"10.2140/involve.2025.18.437","title":"Down-left graphs and a connection to toric ideals of graphs","year":2025,"lang":"en","type":"article","venue":"Involve a Journal of Mathematics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Connection (principal bundle); Combinatorics; Discrete mathematics; Pure mathematics; Geometry","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":[0.0008098402,0.0001514021,0.0005209998,0.0005113027,0.00008244863,0.00003244566,0.0002504856,0.00006772302,0.00003609245],"category_scores_gemma":[0.001115326,0.0001228148,0.0001581747,0.00054092,0.0000753676,0.0001148816,0.00008573974,0.0001767762,0.000002972645],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003554211,"about_ca_system_score_gemma":0.00007052929,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006269689,"about_ca_topic_score_gemma":0.00001842511,"domain_scores_codex":[0.9984974,0.00005792631,0.0009207111,0.0001066655,0.0002723054,0.0001450186],"domain_scores_gemma":[0.9968885,0.001506661,0.0006431713,0.0002933276,0.0005701862,0.00009818823],"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":[0.00002481857,0.0004191812,0.0005981838,0.0005508065,0.0002805983,0.000002801987,0.005741264,0.000005865945,0.005919955,0.9763656,0.008282185,0.001808789],"study_design_scores_gemma":[0.0004421844,0.0002229561,0.0004634519,0.0004971139,0.0002077898,0.00004703852,0.002376667,0.00008556862,0.004612976,0.9899949,0.0009412194,0.0001081349],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9383561,0.0007154687,0.0571024,0.0008197617,0.0001457938,0.0004009956,0.00001045273,0.00002338522,0.002425642],"genre_scores_gemma":[0.9274526,0.0002617577,0.07184581,0.0001775706,0.00002141853,0.00001107296,6.121151e-7,0.00001968463,0.0002095004],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01474341,"threshold_uncertainty_score":0.5008244,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0355860591826157,"score_gpt":0.3321885024146785,"score_spread":0.2966024432320628,"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."}}