{"id":"W2234953642","doi":"10.1142/s0219498818500111","title":"Graded Betti numbers of path ideals of cycles and lines","year":2017,"lang":"en","type":"preprint","venue":"Journal of Algebra and Its Applications","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"","keywords":"Betti number; Mathematics; Path (computing); Mathematical proof; Line (geometry); Projective test; Combinatorics; Pure mathematics; Computer science; 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":[0.0005234491,0.0002586812,0.0008816662,0.0002088169,0.000185184,0.00005608886,0.0005603323,0.0002112926,0.00002122794],"category_scores_gemma":[0.0003344328,0.0002182947,0.0002110962,0.0001057449,0.0002711063,0.0001402873,0.0003922883,0.0004688023,0.00000114992],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001817578,"about_ca_system_score_gemma":0.0001679332,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001916362,"about_ca_topic_score_gemma":0.00001062648,"domain_scores_codex":[0.9980233,0.00006687706,0.00121458,0.0002397943,0.0003049113,0.0001505196],"domain_scores_gemma":[0.9945191,0.0007434117,0.003154986,0.0006470138,0.0007847618,0.0001507381],"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":[0.00005652522,0.0007779608,0.002641645,0.002577545,0.0009596343,0.000002483384,0.003424483,0.000008426357,0.01538599,0.9501503,0.003361324,0.02065365],"study_design_scores_gemma":[0.000567767,0.0001073163,0.01181646,0.0005912488,0.0006045471,0.00005494023,0.0004304638,0.00007815207,0.007593873,0.9760127,0.001874768,0.0002677407],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.984965,0.006212399,0.00521074,0.00161866,0.00005957042,0.0008526641,0.0002101055,0.00001560603,0.0008553151],"genre_scores_gemma":[0.9852251,0.004963328,0.009393644,0.00002394066,0.0001749488,0.00007623406,0.0000122129,0.00003296163,0.00009757271],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0258624,"threshold_uncertainty_score":0.8901798,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06339853633777051,"score_gpt":0.3654093293583114,"score_spread":0.3020107930205409,"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."}}