{"id":"W4406164119","doi":"10.61091/ars161-01","title":"The Zero Forcing Number of Quartic Circulant Graphs of Prime Order","year":2024,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Circulant matrix; Quartic function; Prime (order theory); Order (exchange); Zero (linguistics); Forcing (mathematics); Combinatorics; Pure mathematics; Discrete mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000371244,0.0003064875,0.0003156743,0.001553896,0.00114059,0.001278605,0.0004668552,0.0004687246,0.003276008],"category_scores_gemma":[0.001842723,0.0001978319,0.0002476693,0.0006014045,0.001575406,0.001023158,0.0005478541,0.0007220842,0.0002517644],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008449693,"about_ca_system_score_gemma":0.0006084707,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008523929,"about_ca_topic_score_gemma":0.001351046,"domain_scores_codex":[0.9997991,0.0000352827,0.000008261936,0.00004518225,0.00004507362,0.00006718063],"domain_scores_gemma":[0.9987767,0.000665986,0.0001562085,0.00009638946,0.0001215974,0.0001830615],"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":[0.0002087059,0.00005067903,0.002754313,0.0001146472,0.00001582032,0.0002930789,0.0004233805,0.01199368,0.02757957,0.9405958,0.001774148,0.0141961],"study_design_scores_gemma":[0.00005217662,0.0001015011,0.004327123,0.00006154444,0.00003666923,0.0004731875,0.0003445874,0.08631817,0.01697983,0.887072,0.004169868,0.00006324671],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9475621,0.000250208,0.02962967,0.0003474573,0.00005640791,0.00002283493,0.0001897344,0.0001042851,0.02183745],"genre_scores_gemma":[0.9924349,0.0001452262,0.004985628,0.00003905297,0.00003833909,0.00002650406,0.0001054361,0.00002967793,0.002195218],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003276008,"threshold_uncertainty_score":0.01095939,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005492508806893865,"score_gpt":0.2144486463256557,"score_spread":0.2089561375187619,"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."}}