{"id":"W4410338799","doi":"10.37236/12513","title":"Almost All 9-Regular Graphs Have a Modulo-5 Orientation","year":2025,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"Natural Sciences and Engineering Research Council of Canada; Simons Institute for the Theory of Computing, University of California Berkeley","keywords":"Modulo; Orientation (vector space); Mathematics; Combinatorics; Arithmetic; Geometry","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000903158,0.0001377068,0.0002130369,0.000138992,0.00008797471,0.00003476921,0.0003347312,0.00006731778,0.000006167689],"category_scores_gemma":[0.00002507596,0.0001020386,0.0001488147,0.0004286148,0.00003577448,0.000127592,0.00001578763,0.0005109176,0.000004321954],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002530556,"about_ca_system_score_gemma":0.0001003963,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004464843,"about_ca_topic_score_gemma":0.000005829978,"domain_scores_codex":[0.9988456,0.0001119162,0.0003700139,0.0000692638,0.0002306365,0.0003725992],"domain_scores_gemma":[0.9994039,0.00008323939,0.0001200201,0.0002247485,0.0001254801,0.00004263547],"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":[0.00002864064,0.00003615395,0.0002673357,0.00003190245,0.0003000719,0.000004578885,0.0003889769,0.00233222,0.001068039,0.9931963,0.001989355,0.0003564381],"study_design_scores_gemma":[0.0007046604,0.0001452898,0.0003071649,0.00005282317,0.0001184218,0.00006605297,0.000258725,0.001542498,0.005519491,0.9740359,0.01713254,0.0001164484],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9605503,0.01083699,0.02105613,0.0003484428,0.002436117,0.0001856326,0.000001091019,0.00007101952,0.004514251],"genre_scores_gemma":[0.9986143,0.000855329,0.000002880127,0.00004897208,0.00003764002,0.000004391103,0.000001125959,0.00001696974,0.0004184074],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03806396,"threshold_uncertainty_score":0.4161012,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.003546911379042969,"score_gpt":0.208056211880001,"score_spread":0.204509300500958,"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."}}