{"id":"W4417409221","doi":"10.48550/arxiv.2509.02731","title":"On circular external difference families","year":2025,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni; European Commission; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Multiset; Construct (python library); Cyclic group; Order (exchange); Group (periodic table); Variation (astronomy)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.0007177189,0.0003595537,0.0003404253,0.000993866,0.001204183,0.001053752,0.0004587515,0.0006661456,0.007535189],"category_scores_gemma":[0.003260856,0.0001726738,0.0004896636,0.0007564137,0.001868532,0.002140713,0.002242926,0.001199041,0.0008145075],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001034021,"about_ca_system_score_gemma":0.0004180789,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006576988,"about_ca_topic_score_gemma":0.0004517014,"domain_scores_codex":[0.9992379,0.0001316596,0.0000415117,0.0001465853,0.0002405432,0.0002019467],"domain_scores_gemma":[0.9987167,0.000552116,0.0001342988,0.0002076723,0.0002391051,0.0001502083],"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":[0.00004760108,0.00001450731,0.0005558457,0.00002518122,0.000002649981,0.000112893,0.0002195109,0.002164776,0.001909763,0.9816367,0.0009348836,0.01237569],"study_design_scores_gemma":[0.00003447321,0.0000924739,0.0007158629,0.00005767943,0.0000128009,0.0005468382,0.0002662218,0.03176101,0.004983144,0.9276346,0.03385904,0.00003581353],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4792137,0.001079778,0.3615232,0.0008333315,0.0003565287,0.0001174901,0.0005812473,0.0003973351,0.1558974],"genre_scores_gemma":[0.9417332,0.0004625939,0.02953881,0.000404864,0.0001578952,0.00012424,0.0005267473,0.000131122,0.02692055],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007535189,"threshold_uncertainty_score":0.0252077,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03144044712504589,"score_gpt":0.153119088181045,"score_spread":0.1216786410559991,"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."}}