{"id":"W7104369327","doi":"10.55016/ojs/cdm.v20i1.75594","title":"Congruences modulo powers of 3 for 6-colored generalized Frobenius partitions","year":2025,"lang":"","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Centre Scientifique et Technique du Bâtiment; Chongqing Municipal Education Commission; National Natural Science Foundation of China; Chongqing Normal University","keywords":"Congruence relation; Modulo; Conjecture; Generating function; Function (biology); Primitive root modulo n","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":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch","metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001348912,0.0009181589,0.002494172,0.0007247232,0.0008500385,0.0003111671,0.001179588,0.0005252369,0.0005556574],"category_scores_gemma":[0.0189956,0.0009042377,0.001063142,0.001527812,0.0009760688,0.0004391654,0.0005529029,0.0003770266,0.0001136703],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005909239,"about_ca_system_score_gemma":0.0007174467,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002902195,"about_ca_topic_score_gemma":0.0000959235,"domain_scores_codex":[0.993408,0.0001975572,0.003413457,0.0008667822,0.0007361993,0.001378024],"domain_scores_gemma":[0.9888855,0.004801512,0.00120604,0.001810799,0.00282157,0.0004746175],"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":[0.000131371,0.001208874,0.00001011379,0.003971565,0.0009803018,0.000003118953,0.002140371,0.001088574,0.003469089,0.9672564,0.0196431,0.00009712637],"study_design_scores_gemma":[0.002824474,0.0003052865,0.00001440471,0.002648726,0.00220429,0.000005872745,0.003936629,0.02181834,0.02229541,0.9386998,0.004440397,0.0008063959],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02373102,0.001198074,0.9435566,0.004607779,0.001214296,0.00751946,0.01076727,0.000266974,0.007138516],"genre_scores_gemma":[0.5709805,0.0002858761,0.3971485,0.0003039631,0.0002256439,0.003251424,0.0002398089,0.0001854102,0.02737884],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5472496,"threshold_uncertainty_score":0.9993408,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02259506787082572,"score_gpt":0.3713278834376769,"score_spread":0.3487328155668512,"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."}}