{"id":"W4416938455","doi":"10.1016/j.disc.2025.114918","title":"On subsequence sums of index-1-free sequences over cyclic groups","year":2025,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Brock University","funders":"Fundamental Research Funds for the Central Universities; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Subsequence; Counterexample; Generator (circuit theory); Conjecture; Order (exchange); Sequence (biology); Longest increasing subsequence","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0005506577,0.0003517446,0.0006498652,0.0002352905,0.0001178986,0.00006902995,0.0009109385,0.0001711283,0.0001380385],"category_scores_gemma":[0.001426459,0.0002846539,0.000234308,0.0004338234,0.0002985314,0.0001764657,0.0002280602,0.0002706487,0.00002898938],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007621584,"about_ca_system_score_gemma":0.00007853136,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000373859,"about_ca_topic_score_gemma":0.00005489513,"domain_scores_codex":[0.9977282,0.00006346886,0.0008134431,0.000391241,0.0005910055,0.000412607],"domain_scores_gemma":[0.9970084,0.001027201,0.0004014966,0.001383905,0.0000947126,0.00008429155],"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":[0.00001736952,0.0001642884,0.001037084,0.001063809,0.0001030981,0.000009613494,0.001197557,0.00001271562,0.001687269,0.992148,0.002319536,0.0002396587],"study_design_scores_gemma":[0.0005395034,0.00006862132,0.0008803099,0.0008392389,0.00007979989,0.000005446926,0.0005788651,0.001034971,0.01212534,0.9834462,0.0001121311,0.000289573],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9546946,0.0001192952,0.0141621,0.0002607076,0.0002458067,0.0004385882,0.00004620933,0.0001521653,0.02988055],"genre_scores_gemma":[0.9862227,0.0000452865,0.01177793,0.0001685294,0.00005535714,0.00003817481,0.000007460186,0.00004728716,0.001637314],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03152807,"threshold_uncertainty_score":0.9999605,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02714832407634999,"score_gpt":0.2968632602162857,"score_spread":0.2697149361399357,"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."}}