{"id":"W2725463291","doi":"","title":"On partitions of {1,..., 2m + 1, l} into differences d,..., d + m: Stretched langford sequences","year":2010,"lang":"en","type":"article","venue":"Journal of Combinatorial Mathematics and Combinatorial Computing","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Combinatorics; Pure mathematics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001391676,0.0003371999,0.001105684,0.0002480235,0.0002326012,0.0001346145,0.000537365,0.0002125779,0.00004636629],"category_scores_gemma":[0.004119658,0.000268775,0.0002423545,0.0002743008,0.0003414606,0.0002605726,0.0001865564,0.0007869671,0.000003098422],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000419957,"about_ca_system_score_gemma":0.0001329492,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001026258,"about_ca_topic_score_gemma":0.000004527861,"domain_scores_codex":[0.9969397,0.00009486681,0.001558565,0.0002123022,0.0008656654,0.0003289139],"domain_scores_gemma":[0.9932193,0.00380646,0.001731812,0.0003623877,0.0006660661,0.0002139464],"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":[0.00004738017,0.0007490301,0.0001870923,0.0004533131,0.0001023063,0.00001166429,0.001799306,0.000003852066,0.002773468,0.9934396,0.000185264,0.0002477739],"study_design_scores_gemma":[0.001659047,0.0007393261,0.00005744015,0.0005458507,0.0001287408,0.00004735882,0.0009129661,0.0004768381,0.004457011,0.9906791,0.00003909378,0.0002572009],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9882736,0.00005062336,0.002619161,0.000141135,0.006981005,0.000247319,0.000004302264,0.00004673174,0.001636139],"genre_scores_gemma":[0.9704362,0.00001813508,0.02880684,0.000008410587,0.0006674379,0.000003554804,7.246022e-7,0.00003792018,0.0000207819],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02618768,"threshold_uncertainty_score":0.9999765,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02859802547730626,"score_gpt":0.3082704630651416,"score_spread":0.2796724375878353,"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."}}