{"id":"W1970283777","doi":"10.1006/eujc.2000.0437","title":"Note Concerning an Odd Langford Sequence","year":2001,"lang":"en","type":"article","venue":"European Journal of Combinatorics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Winnipeg","funders":"","keywords":"Mathematics; Arithmetic progression; Combinatorics; Sequence (biology); Set (abstract data type); Arithmetic; Discrete mathematics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.00351604,0.000144835,0.0002875385,0.0001339761,0.00011019,0.00007838677,0.0007086247,0.0000267638,0.000175995],"category_scores_gemma":[0.0009328236,0.0001226279,0.0001120296,0.0003135995,0.00009448434,0.0003134993,0.00009833604,0.0005694637,0.0001269884],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001205252,"about_ca_system_score_gemma":0.00009780945,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001720505,"about_ca_topic_score_gemma":7.948517e-7,"domain_scores_codex":[0.9975594,0.0008280132,0.0005516483,0.0001274992,0.0006292802,0.0003041087],"domain_scores_gemma":[0.9980974,0.0003643813,0.0004549858,0.0003418788,0.000465331,0.0002760421],"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":[0.000408161,0.0009015668,0.01651567,0.0001290029,0.0002407532,0.0153597,0.005217231,0.00008912671,0.003202399,0.9226798,0.01192781,0.02332875],"study_design_scores_gemma":[0.004715855,0.002485907,0.002226935,0.000452269,0.0002008007,0.004581547,0.001720211,0.001678707,0.0009565094,0.8412097,0.1389561,0.0008155013],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8704706,0.0001468592,0.03739167,0.0003542018,0.0005503234,0.00009493233,0.000002135524,0.00006439154,0.09092481],"genre_scores_gemma":[0.9946415,0.00007759194,0.002163662,0.00007542081,0.0002672847,1.90023e-7,7.851878e-7,0.00005855846,0.002714945],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1270283,"threshold_uncertainty_score":0.5000619,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1449351775198851,"score_gpt":0.3802863079236982,"score_spread":0.2353511304038131,"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."}}