{"id":"W2080714423","doi":"10.1016/j.disc.2008.06.012","title":"Existence of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si3.gif\" display=\"inline\" overflow=\"scroll\"><mml:mi>r</mml:mi></mml:math>-fold perfect <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si4.gif\" display=\"inline\" overflow=\"scroll\"><mml:mrow><mml:mo>(</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-Mendelsohn designs with <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si5.gif\" display=\"inline\" overflow=\"scroll\"><mml:mi>K</mml:mi><mml:mo>⊆</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>5</mml:mn><mml:mo>,</mml:mo><mml:mn>6</mml:mn><mml:mo>,</mml:mo><mml:mn>7</mml:mn><mml:mo>}</mml:mo></mml:mrow></mml:math>","year":2008,"lang":"lv","type":"article","venue":"Discrete Mathematics","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Mount Saint Vincent University","funders":"","keywords":"Combinatorics; Mathematics; Integer (computer science); Block (permutation group theory); Discrete mathematics; Computer science","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":["metaresearch","metaepi_narrow","metaepi_broad","sts","scholarly_communication","open_science","research_integrity","insufficient_payload"],"consensus_categories":["metaepi_narrow","sts","open_science","research_integrity","insufficient_payload"],"category_scores_codex":[0.01481472,0.0103007,0.004838853,0.005157137,0.01284377,0.01076165,0.01737938,0.01756084,0.05010842],"category_scores_gemma":[0.01048611,0.01723874,0.01576103,0.009937222,0.01306396,0.0109018,0.01381149,0.01497037,0.01361701],"about_ca_system_candidate":true,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004594759,"about_ca_system_score_gemma":0.009651302,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.008558476,"about_ca_topic_score_gemma":0.005593754,"domain_scores_codex":[0.9308945,0.004191013,0.01581184,0.01387561,0.01768931,0.01753774],"domain_scores_gemma":[0.9464475,0.01131549,0.01688683,0.01360446,0.002395309,0.009350432],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.01072614,0.00382152,0.0000660877,0.01031971,0.01410263,0.008734633,0.009384538,0.01331537,0.01233848,0.7563635,0.1571524,0.003675028],"study_design_scores_gemma":[0.01282027,0.01003007,0.0001338613,0.01137432,0.01419382,0.01636113,0.01128233,0.2991426,0.5860426,0.005725838,0.01845183,0.01444139],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8473517,0.009192137,0.006638147,0.001785687,0.01302513,0.001071714,0.008747551,0.003802615,0.1083853],"genre_scores_gemma":[0.9257808,0.009425226,0.01402928,0.005074915,0.01129922,0.01212481,0.01178583,0.009024174,0.001455801],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7506377,"threshold_uncertainty_score":0.9980436,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02103768154853112,"score_gpt":0.2378014874144261,"score_spread":0.2167638058658949,"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."}}