{"id":"W2051187346","doi":"10.1016/j.disc.2013.03.011","title":"Determinants of grids, tori, cylinders and Möbius ladders","year":2013,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Torus; Planar; Cylinder; Singularity; Grid; Combinatorics; Discrete mathematics; Pure mathematics; Mathematical analysis; Geometry","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003489916,0.000393774,0.0008268401,0.0001235676,0.000104769,0.00006592233,0.0003909924,0.0001821694,0.0001598466],"category_scores_gemma":[0.001274917,0.0003315068,0.0001404618,0.000224259,0.0002512794,0.0003313978,0.0002285085,0.0002040853,0.00005515844],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004411648,"about_ca_system_score_gemma":0.00004035796,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001954749,"about_ca_topic_score_gemma":0.000008658852,"domain_scores_codex":[0.997641,0.00005067116,0.0009929416,0.0003226352,0.0005210738,0.0004716863],"domain_scores_gemma":[0.997161,0.001002537,0.0006273091,0.0008087741,0.0002067421,0.0001936249],"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":[0.00002077498,0.0007478618,0.002592406,0.005309193,0.0002160903,0.00001943404,0.01069672,0.000007144438,0.00258516,0.970193,0.00345984,0.004152426],"study_design_scores_gemma":[0.0007001956,0.0001232784,0.0001441998,0.0003214388,0.0001103781,0.00003449341,0.003085627,0.00330892,0.004637329,0.9870286,0.00008750772,0.0004180471],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9778904,0.0001220613,0.01254488,0.0001110198,0.0004432663,0.001295724,0.00002050733,0.0002088448,0.007363291],"genre_scores_gemma":[0.8282562,0.00004333347,0.1707959,0.00003501595,0.00008880581,0.0001019328,0.000002952188,0.0001163431,0.0005594426],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1582511,"threshold_uncertainty_score":0.9999137,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02793990506582787,"score_gpt":0.3053568767351376,"score_spread":0.2774169716693097,"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."}}