{"id":"W2156110989","doi":"10.1098/rspa.2006.1684","title":"Enumerating the bent diagonal squares of Dr Benjamin Franklin FRS","year":2006,"lang":"en","type":"article","venue":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"","keywords":"Magic square; Diagonal; Bent molecular geometry; Mathematics; Combinatorics; Least-squares function approximation; Numbering; Backtracking; Statistics; Algorithm; Geometry; Engineering","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":[0.0003736677,0.000142688,0.0002321773,0.00001311586,0.0001562088,0.00004919772,0.0003195984,0.00004284916,0.000004057861],"category_scores_gemma":[0.00004624328,0.00007699524,0.0001985715,0.0002681485,0.0003828012,0.00008719244,0.00007156302,0.0001540955,8.166107e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008358178,"about_ca_system_score_gemma":0.000004387841,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009586852,"about_ca_topic_score_gemma":1.454036e-7,"domain_scores_codex":[0.9990812,0.000003600347,0.0002488818,0.0001282103,0.0003231069,0.0002150023],"domain_scores_gemma":[0.9996058,0.0002112059,0.00005955232,0.00005699188,0.00003319405,0.00003326848],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000004154734,0.0002014771,0.00130676,0.002613218,0.0001208614,9.756309e-8,0.006396078,0.1505018,0.07634693,0.7609434,0.001069157,0.0004961154],"study_design_scores_gemma":[0.0001153485,0.00004862729,0.003498344,0.0002919074,0.00004162072,0.000001958726,0.0008596529,0.8991824,0.02754346,0.06817972,0.00005551833,0.0001814678],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.997426,0.0002452363,0.0007173003,0.0001152803,0.00006429999,0.000119014,0.000004103584,0.00005586221,0.001252929],"genre_scores_gemma":[0.9991571,0.000002965254,0.0006618038,0.000005664584,0.0001169037,0.00001629359,1.404774e-7,0.000009753065,0.00002942296],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7486806,"threshold_uncertainty_score":0.3139775,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00460321839815817,"score_gpt":0.1797198780438229,"score_spread":0.1751166596456647,"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."}}