{"id":"W2059530475","doi":"10.1107/s0108767302011637","title":"A revised proof of the metric properties of optimally superimposed vector sets","year":2002,"lang":"en","type":"article","venue":"Acta Crystallographica Section A Foundations of Crystallography","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":34,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Metric (unit); Mathematics; Superposition principle; Square (algebra); Square root; Combinatorics; Pure mathematics; Mathematical analysis; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.008277812,0.002361355,0.002221848,0.003163793,0.001767365,0.003622057,0.003357147,0.003431632,0.01823515],"category_scores_gemma":[0.04649412,0.001266531,0.002598043,0.003782414,0.005254996,0.01271583,0.007314367,0.009998616,0.00696222],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00218371,"about_ca_system_score_gemma":0.001764738,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008535274,"about_ca_topic_score_gemma":0.000566887,"domain_scores_codex":[0.9887639,0.003159655,0.001115102,0.001722222,0.004627274,0.0006118665],"domain_scores_gemma":[0.9740674,0.009840803,0.001687657,0.005665368,0.007836085,0.0009026662],"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":[0.0001100516,0.00003694481,0.0002202782,0.000454031,0.00007115921,0.0003154965,0.0002025663,0.005326446,0.00475201,0.9124242,0.03057455,0.04551227],"study_design_scores_gemma":[0.00004906773,0.0001428228,0.0004176784,0.0001227563,0.00005202294,0.0008185517,0.00006113996,0.02407928,0.005602301,0.9138117,0.05465784,0.0001848547],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.008962354,0.003668813,0.9312569,0.01144899,0.01024651,0.0001361624,0.001472435,0.0007729609,0.03203491],"genre_scores_gemma":[0.3635381,0.007093737,0.5816005,0.009521187,0.008998052,0.0007755582,0.002517396,0.001953494,0.02400202],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.01823515,"threshold_uncertainty_score":0.06100267,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02396950355655137,"score_gpt":0.2246619659921811,"score_spread":0.2006924624356297,"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."}}