{"id":"W2027053128","doi":"10.1007/s11083-010-9176-y","title":"The Order on the Rationals has an Orthogonal Order with the Same Order Type","year":2010,"lang":"en","type":"article","venue":"Order","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Royal Military College of Canada; University of Calgary","funders":"","keywords":"Rational number; Mathematics; Order (exchange); Order type; Constant (computer programming); Identity (music); Combinatorics; Set (abstract data type); Identity function; Type (biology); Algebra over a field; Discrete mathematics; Pure 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":["sts","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.002696107,0.0003492821,0.0002409998,0.00006704442,0.00158779,0.0005406335,0.001129011,0.0001809288,0.007097584],"category_scores_gemma":[0.003792942,0.0001403635,0.00005550944,0.00140798,0.0009678063,0.0001867756,0.0001830074,0.001334228,0.0009937178],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002520271,"about_ca_system_score_gemma":0.0006423561,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003363468,"about_ca_topic_score_gemma":0.003281284,"domain_scores_codex":[0.9969171,0.0005622197,0.0003234251,0.0004347822,0.001108615,0.0006538439],"domain_scores_gemma":[0.9915883,0.004709424,0.000159021,0.001671357,0.001753297,0.0001185834],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0006336263,0.0003972719,0.0006699609,0.00001897049,0.0002273368,0.000009537476,0.001640625,0.00009112988,0.001196555,0.9281275,0.06433275,0.002654786],"study_design_scores_gemma":[0.001686525,0.0009618569,0.003118872,0.00004849445,0.0001210367,0.00009522015,0.002519452,0.003161431,0.0005304308,0.2325744,0.7543052,0.0008770474],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8637155,0.00007526844,0.001765063,0.09989485,0.0006109955,0.001829998,0.0000325764,0.0001970457,0.03187874],"genre_scores_gemma":[0.8972721,0.00005285916,0.01354008,0.01040758,0.001558369,0.0006306728,0.00008982244,0.0004314643,0.07601702],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6955531,"threshold_uncertainty_score":0.9997841,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09220822558538179,"score_gpt":0.348773892274057,"score_spread":0.2565656666886753,"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."}}