{"id":"W2030194314","doi":"10.1016/j.jalgebra.2009.11.032","title":"The immersion of ultrametric spaces into Hahn spaces","year":2009,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Ultrametric space; Mathematics; Immersion (mathematics); Space (punctuation); Pure mathematics; Combinatorics; Metric space; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001488859,0.0006813097,0.0006409648,0.002239727,0.001725657,0.003196296,0.0008870753,0.00109259,0.004918257],"category_scores_gemma":[0.004131017,0.0006020849,0.0007202293,0.000969345,0.005272883,0.008499962,0.004540065,0.0034983,0.0003663794],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00107268,"about_ca_system_score_gemma":0.0005382869,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007676354,"about_ca_topic_score_gemma":0.0005016159,"domain_scores_codex":[0.9989114,0.0003408448,0.00005143877,0.000191081,0.0003560999,0.0001492458],"domain_scores_gemma":[0.9977634,0.0009067102,0.0002924398,0.0001651932,0.0003113056,0.0005609093],"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":[0.0000195126,0.000008689495,0.0001453618,0.00001655014,0.00000636958,0.00003909126,0.0004313134,0.0002176795,0.0005843688,0.995956,0.0002455802,0.002329403],"study_design_scores_gemma":[0.00001148905,0.0000332207,0.0004240037,0.000007386579,0.000005577794,0.000134321,0.0002738714,0.002462733,0.0004358227,0.9928992,0.003301784,0.000010576],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6526819,0.003994733,0.2164951,0.005820134,0.0007396971,0.00006255058,0.0002599557,0.0002829985,0.1196628],"genre_scores_gemma":[0.9585239,0.001258156,0.01454775,0.0004304602,0.0005321448,0.00004748232,0.0001283204,0.00007191001,0.02445993],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004918257,"threshold_uncertainty_score":0.01645321,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02267339307804546,"score_gpt":0.3189065516089823,"score_spread":0.2962331585309368,"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."}}