{"id":"W4393997442","doi":"10.1080/00927872.2024.2334895","title":"Proximal groups: Extension of topological groups. Application in the concise representation of Hilbert envelopes on oscillatory motion waveforms","year":2024,"lang":"en","type":"article","venue":"Communications in Algebra","topic":"Advanced Scientific Research Methods","field":"Agricultural and Biological Sciences","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"","keywords":"Mathematics; Extension (predicate logic); Representation (politics); Motion (physics); Pure mathematics; Topology (electrical circuits); Waveform; Algebra over a field; Combinatorics; Artificial intelligence; 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":[],"consensus_categories":[],"category_scores_codex":[0.001991295,0.0000883756,0.0001659299,0.00007721427,0.0001052762,0.00002912904,0.0008972099,0.00008462325,0.00002624977],"category_scores_gemma":[0.0005425851,0.00003345974,0.00006375507,0.001376855,0.0004266865,0.000206084,0.0002237926,0.000282051,0.000008310451],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006694422,"about_ca_system_score_gemma":0.00001267839,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001514028,"about_ca_topic_score_gemma":0.00034868,"domain_scores_codex":[0.9981202,0.0006624408,0.0004444551,0.0002896449,0.0003281092,0.000155087],"domain_scores_gemma":[0.9976831,0.001559769,0.000108056,0.0005341638,0.00008871273,0.00002619682],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"observational","study_design_scores_codex":[0.00006462092,0.0005866015,0.01680282,0.00004510092,0.000007960592,0.00000225241,0.001930341,0.0001126288,0.2275471,0.184626,0.00009809482,0.5681764],"study_design_scores_gemma":[0.0002250911,0.0002853398,0.8633925,0.0001971762,0.000008038656,0.00000765982,0.003385162,0.01307642,0.01283729,0.1038579,0.002537531,0.0001898355],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9937369,0.0005829164,0.0007990338,0.002986707,0.00005815709,0.0006849509,0.00001181101,0.00002764641,0.001111909],"genre_scores_gemma":[0.9968338,0.0003962248,0.002426133,0.00004736911,0.00002171827,0.0001498293,0.00009425988,0.000001184867,0.000029459],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8465897,"threshold_uncertainty_score":0.1667254,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1097002455400184,"score_gpt":0.3906000080707772,"score_spread":0.2808997625307588,"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."}}