{"id":"W4390298120","doi":"10.20944/preprints202312.2055.v1","title":"Existence of a Hölder Continuous extension on embedded balls of the 3-Torus for the Periodic Navier Stokes Equations","year":2023,"lang":"en","type":"preprint","venue":"Preprints.org","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"London Health Sciences Centre","funders":"","keywords":"Torus; Mathematics; Mathematical analysis; Navier–Stokes equations; Euler equations; Center (category theory); Cartesian coordinate system; Surface (topology); Physics; Mathematical physics; Combinatorics; Geometry; Compressibility; Crystallography","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":[0.002045329,0.000353915,0.0008800541,0.0002054423,0.0002159559,0.00002681063,0.001265617,0.0003274869,0.0003014439],"category_scores_gemma":[0.006645571,0.0002081489,0.0009628756,0.0006417526,0.0002295778,0.00003786236,0.001296636,0.0006862627,0.00008317935],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006324501,"about_ca_system_score_gemma":0.0001762723,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001626369,"about_ca_topic_score_gemma":0.00007170328,"domain_scores_codex":[0.9969163,0.0002288458,0.001024539,0.0007018879,0.0008227461,0.0003056932],"domain_scores_gemma":[0.9925501,0.002621678,0.00127396,0.002724458,0.0007722676,0.00005751322],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.00165701,0.009473046,0.3872681,0.01418338,0.01717242,0.00003160468,0.1140033,0.04563694,0.07673944,0.2879503,0.01483344,0.03105104],"study_design_scores_gemma":[0.003749839,0.0003610967,0.5877584,0.00664941,0.008317155,0.00001394217,0.01926604,0.03743372,0.04190524,0.2810785,0.01084238,0.002624366],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.985619,0.0005218417,0.008208876,0.000988043,0.0009820854,0.002532268,0.0001407887,0.0000810629,0.0009260419],"genre_scores_gemma":[0.992066,0.0001215913,0.001050909,0.00006677317,0.0001053608,0.0004052622,0.00001721586,0.00005439716,0.006112443],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2004903,"threshold_uncertainty_score":0.8488065,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.309126512567912,"score_gpt":0.4047406446680793,"score_spread":0.09561413210016728,"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."}}