{"id":"palomar/PALOMAR-2026-09-21-000002","url":"https://github.com/Vulkin-prog/paper-c-lean/tree/d8edbc44654f623fc68df92612c26a6ef9a90ec2","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-21-000002-v1.json","repo":"https://github.com/Vulkin-prog/paper-c-lean","tags":["math.NT","math.PR","msc:11K65","msc:60F05","probability","number-theory","poisson-laws","empirical-fields"],"score":0,"title":"Microscopic signed fields and empirical Poisson laws","trust":"high","domain":"math.NT","source":"palomar","authors":["Brice Pouly"],"reviews":0,"subject":"math.NT","summary":"Quantitative comparison of the actual position/excess/sign field at growing intensity, retaining the original small-prime conditioning; same-grid dyadic restriction and common measurable readouts. Along literal dyadic scales, empirical window counts converge almost surely to Poisson, while empirical full vectors have a positive total-variation obstruction.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-21","reactions":{},"formalized":true,"formalizes":[{"title":"Long runs and rare patterns of a random completely multiplicative function","identifier":"https://github.com/Vulkin-prog/paper-c-lean/blob/b3cf9aa27700d784efc61e6f82a92cef53320c40/manuscripts/paper-c/paper_c_version_3PREL9_en.pdf","relationship":"adapts"},{"title":"Technical companion to Long runs and rare patterns of a random completely multiplicative function","identifier":"https://github.com/Vulkin-prog/paper-c-lean/blob/b3cf9aa27700d784efc61e6f82a92cef53320c40/manuscripts/paper-c/paper_c_version_3PREL9_technical_companion_en.pdf","relationship":"adapts"}]}