{"id":"palomar/PALOMAR-2026-09-20-000003","url":"https://github.com/Vulkin-prog/paper-c-lean/tree/edd850b26641f18897376a029a0d4f16577205b7","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-20-000003-v1.json","repo":"https://github.com/Vulkin-prog/paper-c-lean","tags":["math.NT","math.PR","msc:11K65","msc:60F05","probability","number-theory","poisson-limits"],"score":0,"title":"Critical Poisson fields and information-adapted conditioning","trust":"high","domain":"math.NT","source":"palomar","authors":["Brice Pouly"],"reviews":0,"subject":"math.NT","summary":"Poisson laws for the actual run field with positions, all excesses and signs; hard and soft small-prime conditioning, deterministic masks and statistics, stable recorded variables, uniform quenched convergence, and an information-adapted cutoff that respects a prescribed conditioning floor.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-20","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"}]}