{"id":"palomar/PALOMAR-2026-09-30-000008","url":"https://github.com/mmislan/palomar-p038-futile-cycle-child-selections/tree/87366c2f6997480f4127b634c813e8daf8199abf","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000008-v1.json","repo":"https://github.com/mmislan/palomar-p038-futile-cycle-child-selections","tags":["math.DS","q-bio.MN","msc:92C42","msc:15A15","msc:15A18","msc:34D20","dynamical-systems","chemical-reaction-networks","phosphorylation","linear-algebra"],"score":0,"title":"Determinants and unstable cores in sequential distributive phosphorylation","trust":"high","domain":"math.DS","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"Vassena and Stadler (arXiv:2308.11486v3, Supplementary Example D) conjectured that sequential distributive phosphorylation cycles have only unstable-positive cores and that every invertible child-selection matrix has determinant of absolute value one. The determinant assertion is proved, and the restriction to unstable-positive cores is disproved. In the n-site cycle, every child-selection matrix has determinant 0, 1 or -1. For every n >= 3, a six-species child-selection matrix is minimally Hurwitz-unstable and has determinant 1, giving an unstable-negative core. For every n >= 2, there is…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true,"formalizes":[{"title":"Child-selection determinants and unstable cores in sequential distributive futile cycles","identifier":"","relationship":"formalizes"}]}