{"id":"hexagon/2610.00367","pdf":"https://hexagonmath.org/pdf/2610.00367v1","url":"https://hexagonmath.org/abs/2610.00367v1","tags":["msc:15A18","msc:34D20","msc:14P10","D-stability","Fritz-John conditions","Lean formalization","critical-point method","diagonal scaling","time-scale robustness"],"score":0,"title":"A critical-point criterion for D-stability in every dimension","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"A real square matrix A is D-stable if DA is Hurwitz for every positive diagonal matrix D. Applying the critical-point method to Johnson’s contact variety establishes that, in every dimension and for every positive choice of barrier weights, D-stability is equivalent to Hurwitz stability and absence of positive solutions of an explicit principal-minor Fritz–John system. In dimension five the system separates into Lagrange and tangency branches; both equivalences are registered in Lean. Further results treat regular-contact persistence, the boundary of the D-stable set, stability under bounded…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-30-000020&version=1"],"human_understanding":"some"}