{"id":"palomar/PALOMAR-2026-09-30-000020","url":"https://github.com/mmislan/palomar-p087-d-stability-critical-points/tree/e0e376f5df0a639c619259a1e4a0a09648d25f93","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000020-v1.json","repo":"https://github.com/mmislan/palomar-p087-d-stability-critical-points","tags":["math.DS","msc:15A18","msc:34D20","msc:14P10","dynamical-systems","matrix-stability","critical-points"],"score":0,"title":"A critical-point criterion for D-stability in every dimension","trust":"high","domain":"math.DS","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"Johnson's contact criterion for D-stability is expressed as an explicit principal-minor critical-point system. For every real square matrix and every choice of positive barrier weights, D-stability is equivalent to Hurwitz stability and the absence of positive solutions of the associated Fritz-John equations. The proof applies a proper exhaustion of the positive orthant to Johnson's contact variety, so that every nonempty contact set contains a critical point. In dimension five, the criterion is written explicitly as a Lagrange system and a tangency system, with coefficients given by…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true,"formalizes":[{"title":"A critical-point criterion for D-stability in every dimension","identifier":"","relationship":"formalizes"}]}