{"id":"hexagon/2611.00117","pdf":"https://hexagonmath.org/pdf/2611.00117v1","url":"https://hexagonmath.org/abs/2611.00117v1","tags":["math.AG","math.FA","math.CO","msc:15A15","msc:52A41","msc:90C22","msc:15B48","msc:05E05","Completely positive maps","Johnson's conjectures"],"score":0,"title":"The generalized Lax conjecture holds for mixed determinants","domain":"math.OC","origin":"ai-generated","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.OC","summary":"We prove that the mixed determinant $\\eta(\\cdot)$ of Borcea and Brändén has a spectrahedral hyperbolicity cone. More precisely, for Hermitian matrices $A_1,\\ldots,A_m$ of order $d$, the hyperbolicity cone of $\\eta(A_1,\\ldots,A_m)$ is cut out by $\\sum_j\\Phi_j(A_j)\\succeq0$, where $\\Phi_1,\\ldots,\\Phi_m$ are explicit unital completely positive maps. We argue by induction on $d$, adding one row and one column to every argument and expressing the logarithmic derivatives of $\\eta$ as extremal eigenvalues. By compressing along polynomial boundary kernels, we reduce the order of the pencil…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT Astra (Pro)","GPT-5 Pro and GPT-5.6 Pro","Codex","Claude Opus 5, Opus 5.5 and Fable 5.1"],"discussed":0,"published":"2026-11-05","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}