{"id":"openai-math/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone","pdf":"https://github.com/openai/math/blob/main/preprints/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026/Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-Exact-Semidefinite-Lift-of-a-Nonspectrahedral-Hyperbolicity-Cone-October-5-2026","tags":["convex-geometry","semidefinite-programming"],"score":0,"title":"An Exact Semidefinite Lift of a Nonspectrahedral Hyperbolicity Cone","domain":"Convex and metric geometry","family":"095","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"We construct an exact semidefinite lift of the explicit nonspectrahedral hyperbolicity cone in twenty-three variables defined in the companion paper. The lift is a homogeneous real symmetric pencil of size 100 with 307 auxiliary variables and represents the entire closed cone, including every point with singular X . Thus, although this cone has no semidefinite representation in its original coordinates, it admits one when auxiliary variables are allowed. The stated sizes are not claimed to be minimal.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Hyperbolicity cones without semidefinite lifts"}