{"id":"openai-math/A-Nonspectrahedral-Hyperbolicity-Cone","pdf":"https://github.com/openai/math/blob/main/preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026/nonspectrahedral-hyperbolicity-cone.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Nonspectrahedral-Hyperbolicity-Cone-September-24-2026","tags":["real-algebraic-geometry","convex-geometry","hyperbolic-polynomials"],"score":0,"title":"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 a homogeneous polynomial of degree 16 in 23 real variables whose hyperbolicity cone has no representation by a finite homogeneous real symmetric linear matrix inequality. This disproves the geometric Generalized Lax conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://www.quasicoherent.blog/posts/generalized_lax/#:~:text=The%20generalized%20Lax%20conjecture%20was%20a%20central%20topic","date":"2026-10-12","kind":"web","site":"Quasicoherent","text":"The generalized Lax conjecture was a central topic of study in the field of hyperbolic polynomials. Hyperbolic polynomials in general serve as a bridge between the seemingly disparate fields of algebraic geometry and convex optimization, as each hyperbolic polynomial gives rise in a natural way to…","added":"2026-11-03","title":"A Digestion of A Counterexample to the Generalized Lax Conjecture","author":"Kevin Shu"}],"formalized":true,"family_title":"Hyperbolicity cones without semidefinite lifts"}