Hyperbolicity cones without semidefinite lifts
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The generalized Lax conjecture predicts that every hyperbolicity cone is spectrahedral. The formalized counterexample is an explicit homogeneous polynomial of degree $20$ in $23$ real variables. It is hyperbolic, but its closed hyperbolicity cone cannot be represented as the positive-semidefinite region of any finite real symmetric linear matrix pencil, in any positive matrix size.
Comparator links
| Result | Comparator statement |
|---|---|
| Nonspectrahedral hyperbolicity cone | HyperbolicCones.lean |