Determine whether the Lovász number is the least entanglement-assisted spectral point

Prove or disprove that the Lovász number is the minimum element of the entanglement-assisted asymptotic spectrum of graphs, equivalently determine whether the entanglement-assisted Shannon capacity equals the Lovász number on every graph.

Background

The paper constructs a continuum of spectral points based on Rényi information radii, but every constructed point dominates the Lovász number. Consequently, the construction does not resolve the conjecture that the Lovász number equals the entanglement-assisted Shannon capacity, which is the pointwise minimum of the entanglement-assisted spectrum.

The authors note that either proving the Lovász number is the minimum spectral point or finding a spectral point below it on some graph would settle the issue.