Classification under strictly positive curvature

Prove that every bounded self-adjoint tuple with Lipschitz conjugate variables satisfying CD(c,∞) for c>0 generates a von Neumann algebra isomorphic to L(F₂), without assuming saturation of the free Poincaré inequality.

Background

After proposing the equality-case classification, the paper states a stronger conjecture: strict positivity of free curvature alone should determine the isomorphism class. The established results provide embeddings into L(F₂), strong solidity, approximation properties, and related structural consequences, but do not prove that the generated algebra is itself L(F₂).

References

More generally, we conjecture that strict positivity of the curvature alone should determine completely the isomorphism class, without any saturation assumption.

— Convexity, the spectrum of free Laplacians and geometric consequences: a free KLS bound  (2610.22109 - Diez, 15 Oct 2026) in Conjecture labeled \ref{conj:positive-curvature-isomorphism}, Section 3, subsection “The curvature criterion and a strengthened free Obata theorem”