The uniqueness conjecture for ancient Ricci flows constructed in Theorem mainthm1

Consider the ancient solutions to Ricci flow constructed in Theorem

. Two such flows have the same underlying topology and the same tangent solitons at $-\infty$. **Uniqueness conjecture.** Up to time reparametrization and diffeomorphism, the ancient solutions to Ricci flow from Theorem

are unique among smooth ancient solutions to Ricci flow having the same underlying topology and tangent solitons at $-\infty$.

The authors note that their proof already gives uniqueness within the same unit ball of the relevant function spaces; the conjecture asks for uniqueness without that restriction.