Nonexistence conjecture for simply-connected strongly inflexible manifolds

A simply-connected manifold is a manifold with trivial fundamental group. A manifold is strongly inflexible if it admits no self-map of nonzero degree other than those constrained by its fixed rational homotopy type.

Nonexistence conjecture. Simply-connected strongly inflexible manifolds do not exist.

If true, this would imply that all finite functorial seminorms vanish on simply-connected manifolds. The source presents this as an open conjecture following results showing that many known examples of simply-connected inflexible manifolds are not strongly inflexible.