The conjecture that every subspace hereditary property is testable

An affine-invariant property $\mathcal P$ is subspace hereditary if, whenever $f:\mathbb{F}^n\to [R]$ satisfies $\mathcal P$, the restriction of $f$ to every affine subspace of $\mathbb{F}^n$ also satisfies $\mathcal P$. Subspace-hereditary testability conjecture. Every subspace hereditary property is testable. This conjecture proposes a converse, up to the technical framework discussed in the source, to the necessity of subspace hereditariness for testability of affine-invariant properties; its resolution is not specified in the source.