Chai's formal-torus conjecture for ordinary points on mod $p$ Shimura varieties

Let $X$ be a subvariety in a mod $p$ Shimura variety passing through an ordinary point $P$. Assume that the formal germ of $X$ at $P$ is a formal torus in the Serre--Tate coordinates.

Chai's conjecture. Then $X$ is a Shimura subvariety.

This is a bi-algebraicity conjecture in the ordinary locus of mod $p$ Shimura varieties. It is presented as an interesting question related to whether formal curves with large-rank special endomorphism modules can be algebraic without being special; its resolution status is not specified here.