Stable Forking Conjecture

The Stable Forking Conjecture states that if $T$ is a simple theory then forking is always witnessed by stable formulas. In particular, if $\operatorname{tp}(a/Cb)$ forks over $C$ then there is a stable formula $\varphi(x, y)$ such that $\varphi(x, b) \in \operatorname{tp}(a/Cb)$ and $\varphi(x, b)$ forks over $C$.