Let $n \geq 20$ and $\kappa \in \mathbb{N}$ with $3\kappa \leq n + 2$. Every polynomial computed by a matrix-symmetric formula of orbit size $< \binom{n}{\kappa}$ is computed by a reduced matrix-symmetric circuit of support size $\leq \kappa - 1$ and support depth $\leq 2\kappa$.

The circuit is the rigidification of the formula, whose support size is bounded by the support theorem. In a formula, every internal gate has a unique chain of ancestors. A path in the rigidification with many support-changing wires can be moved by stabilisers so that each such wire adds a new point to the union of the supports along the path. Lifting the path to the formula, the gates at its end lie in a gate orbit at least as large as the orbit of this union, which bounds the number of support-changing wires.