Manifold-dimension conjecture for real minimal qubit permutation-invariant codes

Fix an error weight $t$, set $n=n_{\rm \min}(t)$, and consider the family of real minimal qubit permutation-invariant quantum error-correcting codes with parameters $(n,t)$. Real minimal PI-code manifold conjecture. This family is a manifold of dimension $t+1$. The conjecture is motivated by numerical scans for small error weights, where the solution set appears to have $t+1$ continuous degrees of freedom.