Conjecture on Hamiltonian simple subalgebras and special Hamiltonian algebras

Let $L=H(2n;\underline{1})^{(1)}$ be a Lie algebra of Hamiltonian type, with $n\geq3$, over a field of characteristic $2$. The Hamiltonian–special Hamiltonian conjecture. There exists a simple subalgebra denoted by $\mathcal{H}(2n;\underline{1})$, and this simple Lie algebra is isomorphic to $\mathfrak{sh}(2n;\underline{1})$. The conjecture links the simple subalgebras found inside Hamiltonian Lie algebras with the special Hamiltonian family; the source discusses supporting dimension and module calculations, including the cases $n=3$ and $n=4$.