For the block-preserving Hamiltonian
$H=P_{47}HP_{47}+(I-P_{47})H(I-P_{47}),$
$[H,P_{47}]=0$ and
$U(t)=e^{-itH}$
satisfies
$U(t)P_{47}=P_{47}U(t).$
Thus $E_{47}$ and $E_{47}^{\perp}$ are invariant, norm is conserved, and $\langle P_{47}\rangle$ is constant.
Machine results: commutator residual $3.32\times10^{-15}$; maximum unitarity residual $6.59\times10^{-15}$; norm and occupancy drift $2.22\times10^{-16}$.
Boundary: finite-dimensional declared Hamiltonian only.