FQSW direct achievability via the source route

For every finite-dimensional pure tripartite source $\psi_{ABR}$, the fully quantum Slepian-Wolf communication rate $\frac{1}{2} I(A;R)_\psi$ is directly achievable: for every slack $\delta>0$ and error tolerance $\varepsilon>0$, all sufficiently large i.i.d. blocklengths admit FQSW operational surfaces with communication rate at most $\frac{1}{2} I(A;R)_\psi+\delta$, entanglement yield at least $\frac{1}{2} I(A;B)_\psi-\delta$, and normalized trace-distance error at most $\varepsilon$.