  We present F-Rosette, a stable space-ground network structure for low-earth
orbit (LEO) satellite mega-constellations at scale. Due to the dynamic
many-to-many space-ground mapping in high mobility, existing LEO
mega-constellations with IP protocol stack suffer from frequent user IP address
changes (every 133~510s per user) and network routing re-convergence (<20%
network usability). To provably stabilize the space-ground network under high
mobility and many-to-many dynamics, F-Rosette adopts a recursive structure over
the Rosette constellation, derives a hierarchical and time-invariant network
address space from a new geographical coordinate system, and ensures efficient
and stable routing via geographical-to-topological routing embedding without
re-convergence. Our hardware-in-the-loop, trace-driven emulations validate
F-Rosette's stability, near-optimal routing (<1.4% additional delays), and
marginal overhead (<1% CPU, <2MB memory) for resource-constrained satellites.
