Vortexable Chern Bands Sit Exactly on the Topological Floor of Flat-Band Superfluid Stiffness

Vortexable Chern bands host ideal fractional Chern insulators. Paired with time-reversed partners by orbital-diagonal on-site attraction, they are the least stiff flat-band superconductors at fixed Chern number $C$, filling, and pairing amplitude. For uniform pairing and a nondegenerate paired state, the exact $T=0$ stiffness determinant is the topological floor times $1+(\text{Torb}\mathrm{/}2\pi \mathrm{\mid }C\mathrm{\mid }{)}^2\le 1+(\text{TLVP}\mathrm{/}2\pi \mathrm{\mid }C\mathrm{\mid }{)}^2$, where $\text{Torb}$ and $\text{TLVP}$ measure departures from vortexability. Enhancement costs vortexability, and the inequality is strict only if internal components share a site, as in heterostrained bilayers.