  Debris discs are our best means to probe the outer regions of planetary
systems. Many studies assume that planets lie at the inner edges of debris
discs, akin to Neptune and the Kuiper Belt, and use the disc morphologies to
constrain those otherwise-undetectable planets. However, this produces a
degeneracy in planet mass and semimajor axis. We investigate the effect of a
sculpting planet on the radial surface-density profile at the disc inner edge,
and show that this degeneracy can be broken by considering the steepness of the
edge profile. Like previous studies, we show that a planet on a circular orbit
ejects unstable debris and excites surviving material through mean-motion
resonances. For a non-migrating, circular-orbit planet, in the case where
collisions are negligible, the steepness of the disc inner edge depends on the
planet-to-star mass ratio and the initial-disc excitation level. We provide a
simple analytic model to infer planet properties from the steepness of
ALMA-resolved disc edges. We also perform a collisional analysis, showing that
a purely planet-sculpted disc would be distinguishable from a purely
collisional disc and that, whilst collisions flatten planet-sculpted edges,
they are unlikely to fully erase a planet's signature. Finally, we apply our
results to ALMA-resolved debris discs and show that, whilst many inner edges
are too steep to be explained by collisions alone, they are too flat to arise
through completed sculpting by non-migrating, circular-orbit planets. We
discuss implications of this for the architectures, histories and dynamics in
the outer regions of planetary systems.
