  We report the discovery of the minor planet 2013 SY$_{99}$, on an
exceptionally distant, highly eccentric orbit. With a perihelion of 50.0 au,
2013 SY$_{99}$'s orbit has a semi-major axis of $730 \pm 40$ au, the largest
known for a high-perihelion trans-Neptunian object (TNO), well beyond those of
(90377) Sedna and 2012 VP$_{113}$. Yet, with an aphelion of $1420 \pm 90$ au,
2013 SY$_{99}$'s orbit is interior to the region influenced by Galactic tides.
Such TNOs are not thought to be produced in the current known planetary
architecture of the Solar System, and they have informed the recent debate on
the existence of a distant giant planet. Photometry from the
Canada-France-Hawaii Telescope, Gemini North and Subaru indicate 2013 SY$_{99}$
is $\sim 250$ km in diameter and moderately red in colour, similar to other
dynamically excited TNOs. Our dynamical simulations show that Neptune's weak
influence during 2013 SY$_{99}$'s perihelia encounters drives diffusion in its
semi-major axis of hundreds of astronomical units over 4 Gyr. The overall
symmetry of random walks in semi-major axis allow diffusion to populate 2013
SY$_{99}$'s orbital parameter space from the 1000-2000 au inner fringe of the
Oort cloud. Diffusion affects other known TNOs on orbits with perihelia of 45
to 49 au and semi-major axes beyond 250 au, providing a formation mechanism
that implies an extended population, gently cycling into and returning from the
inner fringe of the Oort cloud.
