  We report the discovery of HD 110113 b (TOI-755.01), a transiting
mini-Neptune exoplanet on a 2.5-day orbit around the solar-analogue HD 110113
(Teff = 5730K). Using TESS photometry and HARPS radial velocities gathered by
the NCORES program, we find HD 110113 b has a radius of $2.05\pm0.12$
$R_\oplus$ and a mass of $4.55\pm0.62$ $M_\oplus$. The resulting density of
$2.90^{+0.75}_{-0.59}$ g cm^{-3} is significantly lower than would be expected
from a pure-rock world; therefore, HD 110113 b must be a mini-Neptune with a
significant volatile atmosphere. The high incident flux places it within the
so-called radius valley; however, HD 110113 b was able to hold onto a
substantial (0.1-1\%) H-He atmosphere over its $\sim4$ Gyr lifetime. Through a
novel simultaneous gaussian process fit to multiple activity indicators, we
were also able to fit for the strong stellar rotation signal with period
$20.8\pm1.2$ d from the RVs and confirm an additional non-transiting planet
with a mass of $10.5\pm1.2$ $M_\oplus$ and a period of
$6.744^{+0.008}_{-0.009}$ d.
