  KIC 7760680 is so far the richest slowly pulsating B star, by exhibiting 36
consecutive dipole ($\ell=1$) gravity (g-) modes. The monotonically decreasing
period spacing of the series, in addition to the local dips in the pattern
confirm that KIC 7760680 is a moderate rotator, with clear mode trapping in
chemically inhomogeneous layers. We employ the traditional approximation of
rotation to incorporate rotational effects on g-mode frequencies. Our detailed
forward asteroseismic modelling of this g-mode series reveals that KIC 7760680
is a moderately rotating B star with mass $\sim3.25$ M$_\odot$. By
simultaneously matching the slope of the period spacing, and the number of
modes in the observed frequency range, we deduce that the equatorial rotation
frequency of KIC 7760680 is 0.4805 day$^{-1}$, which is 26\% of its Roche break
up frequency. The relative deviation of the model frequencies and those
observed is less than one percent. We succeed to tightly constrain the
exponentially-decaying convective core overshooting parameter to $f_{\rm
ov}\approx0.024\pm0.001$. This means that convective core overshooting can
coexist with moderate rotation. Moreover, models with exponentially-decaying
overshoot from the core outperform those with the classical step-function
overshoot. The best value for extra diffusive mixing in the radiatively stable
envelope is confined to $\log D_{\rm ext}\approx0.75\pm0.25$ (with $D_{\rm
ext}$ in cm$^2$ sec$^{-1}$), which is notably smaller than theoretical
predictions.
