Effective reheating in Gauss--Bonnet inflation with $\mu(\phi,X)$ coupling
We study effective reheating in a scalar--Gauss--Bonnet inflationary model with a phase-space-dependent coupling $\mu(\phi,X)$, in which a compact field-space feature is combined with a bounded kinetic gate. The modified inflationary background determines the pivot-scale quantities and the effective energy density at the end of inflation. These quantities are then used to derive the reheating duration $N_{\rm re}$ and temperature $T_{\rm re}$ through the thermal-history matching relation. We first perform two fixed-pivot reference scans by varying the overall Gauss--Bonnet strength $\lambda_{\rm GB}$ and the kinetic parameter $g_{_X}$ separately. For the reference parameter choices, increasing either parameter increases $N_{\rm re}$ and decreases $T_{\rm re}$ for the selected reheating equations of state. Additional benchmark calculations clarify how these variations depend on the dynamical regime of the model. In the $\lambda_{\rm GB}$ scan, the increase in $N_{\rm re}$ and the decrease in $T_{\rm re}$ persist, although both variations become strongly suppressed when the coupling is more localized or when the end of inflation is controlled more strongly by the E-model potential. In the $g_{_X}$ scan, stronger field-space localization and kinetic saturation can instead lead to a slight decrease in $N_{\rm re}$ and an increase in $T_{\rm re}$ as $g_{_X}$ is increased. When the bounded kinetic contribution is considered together with a weaker overall Gauss--Bonnet interaction, the resulting changes in the reheating quantities become nearly negligible. The fixed-pivot predictions of the representative and alternative benchmarks are compared with CMB constraints.These reheating constraints are then discussed for four representative values of the effective equation-of-state parameter, $\overline{w}_{\rm re}=-1/3,0,2/3,$ and $1$.