a smoking-gun experiment for the $EPI-FSP$ pairing mechanism in $1ML$ $FeSe/SrTiO_{3}$ (and $1ML$ $FeSe/TiO_{2}$). From $Eq.$(\[Delta-n-FSP\]) in the Appendix it is straightforward to obtain the *energy gap* $\Delta_{0}=2T_{c0}$. Note, that $1ML$ $FeSe/SrTiO_{3}$ (and $1ML$ $FeSe/TiO_{2}$) is a $2D$ system and $T_{c0}\sim q_{c}{}^{2}$, while in the $d$-dimensional space one has $T_{c0}\sim q_{c}{}^{d}$. This means that the $EPI-FSP$ mechanism of superconductivity is more *favorable in low-dimensional systems* ($d=1,2$) than in the $3D$ one. Since high $T_{c}$ cuprates are also quasi-$2D$ systems, where strong correlations make a long-ranged $EPI$, it means that the $EPI-FSP$ mechanism of pairing may be also operative in cuprates [@Kulic-PhysRep]. Note, that in estimating some semi-microscopic parameters we shall use as a reper-value $T_{c0}\approx100$ $K$, while in real systems $T_{c}\sim(60-80)$ $K<T_{c0}$ is realized. However, $T_{c0}$ is the mean-field value obtained in the Migdal-Eliashberg theory, while in $2D$ systems it is significantly reduced by the phase fluctuations - to the Berezinski-Kosterliz-Thouless value. There is an additional reduction of $T_{c0}$ (which might be also appreciable) in the $EPI-FSP$ systems, which is due to internal pair-fluctuations - see discussion below.

One can estimate the coupling constant $\lambda_{m}=\left\langle
V_{epi}(\mathbf{q})\right\rangle _{q}/2\Omega$ in $1ML$ $FeSe/SrTiO_{3}$ from the value of $T_{c0}$. Then for the reper-value $T_{c0}\sim100$ 