High-order corrections to tauon mass in a microscopic cosmological model

According to our microscopic cosmological model, masses of charged leptons are induced by curvatures of hyper-spherical surfaces embedded in a 3D time-like subspace, leading to a solution of the lepton mass hierarchy problem and to a prediction of tauon mass for the first approximation. In the present study, for finest-tuning higher order approximations, there are some corrections added to higher curvatures by contributions from lower ones. In the result, the calculation in the third approximation $m_{\tau}(theor)=1776.40$ MeV fits the experimental tauon mass $m_{\tau}(exp)=1776.82(\pm.16)$ MeV within $0.024\%$ of precision, reaching a fairly passable consistency better than $3\sigma$. On one side, it implies that for a firm consistency, a hyper-fine adjustment of calculation by some additional mechanism is needed. On the other side, our theoretical quantity demonstrates an explicit physical interpretation, which is in opposite to another theoretical calculation with a wonderful predictability by the empirical Koide formula $m_\tau(Koide)=1776.97$ MeV, i.e. within a deviation less than $1\sigma$, unfortunately, being physically unexplained. In the circumstances, a new attempt for upgrading experimental accuracy of tauon mass is desirable.