Uniqeneness of The Time-Dependent Controller’s Designed Parameter (TDCDP) of Fokker Planck Kolmogorov(FPK) Probability Density Function(PDF) with Applications of Lambert W Function to Number Theory, Quantum Computing and Bitcoin Protocols

Abstract

This work is the first in the literature to tackle the difficult open problem of proving the uniqueness of the TDCDP (time-dependent controller parameter) of the (Fokker Planck Kolmogorov) probability density function. Additionally, the temporal impact on TDCDP is also revealed for two states, namely corresponding to $n=1,2$. After that, some potential applications of Lambert W function in the context of number theory, quantum computing, and Bitcoin protocols are emphasized. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.