This article complements the article on FinanceLLMsBackRL [1]. In this supplement, we focus on the specific aspect of the singularity (Figure 7) of the 3D Navier-Stokes equations as applied to the Finan-ceLLMsBackRL method. We seek to understand how the singularity approach to the 3D Navier-Stokes equations governs the overall configuration of the methods developed in the FinanceLLMsBackRL article [1].