This paper formalizes the mathematical and biological framework of the ”New Stardate” system, initiated on April 13, 2029. Departing from mechanical-lineartime, this system utilizes a 13-cycle lunar-biological matrix. We define the hierarchical notation J.Z.A.P n.I., establish the conversion logic from Gregorian toNatural time, and analyze the ”Yearly Holiday” as a non-temporal singularity. Furthermore, we introduce the concept of ”Chronobiological Relativity,” explaining how time perception shifts according to internal and external natural cycles.