The Puranic Yuga Cycle as Precession Arithmetic

The Puranic yuga cycle encodes time divisions based on the unit 432,000 years. This unit and its multiples — Dvapara (864,000), Treta (1,296,000), Satya (1,728,000), Mahayuga (4,320,000) — have been widely dismissed by contemporary scholars as mythological inflation of smaller observed cycles. This note demonstrates that 432,000 is derivable from first principles of orbital mechanics without any fitting, mythology, or numerological selection. The derivation proceeds as follows: (1) the precession period of the equinoxes T₃ = 25,920 years is computed from the three-helix framework established in JCE Architecture Series Notes 1–4; (2) T₃ divided by 60 (the sexagesimal base governing ancient Indian and Babylonian astronomy) yields exactly 432; (3) Kali Yuga = 432 × 1,000; all four yugas follow as integer multiples of this unit scaled by 1,000, 2,000, 3,000, and 4,000. Additionally, T₃ / 27 = 960 exactly — the precession traversal time per nakshatra — giving the construction: 27 nakshatras × 960 years = 25,920 years = T₃. The intermediate result T₃ / 240 = 108 connects to a third sacred invariant present across Vedic, Jain, and Buddhist traditions. None of these results require fitting to the Puranic numbers. They are consequences of precessional astronomy expressed in the sexagesimal counting system that the ancient observers demonstrably used.