The Dharma-Clock: A Non-Linear Rate-Law Model of the Yuga Cycle, Calibrated to Epic Chronology and the Precession of Orion's Belt

The Puranic yuga lengths (lakhs of years) place events such as Rama’s birth before the human species existed, and no constant conversion factor can reconcile them with the epic chronology. This preprint proposes the Dharma-Clock, a non-linear rate law in which cosmic yuga time advances relative to Earth time as dτ/dt = k·D^p (p = 2.774, k = 77.57). The model fits the chronology (Rama 5114 BCE, Mahabharata war 3139 BCE, Kali from 3102 BCE), survives robustness tests against seven alternative functions and three historical chronologies, and, when tied to the precessional culmination of Orion’s Belt over Giza, places the end of Kali Yuga around 2453–2468 CE. In the mapping, Kali, the shortest yuga in cosmic time, becomes the longest in Earth time. The paper states its limitations and registers falsifiable predictions dated 6 November 2026. It is an exploratory modelling exercise by an undergraduate student, not peer-reviewed.