A New Astronomical Baseline for Chaturyuga: A Non-Linear Keplerian Model and Relativistic Time-Dilation Framework for Siddhāntic Precession

Abstract This paper presents a rigorous mathematical and relativistic calibration of the ancient Indian Chaturyuga cycle by fitting a non-linear Keplerian model to the precession of the equinoxes. By replacing the standard, linear assumption of uniform axial precession with a dynamic, eccentric binary solar orbit (e = 0.0364877), this framework maps the cosmic ages onto an empirically verifiable timeline. The long-standing chronological paradox of the non-linear 4:3:2:1 temporal ratio between the sub-yugas (Krita, Treta, Dvapara, and Kali) is resolved by introducing a general relativistic Schwarzschild time-dilation factor that acts on the planetary system as the Sun sweeps through varying field densities relative to a barycenter. Text-critical deconstruction of the Sūrya Siddhānta (Chapters 1 and 3) and the Āryabhaṭīya (Gītīkāpāda and Kālakriyāpāda), alongside the retrieval of the early ṣadbhiḥ manuscript variant, exposes a highly advanced, dual-metric computing architecture. While the macro-astronomical 4,320,000-year Mahāyuga functions as an integer-scaling matrix optimized for geocentric whole-number mean-motion calculations, the physical core of the Chaturyuga is isolated as a continuous precessional cycle spanning exactly 24,070 tropical solar years. Using a high-precision Newton-Raphson optimization engine, the system anchors its operational orbital metrics to exact physical coordinates: the Kali Yuga Epoch is established at the un-dilated orbital apoapsis (0° phase anomaly) on March 21, 232 CE, matching an empirically verified planetary alignment within 17° of the tropical vernal equinox vector and a horizontal alignment of the lunar line of apsides. Conversely, the Krita Yuga benchmarks are anchored to the high-velocity periapsis (180° phase anomaly) in 11804 BCE and 12267 CE, forcing a comprehensive planetary mean-longitude realignment at the initial point of tropical Aries (Meṣādau). This pulls the historical baseline forward from the flawed 3102 BCE orthodox timeline by over three millennia, demonstrating a perfect synchronization between solar binary mechanics, macrocyclic planetary conjunctions, late antiquity paleoclimate inflections, and human socio-cultural evolution.