Formulation of Sabto's Empirical Chrono-Density Equation: A Mathematical Modeling Based on Terrestrial Material Coefficients and Carbon-14 Isotopic Deviation in the Archaeological Case of Jericho (Tell es-Sultan)

ABSTRACT This manuscript introduces a novel mathematical formulation termed Sabto’s Empirical Chrono-Density Equation as an alternative framework to detect chronological dating anomalies in archaeological sites. Historically, conventional radiocarbon (C 14) laboratory testing on the destruction layer of ancient Jericho (City IV) yields an average raw dating of ~1550 BC. This result exhibits a spatiotemporal stretch or expansion of 144 years (precisely calibrated at 141.4 years) compared to the established linear historical timeline of ~1406 BC. Utilizing a purely empirical physical approach, this study integrates localized soil baseline data extracted from geological literature (the terrestrial material coefficient) with the exact percentage of isotopic carbon decay deviation measured by laboratory instruments, completely independent of manual historical text inputs. The simulation of this quadratic equation successfully demonstrates a highly stable chrono-density metric locked at a decimal value of 12.46326. This model effectively reconciles two conflicting datasets into a single, cohesive mathematical registry without altering the physical atomic structure of the site matrix. Keywords: Sabto’s Equation, Chrono-Density, Terrestrial Material Coefficient, Radiocarbon Dating, Jericho Anomaly.