The Rest-Day Subtraction Model: Reconciling Toraitic Cultic Cycles with Astronomical Timekeeping

Scholarly inquiries into ancient Israelite timekeeping have historically operated under a binary framework, contrasting the lunisolar rabbinic calendar with the solar 364-day scheme preserved in the Qumran corpus and the Astronomical Book of Enoch. Both paradigms encounter friction when evaluated against the astronomical solar year (365.2422 days). This paper introduces a novel structural hypothesis: the Rest-Day Subtraction Model (RDSM). Rather than viewing sacred rest days (Shabbatot and Mikra’ei Kodesh) as ordinal markers that advance secular calendar time, we demonstrate that evaluating the operational workweek (312 base workdays) alongside probability-weighted festival collisions yields an average annual labor output of ~ 297.25-297.80 active workdays. Over a 50-year Jubilee cycle (Yovel), this active labor tally (14,888 days) converges with the astronomical requirement when intercalary rest cycles are integrated. This model provides a mathematical bridge between cultic observance and solar mechanics without disrupting the unbroken septenary week.