Mathematical Semiotic Modeling of the 45-Week Effective Education Calendar: 15,198-Hour Integral and the 25-Minute Circadian Cycle

This study develops a mathematical semiotic model of the Indonesian education calendar based on 45 effective weeks. From a total calendar of 365 days, after subtracting 104 weekend days, 10 days of first-semester break, 10 days of second-semester break, and 15 national holidays, 226 effective days are obtained, or 45.2 weeks, rounded to 45 weeks. The parabolic model f(x) = -x² + 45x + 0.25 is used to represent the dynamics of learning load. The vertex of the parabola at x = 22.5 is interpreted as 3 June, the beginning of the Even Semester Examination. The peak value f(22.5) = 506.5 hours is converted into 21.1 days, so that 3 June + 21.1 days = 24 June as the report-card distribution date. The integral from 0 to 45 of f(x) dx = 15,198 hours is interpreted as institutional hour accumulation. The division 15,198 / 12 = 1,266.5 hours/year is consistent with the Merdeka Curriculum load of 1,260-1,320 lesson hours per year. Physiological analysis with a 25-minute focus + 5-minute break ultradian cycle yields a net learning time of 3.75 hours/day, which constitutes the core of the gross 4.75 hours/day in class. Keywords: Education Calendar, 45 Effective Weeks, Mathematical Semiotics, Parabolic Model, Circadian Cycle, Merdeka Curriculum