A3H++ Theorem: Direct, Additive, and Constant Time Complexity Day-Index Algorithm

Abstract

This paper presents the full mathematical formalism of the A3H++ Theorem, a highly optimizedmethod for Gregorian calendar day-indexing operating in constant O(1) computational complexity.Breaking away from historic frameworks such as Zeller's congruence, the A3H++ Theorem completelyeliminates the need for artificial monthly shifts (which historically forced March to be the origin of theyear) and removes local conditional logical code forks. By relying on a top-down analytical matrixevaluation of the month-end anchors, the algorithm unifies chronological progression into a pureadditive structure. This model is separated into two hermetic components: a long-term block forcompleted years and a short-term block for the current year. Structural calendar anomalies, includingthe linear irregularity of February, are natively absorbed