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This work presents a formal mathematical and arithmetic framework for the construction of the ancient 260-day Mesoamerican ritual calendar. We demonstrate that the fundamental calendar relation (365×52=260×73) is a direct representation of Kepler's third law of orbital motion in synodic coordinates. Using a generalized definition of a short calendar count derived from symmetrical archaeoastronomical alignments about a solstice, we evaluate approximate solar year counts. Our model shows that an approximate 364-day year uniquely gives rise to the 260-day calendar (introducing the fundamental number 13) and a 360-day calendar (introducing the fundamental number 18), which naturally produces the 5 special nemontemi days. The resulting Type-A and Type-B alignments explain the historical use of specific "monad" fractions in the layout of major ceremonial centers like Teotihuacan and Tenochtitlan.