The Day-Date complication is a mechanical system that tracks both the day of the week and the date of the month using a set of gears and jumpers. The Hour Gear (Z1) drives an intermediate gear (Z2), which engages the Day and Date Stars. The Day Star (7 teeth) advances once per day, aligning with the weekly cycle, while the Date Star (31 teeth) progresses daily to display the correct date. Fingers push the stars forward, while jumpers secure them in place, ensuring accurate and precise movement. This elegant mechanism is commonly found in mechanical wristwatches, providing a reliable and intuitive way to track time.