Not everyone in India accepted the Puranic proportions. Aryabhata, writing in 499 CE, needed the yugas for a different purpose: astronomy. His system reckoned planetary motions as whole numbers of revolutions completed within a mahayuga of 4,320,000 years, and for computational symmetry his Aryabhatiya divides that period into four equal quarters of 1,080,000 years each, discarding the 4:3:2:1 ratio of the lawbooks and Puranas.
On his scheme the Kali Yuga is not the short final tenth of the cycle but a full quarter of it, a difference of 648,000 years in the length of the age we are said to be living in. The choice was controversial; Brahmagupta, a century later, attacked Aryabhata for departing from received tradition on exactly this point. Yet it was the astronomers' yuga that fixed one date everyone now cites: the epoch of the Kali Yuga at 3102 BCE, established as the moment from which planetary mean positions are computed, a convention the later siddhantas carried forward and Puranic chronology absorbed. The disagreement is worth preserving rather than smoothing over. It shows the yuga functioning simultaneously as moral myth and as calculating device, and the two communities that used it bending the same number toward their different ends, the moralists keeping the decline, the astronomers keeping the arithmetic.