Your challenge, with a POD after 500 BC, is for a China-esque "eternal empire" (where dynasties might rise and fall, but the concept of said empire being a permanent entity is part of the mindset of the people) to arise in the Indian subcontinent. Bonus points if the south of India is considered a central part of said China-esque Indian Empire as opposed to a series of tributary kingdoms which a competent emperor might conquer.