Which evidence is commonly used to discuss Mauryan expansion toward southern India?

Chandragupta Maurya founded the Mauryan dynasty around 322/321 BCE after overthrowing Nanda power in Magadha, with Chanakya or Kautilya traditionally credited as his strategist and adviser. This question belongs to the political, religious and diplomatic history of the Mauryan age. Mauryan history is reconstructed from several different bodies of evidence: Ashokan inscriptions, archaeological remains, the Arthashastra tradition, Buddhist and Jain narratives, Puranic genealogies, and Greek or Roman accounts. Contemporary inscriptions are especially valuable for royal titles, donations and administrative messages, whereas later religious traditions often preserve influential memories that should be identified explicitly as traditions. Bindusara and Ashoka were later Mauryan rulers, while Brihadratha was the dynasty’s last ruler; none can be called its founder.