The description accurately matches the Ajivika philosophy. It was indeed founded by Makkhali Gosala in the 5th century BC, existing as a contemporary and rival of early Buddhism and Jainism (heterodox schools challenging Vedic authority). Historical sources, including Buddhist and Jain texts, mention Makkhali Gosala and the Ajivikas. The mention of its popularity during the reign of Bindusara (father of Ashoka) is also historically supported. Evidence suggests its presence and influence in South India for a considerable period. Ajivika philosophy was characterized by a strict doctrine of determinism (Niyati), where destiny was considered absolute.