Final answer:
Diodorus Siculus details in his Library that Zeus succeeded his father Cronus by asserting his dominance through the Orphic tradition, notably by punishing the Titans with his thunderbolt after they ate Dionysos, and from their ashes created mankind, signifying his role as the architect of the cosmos.
Step-by-step explanation:
The first explanation that Diodorus Siculus gives in his Library for how Zeus succeeded his father Cronus is rooted in the Orphic Theogony, which presents a version of Greek mythology that emphasizes the supremacy of Zeus as a deity. In the Orphic tradition, Zeus asserts his dominance in several significant events. After overthrowing Cronus, Zeus engaged in a sequence of powerful acts, including a defining moment where he punished the Titans for their cruelty towards his son Dionysos. The Titans had slaughtered and eaten Dionysos, and in retaliation, Zeus decimated them with his thunderbolt. From the ashes of the destroyed Titans, mankind was created, carrying a divine heritage.
This act of punishing the Titans and thereby creating humankind signifies Zeus's role as the ultimate architect and ruler of the cosmos, reaffirming his status as the head, middle, and end of all creation, as stated in the phrase 'Zeus is the head, Zeus is the middle and from Zeus everything is fashioned'. This assertion of Zeus's power is central to the Orphic portrayal of the universe's origin and order, standing in contrast to Hesiod's earlier work, which offered a different theogonical perspective.