How were the Egyptian gods Horus, Re, Atum, Ptah, and Osiris connected to the pharaoh?

In ancient Egyptian religion, the pharaoh served as the essential mediator between the gods and humanity, maintaining the cosmic order known as maat. The relationship between the king and the deities was central to his divine status and authority:12

• Horus: The reigning king was considered a living manifestation of Horus. This identification was so fundamental that the "Horus name" was the most important of the pharaoh’s five royal titles, often displayed on monuments within a serekh.31
• Re: Kings were titled "Son of Re," a name given at birth that emphasized their solar connection. As the sun god, Re represented the source of justice and order, and the pharaoh shared with him the responsibility of defending the world against chaos.415
• Atum: As a creator god who engendered other deities, Atum (often associated with the solar cycle) was part of the divine lineage from which the pharaoh derived his authority as a ruler of the cosmos.4
• Ptah: As the creator god of Memphis, Ptah was closely linked to the monarchy through royal coronation ceremonies and festivals, such as the Heb-Sed, which were traditionally held in his city.6
• Osiris: Upon death, the pharaoh was identified with Osiris, the god of the dead and the underworld. This transition allowed the deceased king to pass his sacred powers and position to his son, the new living Horus.17