empire_creation_hof_requirements_trigger

empire_creation_hof_requirements_trigger = {
	trigger_if = {
		limit = {
			empire_faith_gate_enabled_trigger = yes
			government_subject_to_faith_empire_trigger = yes
			faith_allows_empire_trigger = yes
		}
		# Spiritual head path
		trigger_if = {
			limit = {
				faith = { has_doctrine = doctrine_spiritual_head }
				exists = faith.religious_head
			}
			custom_tooltip = {
				text = empire_faith_gate_hof_spiritual_good_terms
				faith.religious_head = {
					opinion = {
						target = root
						value > 0
					}
				}
			}
			custom_tooltip = {
				text = empire_faith_gate_powerful_vassals_approve
				any_powerful_vassal = {
					percent >= 0.5
					opinion = {
						target = root
						value > 0
					}
				}
			}
		}
		# Temporal head path
		trigger_else_if = {
			limit = {
				faith = { has_doctrine = doctrine_temporal_head }
				exists = faith.religious_head
			}
			OR = {
				custom_tooltip = {
					text = empire_faith_gate_hof_temporal_is_hof
					this = faith.religious_head
				}
				custom_tooltip = {
					text = empire_faith_gate_hof_temporal_good_terms
					faith.religious_head = {
						opinion = {
							target = root
							value > 0
						}
					}
				}
			}
			custom_tooltip = {
				text = empire_faith_gate_powerful_vassals_approve
				any_powerful_vassal = {
					percent >= 0.5
					opinion = {
						target = root
						value > 0
					}
				}
			}
		}
		# Path for faiths with no head, where the exempt rule setting lets them skip approval entirely
		trigger_else = {
			trigger_if = {
				limit = { has_game_rule = empire_faith_gate_on }
				custom_tooltip = {
					text = empire_faith_gate_powerful_vassals_approve
					any_powerful_vassal = {
						percent >= 0.5
						opinion = {
							target = root
							value > 0
						}
					}
				}
			}
		}
	}
}

As written in game/common/scripted_triggers/00_empire_faith_gate_triggers.txt.