"According to fiat" is a phrase that means something is done or established by an official authority. There are many synonyms for this phrase such as "by decree", "by official order", "as per regulation", "by edict", "by mandate", "by ukase", "by authoritative instruction", "by commandment", "as per the law" and so on. All of these phrases convey the same idea of something being established or mandated by a governing authority. They are commonly used in legal, political, and bureaucratic documents to indicate that a decision or action is being made in accordance with the established laws and regulations of the governing body. When used appropriately, these synonyms can help to convey a sense of authority and legitimacy.