'Established' in the Bible

Therefore, because of the account found in this letter and what they had faced in this regard and what had happened to them, the Jews established as binding on themselves, their descendants, and all who joined their company that they should observe these two days without fail, just as written and at the appropriate time on an annual basis.

to establish these days of Purim in their proper times, just as Mordecai the Jew and Queen Esther had established, and just as they had established both for themselves and their descendants, matters pertaining to fasting and lamentation.

Esther's command established these matters of Purim, and the matter was officially recorded.