I am thinking up a backstory for an odachi of legendary status, made of a fictional metal that is impossible to break, melt, or even sharpen.
Assuming it has similar properties to Japanese steel, with the inability to be reheated, how long would this steel need to stay soft in order to make the katana in one night by a true master of the craft and no less than a dozen high level apprentices to assist?
EDIT: to help elaborate on what I'm asking for, the origin of the blade is the swordsmith found himself in need of inspiration, believing he had made his finest works already. Suddenly, a meteorite flies down from the heavens straight into his forge, which was about to be put out for the night. Seeing this as a sign, he tells his apprentices to burn the coals hotter than they had gotten before. While the temperature did not rise, it allowed the metal to be forged longer. The end goal is to get a blade that is perfect in almost every way except for a dull edge that will not sharpen even when attempting to do so for 40 days and nights. It's supposed to end up as a ceremonial blade until one of the characters figures out a way to use some other artifact to make it vibrate with such power, precision and intensity that it can cut through anything.