The fiat origin, chartalist or State Theory of money argues that state authority defines money and enforces it, taxation being a key pillar of this enforcement. Therefore money was created, standardised and enforced by Kings, Pharaohs and other rulers decreeing what should be used as money.

More recent chartalists accept the evidence of previous use of commodity money but argue that standardisation was imposed by authorities.

The perfect archaeological evidence for them would be a govt decree establishing that taxes must be paid in a certain good (eg: silver), thus establishing it as money.

Of course the counterargument from mengerians would be that the State was just recognising a previously existing standard, so to make the evidence stronger it would need to show a previously existing state of barter, followed by the decree, followed by the universal use of the money imposed by that decree.

So an example of good archaeological evidence for this theory would be the same sumerian tablet as before, showing a variety of goods and measures, then a Hammurabi-style stele with the decree, then tablets showing standard prices in the money established. The abrupt change should be easier to prove with tablets from the same century.