I didn’t think that there were any blank squares: ‘Some clues contain extra material that should assist with filling the grid’. It can be no surprise to anyone following the thread that the first fill gives a certain numerical artefact. The extra letters ‘give information’ that enable the first fill to yield a second numerical artefact.
My problems: (1) ‘The information gained … must literally be used to adjust the initial grid to one that appears totally satisfying’. Well, I’m quite satisfied with my second fill, but ‘totally satisfying’ (rather than merely ‘satisfying’) implies to me that there is a special interpretation to be made (‘totals’ does have a special significance in relation to the artefacts, of course); (2) The title: the square root of 576 is 24, which is the difference between the two values of a characteristic of the artefacts. However, I’m not using that in my adjusted grid; (3) I don’t see why replacing numbers with letters to give real words in the grid is more satisfying than having numbers, but so many commentators think it is that my aesthetic sensibilities must be letting me down. Presumably some simple code is used, A=1, B=2, etc., although that particular code gives me nonsense in some parts.