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Emcee, I'm not sure that is any special significance about TIME in the title. If there is, it escapes me. I wouldn't worry about it.

Phil535, I think there are eight possible triplets, not four, though there are only four that will work for the puzzle. Two of the unused set use 25 as the two-digit square and two use 81.

Orson, re the letters used, my guess is that the setter wanted to span A-Z. GHI might not be suitable because of possible confusion of I with 1, and MNO because of possible confusion of O with 0.
As for difficulty, all that is needed to get started is list of squares. It doesn't take that long to scan and select the twenty-one suitable 4-digit squares to add to the six 2-digit squares and the thirteen 3-digit ones. If 16, for example, is selected as a provisional 2-digit square, there are only two possible 4-digit square to go with it because all the others have a 1 or 6 in them.

escuan / orson

I found a good entry point here was the NW corner of the puzzle, where J, K and L sit conveniently next to each other, with two complete crossing entries which helped get that first triple solved quickly. After that, it just seemed to flow naturally.

As Murky says, there are far fewer possibilities for these particular triple groups than you might at first imagine... Good luck.

As for the title...it seems to me that the highlighted rows and columns had the appearance of another sort of square, as used by an engineer perhaps? And I keep reading the title as SQUARE TIMES UMS ... maybe someone else can push this along?

schorley,

I wondered the same type of thing regarding the title: maybe some form of cryptic subsidiary indication e.g. Square Time Sums = S + T + ADDS.

I'm not aware of any special name for these special numbers that the title could allude to.

"Time" must have some significance otherwise why put it in?

I am in the process of writing a blog for LWO that will address some of the comments and queries that have cropped up here and on another site. As always all comments are much appreciated. The use of ( A, B, C ) then ( J, K, L ) etc instead of ( D, E, F ) was as murky said to spread them out as if the had been sequential then solvers may have made mistakes by putting things in the wrong triple.

Could the significance of "time" in the title have anything to do with a common abbreviation of time being t, so T square, and that's what the shape of the final highlighting looks like? Just musing.

Interesting comments on difficulty, which maybe tie up with an article in the paper about crossword lovers being more likely to be mathematicians than wordsmiths. I am certainly more of the former and do find the numbers easier - maybe because they are never going to be unknown words!. I also got going from the logic of the NW combined with using the 2 digit numbers in trial and error with what 17d could possibly be according to the rules. Writing down all the 3 digit and some 4 digit squares and eliminating those that broke the rules also helped a great deal.

Thank you for the hints. I'm now on my way!