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Thanks Djawhufc

I think you've cracked it, djawhujc, except that the preamble says, of the rectangle, that it should be "treated symbolically using only initial cells." I take the "only" to mean that we put the Greek letters in the nine "initial" cells, as you suggest, but then erase the other 40 cells, just as we are required to do with the remaining 42 cells of the square. Or am I reading too much into it? Amazing that while the previous week's crossword didn't produce a single forum comment, this one's provoked no less than 52! If Shackelton has been reading it, he must be laughing his head off.

I took it to mean that first cell of each word would be the Greek symbol with the rest of the word intact

So sign for Alpha for example and the lpha in English. I may be wrong though. I took initial to mean it was the only thing altered.

I put this aside for a few days as I had little time for it. I don't think it makes much sense to have a mixture of Greek letters and Roman letters in the lower rectangle. I take it that the intended solution involves replacing the first letter of each word denoting a Greek letter, then deleting the rest. The key sentence in the preamble is "an adjacent rectangle...must be treated symbolically..."