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Nice and easy with a bit of coding to do some of the legwork, but I bet this would be a bit of a slog if you were intending to do it by hand. An admirably constructed puzzle for sure, but not a wildly fun solve for me at least. One for the purists, perhaps.

I'll be curious to see if there's a nice bit of algebra that facilitates the final step in a more elegant way than just doing an exhaustive search.

An enjoyable solve. Not as daunting as the preamble might suggest. And none of the usual laborious trawling through lists of primes, squares, etc.

Can I check - does the preamble mean that all the answers to the clues and corresponding entries have i) no zeroes and ii) no repeated digits.

Well done nxe and felipedon. Apart from two of the letters, I can't see any way into DURATIONS.

dylan - have you tried working out which letter is 1?

andyp -

Ha - I’ll try again.

Andy - your reading of the preamble is correct

I think I know DRTIN for sure. Is that the best way to start?

Broadly how I started although I made some educated guesses generally but probably got A next then S then O and U.

As all answers are 4 distinct non-zero numbers, it’s quite easy to check a couple and work out if an option is wrong.

All done - despite some errors in DURATIONS originally, once that was fixed the rest came out without as much brute force needed as originally feared.

Thanks Miles for something very different - it amazes me how the setters dream up these things, let alone then turn them into a puzzle!