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If, like me, you're giving the numerical a miss, I strongly recommend this weekend's Inquisitor by Ifor. It is superb and a heck of a challenge - you won't get that "weekend off" after all. It seems to be impossible until the penny drops (which took me several hours), then you realise that this is a top-notch puzzle from a fine setter at the top of his game.

Agree. Very satisfying. Got a little distracted by the unclued entry as we found 3 plausible moduli (or is it moduluses?). So it was the usual grind, generating gibberish until the right message emerged. For non-mathematicians, think the compiler’s preamble might have just illustrated how to deal with pairs like 28 or 29, using his example of 30.
Remember happy times over a beer in the pub in the late 70s as the locals competed!

There seems to be a down clue missing? Starting in the square with capital J.
Every other one has a clue. Can you confirm it's solvable without. I'm making headway slowly.

Lumen. Yes perfectly solvable without the down clue

As M is simply 2f, the "down clue" is not needed. It all works fine.

Many thanks again Tatters for your public service. My husband joins me for the numericals so this is one of the four weekends a year he is not a crossword widower :-D We enjoyed this a lot. The message certainly took a bit of finding, but logic came in again with considering appropriate moduli I thought. And the emergence of the theme raised a smile. Thanks for a great crossword Pandiculator.

All done, but I didn't see how to uniquely solve the *cell, and its two neighbours, without trying all four possible solutions in the decoding part. The rubric implied I should have been able to complete the grid without having to first try the decoding. Was I missing something?

For non-mathematicians like me could you confirm how numbers smaller than * but > 26 should be decoded? For example if * is 50 and the pair is 44 does that reduce to 44-26 = 18 or something else?

I have 5 possibilities for the filled grid but only one seems likely given our alphabet.

I am puzzled by the instruction "Taking the filled grid’s digits in row order, each pair can yield a letter ". There are an odd number of cells in each row so do we pair the last digit from row 1 with the first digit from row 2, etc? Pairing digits vertically also seems wrong.

Bananabean, yes, you read from one row to the next, when there are an odd number of cells in a row.