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I've nearly finished this and I think I understand the thematic material and what's required... but I'm missing three answers.

Can anyone please give me a nudge on 15ac, 4d and 29d?

Based on what I have elsewhere I'm only expecting one further clash.

15Ac I THINK is a triple-meaning, but can't parse one word. 4d is VERY hard, but is a double meaning. 29d is a person's name.

I agree with your interpretation. I find that when the condition of the shapes having to contain elements of a series is satisfied, clarity ensues. The key for me was to find the first shape, and thereafter to exploit symmetry. Top left is a good place to start, I venture to suggest!

Also, you're right about there being only one more clash. It affects 4d.

Heisenberg - in 29dn use abbreviations and jumble. In 15 the definition is the first two words. DD = gave as a gift. For 4dn it is COR- E.
I found the calculation useful as a check to make sure I had no mistakes in the words!

Thank you both. I had forgotten DD and hadn't realised 29 was a person.

I already had the shapes apart from those gaps, but I'd been led astray by one of the clashes, where selecting the wrong letter still gives a total within the multiple thematic sequence. That made it impossible to predict the missing entries based on which multiples I thought were still to be decided.

I get the striking example. Is there also something thematic in the source material referenced in the 10th letters that I've forgotten about?

Never mind, I see now it's the Q in the original!

The shape proposed by saddleworthian in post 27 for the top left seems to me to give a total of 27 (five As, five Bs, one C, one I) plus either E (5) or O (15), neither of which bring the sum to a thematic multiple. Where's my error? I can see that the shape might also be 5-3-5 reading down, but that's no better....

Try looking at that 5x3 section in the top-left corner and removing 2 high-value squares to get to the expected thematic total and that's your first shape.

Thanks for that, I gave up too soon, as so often....