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As hoped for, posting unblocked the jam and I have the clashes now. Just 41d to go....

Tricky to be more specific than earlier about 41d SH but the answer sounds 'watery'.

Puzzle done, highlighting and thematic shape done, six lines drawn… but I’m uncertain about the final instruction - ‘the clashes at their intersections showing the third concept’s topic’. I know what that topic is but do we need to draw a line connecting the points, as shown in the illustration of the theme? Surely that would be a seventh line…?

I have submitted my entry without a seventh line. After all, if one has resolved the clashes correctly, it's clear that one has "got" the third concept's topic.

Thought this was really nice, the anagrams held me up for a while as I thought they were the clashes! Enjoyed working out how to draw the lines. As others, needed a hint from here to get 41d.

Can't parse 31a.

Did anyone else think that "clashes at their intersections" in the preamble should read "entries at their intersections"? Because it needs the other intersection, which isn't a clash. And anyway, it's the entries you use, not the clash itself. Unless I'm missing something...

'Did anyone else think that "clashes at their intersections" in the preamble should read "entries at their intersections"?'

Agreed. The clashes have been resolved, it's the entries that reveal the topic of the third concept.

Adeano - 31a: the definition is the first word; the solution is an anagram of the last word.

Thank you! That did not occur to me at all, obvious now you point it out.

orientfan - Glad it's not just me!