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Yes, williamseal.
lumen ? = ver...

Yes that's what I have, and they replace something significant too.

Jings, Crivvens and help ma Boab! That was fun and very clever in what changed - and what did not - in the end game. I confess to being a dedicated fan of the subject, so may be prejudiced.

Very much a Listener newbie so delighted to finish this one ( I think). I can't though, for the life of me, parse 37ac.

slithytove, chess notation for knight inserted in the middle of a four letter word meaning place of authority, and if you drop the A you get base, as in logarithms, to give the final letter.

Thanks, Quisling. That about completes the puzzle for me, and fits with my thoughts on 26d as far as the def. It's the parsing that I can't get. I figure PA for per annum, but the rest eludes me.

Maths... the 'team' unveiled gives you two letters as you remove its covering/outer letters and add 'new'.

Ah, so United is the extra word. That's what was throwing me. Thanks much, Malone.

Thanks quisling. O Level maths is a long time ago...