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Arghh! I thought I had - I scrolled down all the definitions to see if there were any American references but gave up when I didn't see any - I even started to wonder if it was the name of a film, book or TV character!

Thanks again for all your help with this Candledave, it's much appreciated.

On to the endgame ...

Like others, I thought the three blank cells were for after the erasing bit. As soon as I started looking at them 'Kerching!' the penny dropped. Very clever. Thanks Poat.

Unlike Drxx, I think the punctuation is very helpful. There are three objects. A colon introduces the list of the three objects, separated by commas and followed by a semicolon, after which we have the definitions.

What fooled me was the use of the symbols n and N, which would normally represent two different numbers. I eventually realised that the capital letter was used at the beginning of a sentence!

Despite this I haven’t completed the endgame. Perhaps it would help, without giving too much away, if someone could tell us whether the third object points upwards or downwards.

rad, it points up ..

In case others haven’t noticed, there’s an entire second thread with 4574 in the title ..

Thanks, Lord B. That leaves a pleasingly symmetrical region. Now to split it up and find the names ...

I naturally assumed that N and n were independent. That suggests to me that the setter is not a mathematician, and so the objects we are looking for are not what I was expecting. Still waiting for the penny to drop.

I’ve got the partition now, and three possible letters making possible names, but with no obvious relevance to the rest of the puzzle,and not forming a ‘complete’ sequence, whatever that may mean.

Got it now! With relief rather than exhilaration! Thanks to all.

Regarding the punctuation, rad - if everything following on from the colon was as you suggest, I wouldn't have any issues but there's a clumsy kind of sub-heading after the first item and it's just floating around in the middle (and signifying very little at the same time).

It’s difficult to discuss this here without giving too much away, but I think every word is relevant and helpful. A bit odd in places, but as usual with these cryptic messages it all makes sense in the end!