Crossword Genius

A thousand small homes over island capital (9)

Ross

I believe the answer is:

stockholm

I'm a little stuck... Click here to teach me more about this clue!

'capital' is the definition.
(capital of Sweden)

'a thousand small homes over island' is the wordplay.
I cannot quite see how this works, but
'thousand' could be 'k' (synonyms) and 'k' is located in the answer.
'small' could be 's' (abbreviation - e.g. clothes size) and 's' is found within the answer.
'over' could be 'o' (cricket abbreviation) and 'o' is located in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for stockholm that I've seen before include "Scandinavian capital" , "Sweden's capital city" , "Capital of Sweden" , "Swedish city" .)

I've seen this clue in The Times.
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