Critical when abbreviated in notes (5)

I believe the answer is:

acute

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'critical' is the definition.
(similar in meaning)

'abbreviated in notes' is the wordplay.
'abbreviated' becomes 'cut' (I can't justify this - if you can you should believe this answer much more).
'in' is an insertion indicator.
'notes' becomes 'ae'.
'cut' placed within 'ae' is 'ACUTE'.

'when' acts as a link.

Can you help me to learn more?

(Other definitions for acute that I've seen before include "Shrewd; serious" , "Incisive" , "Sharp or crucial" , "Shrewd; severe" , "Sharp-pointed - keenly perceptive" .)

I've seen this clue in the Evening Standard.

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