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Crossing States, cutting through path one's left (9)

Ross

I believe the answer is:

traversal

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'crossing' is the definition.
(I know that traversal is a type of crossing)

'states cutting through path one's left' is the wordplay.
'states' becomes 'avers' (to aver is to declare or state).
'cutting through' is an insertion indicator.
'path one' becomes 'tra' (I am not sure about this - if you are sure you should believe this answer much more).
'left' becomes 'l' (common abbreviation).
'avers' inserted within 'tra' is 'traversa'.
'traversa'+'l'='TRAVERSAL'

Can you help me to learn more?

(Other definitions for traversal that I've seen before include "Action of crossing" , "A crossing (of something)" , "Act of crossing" , "Coming across" , "crossing over bridge" .)

I've seen this clue in The Independent.
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