Crossword Genius

Crossing path with one going around states (9)

Ross

I believe the answer is:

traversal

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'crossing path' is the definition.
'traversal' can be an answer for 'crossing' (I've seen this before). I am not sure about the 'path' bit.

'with one going around states' is the wordplay.
'with' indicates putting letters inside.
'one' becomes 'a' (a thing is one thing).
'going' becomes 'trl' (I can't justify this - if you can you should believe this answer much more).
'around' indicates putting letters inside.
'states' becomes 'avers' (to aver is to declare or state).
'a' inserted into 'trl' is 'tral'.
'tral' going around 'avers' is 'TRAVERSAL'.

Can you help me to learn more?

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

I've seen this clue in The Times.
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