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Croatian boxers reportedly bringing carp (5,5)

Ross

I believe the answer is:

split hairs

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'carp' is the definition.
(both can mean to complain or find fault)

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for split hairs that I've seen before include "Worry about minutiae" , "Make pedantic distinctions" , "Quibble" , "cavil exceedingly" , "salon complaint?" .)

I've seen this clue in The Guardian.
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