noun
letter of challenge; written challenge to a duel
A formal written challenge, historically used to demand satisfaction or a duel. Now mostly encountered in historical or dramatic contexts.
彼は決闘を申し込むため、相手に果たし状を送った。
He sent a letter of challenge to his opponent to demand a duel.
More explicitly refers to a duel; 果たし状 can be used for challenges beyond duels, though duels are the most common association.
Compound of 果たし (from verb 果たす 'to carry out, to settle') and 状 ('letter, document'). The exact historical derivation is uncertain, but the term is associated with samurai-era formal challenges.