@Fn Lucci
Mihawk is the man hailed and introduced as the WSS on multiple occasions over and over again
Moreover, he is appointed as the goal of one of the main characters.
Stephen Paul's translation as well
Mihawk is a man canonically superior to an Admiral
a man who awaits a day someone will emerge to surpass Shanks, a Yonko, in order to present a challenge to him
a man who is hailed as the rival of a Yonko Shanks, and even superior judging by his title
Someone whose duels WB considers legendary
WB hasn't heard Shanks' name in years implying that Shanks didn't fight any remarkable foe after Mihawk: not Kaido, not Linlin and of course not Whitebeard.
The explanation by denden, about the legendary duels between them
someone who immediately pops up in Shanks' mind when being asked about his scars
someone who has stated that he as the strongest will await at the top no matter how long it takes Zoro to reach it, years if need be
Mihawk is
"Strongest Swordsman in the World"
Sekai Saikyō no Kenshi - 世界最強の剣士
KENSHI EXPLANATION AND POINTING OUT THE FACT THAT IT ONCE AGAIN REFERS TO THE STRONGEST BY STEPHEN PAUL, THE OFFICIAL TRANSLATOR
So kenshi encompasses those who fight/use a sword. And as a
kenshi/swordsman they are weaker than the
Sekai Saikyō no Kenshi/Strongest Swordsman in the World.
Oda went out of his way to call Cabaji a swordsman, to call Law a swordsman, to call Fujitora a swordsman.
Oda went out of his way to state that Mihawk is the strongest swordsman in name and actuality in different sources
If you sincerely think and expect Oda to give one of his most important characters an empty dream and think that after the battle Mihawk's gonna say 'well joke's on you brah I am not actually the strongest swordsman ha ha ha', I am bewildered by that and don't really know what to say.
Shonen tropes indicate that Mihawk, until he is surpassed by Zoro, will be the strongest swordsman of all time, and Zoro upon surpassing him will become the strongest swordsman of all time as well. Whatever feat swordsmen perform Mihawk can reciprocate at a higher level. Any and all hype a singular or all swordsmen receive in the One Piece manga is hype for Mihawk, who stands atop them all.