The latest chapter makes it unambigously clear:
To break down what happened.
Zoro unleashes his Haoshoku and knocks down fodder:
King notices it and comments on Zoro's "kingly ambitions":
Immediately, after, we're shown what those "kingly ambitions" of Zoro's are.
He thinks back to his promise to Luffy to become the World's Strongest Swordsman:
And then explicitly states that King is right, as he made such promises to his captain and his best friend:
Mihawk is the current World's Strongest Swordsman. To aspire to be the World's Strongest Swordsman, is to seek to reign above all swordsmen, to become a King. If Zoro who merely holds that ambition is a Conqueror, then how much more so the current occupant of the title?
He who reigns at the top and is waiting for Zoro:
The very one that Zoro seeks to surpass:
And it goes without saying that if Zoro is capable of Haoshoku coating then Mihawk also would be.
But more than just being any ordinary Conqueror, Mihawk is probably one of the greatest of Conquerors.
Zoro awakened as a Conqueror in order to pass Enma's test:
How much more so Mihawk who not only mastered the "finest blade" in the world but (most likely) also forged it into kokuto:
1- Lolo novel specifically told us that Mihawk's title is not set in stone. People were discussing who is the Greatest Swordsman; Vista, Shanks, Mihawk, Dressrosa Lolo? They could all be Greatest Swordsman according to the Novel, I didn't say this, the Novel says it.
Zoro Novel: ''One marine claims that the strongest swordsman in the world is definitely Mihawk, the other marine claims it's Zoro. They witnessed their sword techniques in marineford and dressrosa. Mihawk cut down gigantic ice block. Zoro cut down gigantic Pica.''
''They start talking about other candidates: Vista, Shanks and Ryuuma. A marine says Vista was able to fight Mihawk equally for a short moment. Ryuma is strong, but he is already dead. According to another marine, Shanks is said to be the rival of Mihawk. He faced Akainu without fear. 2 of the marines have heard that Shanks is a very strong swordsman. But another marine says it's not that Shanks showed his great technique with his sword in Marineford.''
--- Translation by Sandman
2- Mihawk never showed the ambition to surpass anyone, he never showed the ambition to become the greatest swordsman, if people calls him greatest swordsman, it doesn't make him that he wants to be one. Or surpass anyone while being one. He and Lolo are different in this area. Lolo showed that he wants to surpass Mihawk, Mihawk never showed the ambition to surpass anyone. It's not usable for Mihawk. We don't even know how Mihawk become greatest swordsman. And it's even debatable that he is not according to Lolo novel.
3- Just because Oda gave a Haki type for Lolo to surpass a certain character, that doesn't mean that certain character has the same ability.
Example; Luffy wants to be PK and has ambition to surpass Yonko, thus he learns Future Sight CoO. That doesn't mean
every single Yonko has Future Sight just because Luffy learned it.
Or another example; Luffy learns the
internal destruction Ad.CoA, superior to even Barrier Ad.CoA, that doesn't mean Kaido, Big mom, Shanks and Blackbeard
can all use internal destruction Ad.CoA just because Luffy can use it and wants to surpass Yonko, and just because he has kingly ambitions. That doesn't mean Yonko can use Future Sight and Internal Destruction Ad.CoA.
4- According to Lolo fans,
Lolo can never surpass Mihawk, because whenever Lolo does something,
they think Mihawk can do it as well. This logic is incredibly flawed and with this logic, Lolo can never surpass Mihawk, because according to Lolo fans every ability that Lolo has Mihawk will have it too, plus Mihawk will always be more experienced than Lolo, so it's not possible for Lolo to surpass Mihawk with this logic, due to Mihawk having every ability that Lolo has + has more experience.
-Either, Lolo will have Ad.CoC and Mihawk won't have, so that will be the key difference between the two.
-Or, both have Ad.CoC, but Mihawk's Ad.CoC will be weaker than Lolo's Ad.CoC and Mihawk will lose.
Even in the second most wanked Mihawk scenario, where Mihawk will have Ad.CoC BUT Mihawk's Ad.CoC will be inferior to even Lolo's Ad.CoC level, so even then there is no way Mihawk can match with Yonko and Yonko level Ad.CoC power level, when it's inferior to even Luffy's underling Lolo's Ad.CoC, so
Mihawk will be inferior to Yonko level even in the most wanked scenario where Mihawk automatically will have every ability that Lolo has.
5- Funny enough, Lolo never remembers any lesssons from Mihawk on Wano yet, not even CoC Haki demonstration or any Ad.CoA Haki demonstration, while Luffy specifically sees Rayleigh's CoC, and remembers Rayleigh's Ad.CoA application in flashback and Rayleigh's Future Sight mentions, Rayleigh heard about that Future Sight so he warns Luffy, while Lolo never remembers anything from Mihawk, not even warnings about those superior abilities, instead Lolo think about Oden's sword on Wano, Oden's Haki, and Kinemon's Fire cutting techniques to improve himself, if Mihawk had all these abilities, at least Oden's Haki level, then Oda should've shown Mihawk's flashback as well, not only mention Oden's Haki level, and Kinemon's fire cutting technique. Lolo was pushed to his limits several times, he never remembers Mihawk's training and he never gets stronger by remembering those trainings, it's Oden's sword, trying to reach Oden's Haki level, and learning Kinemon's fire cutting abilities made Lolo stronger on Wano.
6- Lolo already begged Mihawk for training,
if Luffy begged Kaido for training, Luffy vs. Kaido wouldn't happen. Only Lolo fanboys still believes Lolo vs. Mihawk will happen despite Lolo begging Mihawk for training, Oda specifically did this to remove Mihawk from the equation where he and Lolo fights to death, not only this he also removed Shichibukai so they really won't fight again, unless mihawk joins Shanks and Luffy fights Shanks and Lolo fights mihawk, this is very unlikely, instead Oda put first King there to unlock Ad.CoC, then both King's and Mihawk's superior Shiryu will be Lolo's next opponent. Lolo vs. Mihawk won't happen, so Lolo vs. Mihawk clashing with Ad.CoC won't happen as well. Mihawk is old news.
Debunked all too easy.
Yes I think to be a top tier in one piece you have to have a special will, a special drive = COC.
Only BB has a chance not having it because he is a special case.
This is why you guys are hypocrites LOL.
The first post thinks Mihawk should have CoC based on Lolo will surpass him, and Mihawk was never even mentioned in this chapter, just that Lolo shows the ambition to surpass Mihawk, that doesn't mean Mihawk has that same ambition when they called him greatest swordsman. Mihawk's title is still not set in stone as Lolo novel told us. And it's possible that Lolo will surpass Mihawk with Ad.CoC difference, since he will be superior to Mihawk.
Chinjao shows CoC, AND TELLS Luffy only Blackbeard has potential to surpass others and become PK, Chinjao directly mentions Blackbeard's name, and yet you say it's possible he doesn't have it. But somehow Mihawk will definitely have that, when it's also obvious that Luffy's underling Lolo will surpass this guy, and it will be
Luffy > Luffy's underling Lolo > Mihawk, just how powerful Mihawk can be in this equation? Even if he has it, it will be like Yamato level at best, definitely inferior to Lolo's Ad.CoC, let alone to Yonko level heaven splitting Ad.CoC level. So it wouldn't make Mihawk stronger than YC1s or Yamato in any case.