One Piece Episode 1167 Preview
A brutal fight left Bartolomeo and his crew badly injured. Things got even worse when one of Shanks’ men tried to force Bartolomeo to poison Luffy, but Bartolomeo refused to betray Luffy and ate the poison himself. It turned out Shanks was simply testing Bartolomeo’s loyalty, and they were eventually released. However, Yasopp wasn’t satisfied and destroyed their ship, leaving the fate of Barto Club uncertain. This incident showed a different side of Shanks – while usually cheerful, he’s willing to take drastic measures when necessary.
![The study demonstrates that bounds on [latex]\kappa_{1,N}(s)[/latex] - as detailed in Proposition 2 and applicable specifically to horizon length <i>N</i> - are refined by incorporating the term [latex]F_{N}(1+s)^{2}[/latex] to encompass all horizon lengths, with the lower envelope of these refined bounds - represented as a solid black line - providing a conservative estimate [latex]\kappa_{1}[/latex] as established in Proposition 3, for parameters γ=1, L=1.1, and B=10.](https://arxiv.org/html/2604.08521v1/CDC_visualisation.png)
