One Piece Episode 1157 Preview: Nami And Usopp Under Attack
A brutal fight left Bartolomeo and his crew badly injured. Things went from bad to worse when one of Shanks’s men tried to force Bartolomeo to poison Luffy. Loyal to Luffy, Bartolomeo ate the poison himself. It turned out Shanks was simply testing Bartolomeo’s dedication, and they were eventually released. However, Yasopp wasn’t willing to let them leave without a final message – he destroyed their ship, leaving the fate of Barto Club uncertain. This incident showed a different side of Shanks, revealing that despite his cheerful nature, he’s willing to take serious action 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)
