3 problems

Skew Brownian permuton well-definedness conjecture. The skew Brownian permuton is well-defined for every parameter pair

Existence and uniqueness conjecture. Existence and pathwise uniqueness for the solutions of these SDEs hold for every

Biased-sign construction conjecture. For $\rho=1$ and every $p\in[0,1]$, the solutions $\bm{\mathscr Z}_{1,1-p}^{(u)}$ can be constructed using independent biased signs satisfying