4 problems

Let $\mathsf{\mathscr{E}}$ be the exceptional time set and let $\mathsf{\mu}$ be the associated local-time measure, which is supported inside $\mathsf{\mathscr{E}}$. Full-support c…

For a fixed interval $[a,b]$, let $\mathsf{\overline{\mu}}_r[a,b]$ be the finite-radius approximations to the local-time measure and let $\mathsf{\overline{\mu}}[a,b]$ denote their…

Let $\mathsf{FETIC}$ be the law of the configuration at the first exceptional time, and let $\mathsf{IIC}$ denote the incipient infinite cluster measure. Singularity conjecture. Th…

Nearest-neighbor noise-sensitivity conjecture. If $t_n \gg (n^2\alpha_4(n))^{-1} \approx n^{-3/4}$, then