4 problems

Exceptional-case conjecture. For these four cases, $\operatorname{R}(f)$ is exactly the set consisting of the largest and second-largest exponents.

Generalized Hertling conjecture for the Tjurina spectrum. The exponents satisfy

Maximal-exponent conjecture. The maximal spectrum number of $f$ is not contained in its Tjurina spectrum.

Shi–Wang–Zuo's generalized Hertling conjecture. The original inequality