4 problems

Microscopic index conjecture. The index $omega_N$ provides a microscopic definition of the chiral central charge modulo $24$.

Twist-defect invariant conjecture. The resulting invariant $\theta_N$ is fine enough to capture $c_-$ as a real number, not only $c_- \bmod 24$.

Refined invariant conjecture. There exists a $\boldsymbol{Z}$-valued invariant for 2d invertible phases which, under special circumstances involving the emergence of conformal symm…

UMTC–central-charge classification conjecture. Two-dimensional topological phases are labeled by both a UMTC and the number $c_-$ called the chiral central charge.