6 problems

Perfectness conjecture. Every perfect finite-order planon-only theory of excitations can be realized by a suitable quantum lattice model.

Perfectness conjecture. Every perfect theory of excitations can be realized by a quantum lattice model with a spatially local Hamiltonian.

Constraint-map conjecture. The constraint map of a $k$-planar X-cube model has this form, generalizing the corresponding maps for the anisotropic model and the 3- and 4-planar X-cu…

Geometric-data conjecture. Within this construction, the intersection geometry is the only geometrical data needed to specify a unique fracton order.

$k$-planar X-cube conjecture. The resulting fracton order is $k$-planar, foliated, and $p$-modular, and depends only on $k$ and on the intersection properties of the chosen orienta…

Classification conjecture. With a suitable definition of enhanced $p$-theories and a better understanding of which $p$-theories are realizable, classifying $p$-modular fracton phas…