The conjecture that all gapped fracton schemas are lax-topological

A lax-topological $D$-dimensional Hamiltonian schema satisfies $TQO0$, $TQO1$, and $TQO2$, and there exist constants $\alpha$ and $\beta$ depending only on $D$ such that

$$GSD(H_\Delta)\leq \alpha e^{\beta L^{D-2}}$$

for every Hamiltonian $H_\Delta$ from the schema on a linear-size $L$ cellulation $\Delta$ of a space manifold $Y$. A gapped fracton schema is a Hamiltonian schema describing a gapped fracton phase. The conjecture. All gapped fracton schemas are lax-topological. This would place gapped fracton phases within the stated growth bound, extending the lax-topological framework beyond ordinary topological phases. The surrounding discussion notes that Haah codes saturate the bound, while it remains open whether intermediate maximum growth functions occur between TQFTs and Haah codes.