Orbifold correction conjecture for quantum Singleton bounds

Let $X$) be a weighted projective variety with orbifold singularities, and let $C$ be a quantum stabilizer code constructed from self-orthogonal algebraic geometry codes on $X$. Write $n$ for the code length, $k$ for the number of encoded qubits, $d$ for the minimum distance, and let $\chi_{\mathrm{orb}}(X)$ denote the orbifold Euler characteristic. Orbifold correction conjecture. The minimum distance satisfies

$$d \leq \frac{n-k+2}{2}-\frac{\epsilon}{2},$$

where $\epsilon=f(\chi_{\mathrm{orb}}(X))$ is a positive function of the orbifold Euler characteristic, motivated by twisted sectors in orbifold quantum cohomology. This conjectural refinement proposes that weighted-orbifold geometry can improve the usual quantum Singleton bound; the source provides motivation from orbifold cohomology but no proof or resolution.