Completeness of defect-generated conformal-block combinations

Determine whether sphere four-point correlators generated by arbitrary configurations of topological defects in diagonal minimal models realize all possible linear combinations of the conformal blocks \mathcal{G}_{k,\overline{k}}^{\langle12|34\rangle} with left and right representations independently drawn from the Kac table.

Background

Topological defects modify channel spectra and structure constants. In a diagonal minimal model, introducing defects permits intermediate fields whose left- and right-moving representations differ, producing sums over pairs of Kac-table representations.

The paper leaves unresolved whether varying defect configurations, including defect junctions, spans every possible linear combination of the resulting conformal blocks. Resolving this would characterize the maximal conformal correlator system generated by topological defects.