Comparison of conformal blocks with H^0 of the semistable-modification extension beyond the rational case

Determine whether, for a general vertex operator algebra V (beyond the rational case), the spaces of conformal blocks obtained by extending the sheaf of coinvariants to the boundary via the semistable-modification approach (as in the construction of the extended sheaf over the universal curve) agree with the zeroth cohomology H^0 of the extension of chiral homology constructed using semistable modifications in this paper.

Background

The paper extends chiral/factorization homology to the Deligne–Mumford boundary using semistable modifications and proves gluing formulas, recovering the Verlinde-type behavior at the level of H^0 under finiteness assumptions. Classical extensions of conformal blocks to the boundary for vertex operator algebras were constructed in prior work (e.g., by extending the sheaf over \bar{X}g via identification with \bar{M}{g,1}).

While this new extension provides a multi-point and derived framework, the authors do not know if the resulting conformal blocks coincide with the H^0 of their extension outside the rational VOA setting, leaving the general comparison problem open.