Explicit affine sl(2) categorical S-matrix

Derive an explicit matrix formula for the categorical S-operator on the affine sl(2) fusion-chain conformal block spaces beyond the abstract construction in terms of fusion, associativity, and braiding data.

Background

The paper constructs an abstract categorical S-operator for torus n-point conformal blocks and gives its formal mapping-class-group properties. For affine sl(2), however, converting the ribbon-graph construction into an explicit matrix requires tracking the relevant F-, G-, and R-moves, fusion-tree changes, and ribbon framing conventions. The paper identifies this calculation as unresolved, including already for the two-point case.