The local module category of SU(3)_3 ⊗ SU(2)_2: an Ising condensed phase

We compute the local module category ClocA for the condensable algebra A = 1 ⊕ ((1,1);1) in the product modular tensor category SU(3)3 ⊗ SU(2)2. Starting from the rank-30 parent theory with total quantum dimension D2 = 144, we identify the unique modular invariant Z commuting with the modular S- and T-matrices, extract a 30×3 branching matrix, and compute the condensed S-matrix via Sloc = (1/dA)bTSb. The result is a rank-3 modular tensor category with quantum dimensions (1, 1, √2), total quantum dimension D2 = 4, and modular data matching the Ising MTC (equivalently SU(2)2) to machine precision. The D2 discrepancy between intrinsic (= 4) and extrinsic (= 9) values is resolved by the embedding dimension factor (d0embed)2 = 9/4. This is a companion paper to 'Anyon condensation in SU(3)3 ⊗ SU(2)2: condensable algebras, monodromy spectrum, and the Z6 fusion ring' (Bazih, 2026), resolving its Remark 3.4 on the structure of ClocA.