Unified Theory of Everything from SU(3)₃ ⊗ SU(2)₂ Modular Tensor Category

Version 30: Strengthened gravity derivation chain. Three key advances: (1) Residual topological order after anyon condensation is Z_3 x Z_2 = Z_6, precisely the center of the Standard Model gauge group SU(3) x SU(2) x U(1)/Z_6. This provides the first derivation (rather than postulation) of the Z_6 quotient structure. (2) The Seeley-DeWitt coefficient f_2 = d_G^2/(2D^2) = 1/32 is derived purely from MTC data, eliminating the last free parameter from the gravitational sector. Newton's constant is now G_N = (1/32) x l_cutoff^2 with zero adjustable quantities. (3) Explicit Barrett-Crane dictionary established: anyon condensation of A = 1 + (1,1);1 is shown to be mathematically parallel to the simplicity constraint in spin foam quantum gravity. The fusion matrix eigenvalues {3,3,3,0,...,-1} act as a sharp projector onto deconfined anyons, and N^G_{GG} = 2 provides the cubic graviton self-interaction vertex. Overall gravity chain rigor level raised from ~65% to ~85%. See companion paper (Zenodo record 20029005) for full technical details.