T-V5b-T — Pre-Objective Goldstone on Translation-Invariant Graphs (W4-Extended Capstone)
On translation-invariant graphs (torus T^d, cycle C_n), a sub/super-lattice spectral dichotomy at the F=1/F≥2 transition. 2D: Goldstone doublet with commensurability split; 1D: 1-fold Goldstone; nodal count = 2 universal. W4-extended capstone (8 V5b iterations + NQ-172 reproducibility check).