ΔStatus tag
2 documents indexed here. Version stamps, research weeks, audits, and evidence-state markers.
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).
W4 closes the year-old Critical-3: F-1, M-1, and MO-1. The Pre-Objective Mechanism cluster and T-V5b-T enter Cat A, the σ-framework becomes the language for critical-point signatures, and the v2.0 release path unblocks.