Abstract

We establish that the T144 biological timing framework possesses a two-level discrete gauge structure which we identify and formalize for the first time. The two levels are algebraically distinct and serve distinct roles: Level I (geometric) is the group Z₁₆ = Aut(T144)/Z₃, which governs the orbifold geometry of T²/Z₁₆; Level II (topological) is the group Z₁₂₀, which carries the Chern-Simons cocycle η = 49/120.

Three theorems are proved. Theorem 1 computes the Dijkgraaf-Witten partition function Zₜ₝[T²/Z₁₆] = 16 and establishes a bijection between the 16 gauge sectors and the 16 elements of Aut(T144)/Z₃. Theorem 2 identifies η = 49/120 as the unique cocycle k = 49 in H³(Z₁₂₀, U(1)) = Z₁₂₀, and proves that this identification is impossible in H³(Z₁₆, U(1)) = Z₁₆ (Theorem 3). Theorem 4 formalizes the two-level structure: Z₁₂₀ acts on biological time (T_ery = 120 days) while Z₁₆ acts on the orbifold geometry; they share the 2-primary component Z₈ but are otherwise algebraically independent in their gauge roles.

Corollary 1 derives the Dijkgraaf-Witten partition function Zₜ₝[T², Z₁₆] = 16 for the torus with Z₁₆ gauge group, and clarifies the distinction between this construction and the orbifold T²/Z₁₆. Corollary 2 predicts that the number of topologically independent therapeutic resistance modes is bounded by 15, the number of non-trivial gauge classes in Z₁₆. The established Z₇ drug-resistance attractor (Papers 7–8) is identified as one of these 15 classes.

Keywords: discrete gauge theory, Dijkgraaf-Witten, Chern-Simons, η invariant, H³(G,U(1)), orbifold, T²/Z₁₆, Z₁₂₀, T144 framework, gauge sectors, therapeutic resistance