η = Cl(7) / Z₁₂₀ The Spectral Invariant of T144 as the Ratio of the Bott Critical Level to the Biological Timing Group

Abstract We establish the identity η = Cl(7)/Z₁₂₀, where η = 49/120 is the Atiyah-Patodi-Singer spectral invariant of T144, Cl(7) denotes the seventh level of the real Clifford tower (the unique last semi-simple level before the Bott return), and Z₁₂₀ is the T144 biological timing group. The numerator 49 = 7² is the spectral signature of Cl(7) = M₈(ℝ) × M₈(ℝ): its two irreducible components each contribute 7 to the Donnelly cotangent sum, yielding 7² = 49. The denominator 120 is the order of Z₁₂₀ = Z₃ × Z₅ × Z₈. This identity closes a chain of forced algebraic implications: Z₈ → Bott periodicity → Cl(7) as anti-identity → 7² = 49 → η = 49/120 → discriminant Z₁₂₀ = A₄₉ ∪ B₇₁. Each step is determined by the previous. There are no free parameters. Additionally, the two semi-simple levels of the Bott cycle satisfy 3 × 7 ≡ 5 (mod 8), revealing that Z₅ — the meiotic factor of Z₁₂₀ — is encoded in the product of the two Bott dédoublement levels. The T144 framework is therefore not an arbitrary grouping of biological observations: it is the unique biological realization of the Bott-Clifford structure at the level where the algebraic tower undergoes its final bifurcation before closure. Keywords: Cl(7), Bott periodicity, semi-simple Clifford level, η-invariant, Z₁₂₀, T144, anti-identity, spectral signature, biological timing, forced algebraic chain