α fine structure: Λ Minimum Step to Mode Identity

Mode Identity Theory's scaling law A/A_P = Ω^(−n/2) · C(α) has been applied to three cosmological observables: Λ (~10⁻¹²²), H₀ (~10⁻⁶¹), and a₀ (~10⁻⁶²). Each uses integer manifold index n = 1, 2, 3 and a Fibonacci well on the 120-grid. This paper extends the scaling law to the fine structure constant α ≈ 1/137, a dimensionless coupling. The extension uses three structural modifications: the bosonic 60R-grid (photons are bosons), the matter well 13/60 (EM couples matter to matter), and a fractional exponent 1/60 = 1/|I| (one grid step of the vacuum hierarchy).

The result, α = C(13/60) × Ω_Λ^(−1/60) = 0.00733, agrees with CODATA (0.0072974) at 0.44%.

The exponent follows from the same structure that produces the grid: S³ carries |2I| = 120; bosonic projection gives |I| = 60; the minimum resolved step on the 60R-grid is 1/60. The extension from integer manifold index to fractional grid-resolution index is a new structural claim (the Grid-Hierarchy Conjecture), motivated by the framework. All other inputs are derived from MIT topology or independently measured; zero free parameters. Uniqueness analysis confirms the formula is the sole combination passing all six MIT structural constraints.

Latest derivation of this paper can be found at github.com/fine-structure