Derivation of the fine structure constant from vacuum topology

A Geometric Fixed-Point Derivation of the Fine-Structure Constant with a Weak-Seam Correction from the Second LC Tail Layer This work presents a geometric fixed-point construction for the inverse fine-structure constant from the discrete structure of an oriented LC time-torus cycle. The active projection of a six-link internal cycle selects the levels {0,1,3,5}, which generate the anchor block Δ = 3¹ + 3⁰ = 4, the outer shell block Σ = 3⁵ + 3³ = 270, and the normalization scale D = 3⁵ = 243. Return of the nested tail through the two outer shells yields the suppression coefficient λ = 3⁻⁸. The infinite matryoshka tail is summed to obtain the scalar fixed-point equation h(T(h) − 3⁻⁸ S(h)) = S(h)². Compared with the rubidium atom-interferometric measurement α⁻¹_Rb2020 = 137.035999206(11) (Morel et al., 2020; PDG 2022), the deviation is Δ = −2.4×10⁻¹¹, corresponding to approximately 0.002 standard deviations. Thus the derived constant falls precisely on the central rubidium value, well within the experimental uncertainty. This work is part of the broader fundamental research program “Topology of the Vacuum” by Stanislav Kalmykov.