A First-Principles Derivation of the Fine-Structure Constant from Holographic Bit-Mode Balance

We present a parameter-free derivation of the dimensionless fine-structure con-stant α, based on a holographic accounting of surface information (bits) versus in-terior quantum degrees of freedom (Dirac modes) inside a minimal, self-stabilising “micro-horizon” surrounding an electron. Four conceptually independent inputs enter: (i) the Bekenstein–Hawking surface bit count, (ii) the degeneracy of the lowest Dirac modes under MIT boundary conditions, (iii) a curvature-sensitive logarithmic Seeley–DeWitt correction, and (iv) a uniform-WKB (zeta-regularised) high-ℓ tail that captures large angular-momentum modes. Combining these yields α^−1 = 137.035998(20), in numerical agreement with the CODATA 2023 value to better than 0.001%.The construction is scale-agnostic: applying the same bit/mode logic to the muon reproduces the same coupling within uncertainties, and the formal structure extends upward in scale to the cosmological horizon, offering an analogous account of the cosmological constant Λ in terms of surface bits per gravitational soft (null) mode.Finally, we outline how energy-scale dependence (running α) emerges naturally from the logarithmic term and discuss falsifiable predictions for sub-ppm “step” structure at high momentum transfer.