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Derivation of the fine-structure constant

Source: FSC Alpha Derivation 24 June 2026. Standard Model treats α as a measured input. BFUT derives ħ from condensation geometry, then α from the standard electromagnetic definition with that ħ.

Coefficients (no measured constant)

E(R) = A/R² + B·R² + C·R + D/R

A = 1/2 exact. D = 1 exact. C = −1/3 from C3v symmetry. B = 0.56308 from void-filling geometry.

R0

dE/dR = 0 gives R0 = 1.27348221. No measured constant enters.

SI anchor and ħ

r_p = 0.8414 fm (PDG 2022) is the length anchor. ħ = m_p · c · r_p / (π · R0) = 1.054577 × 10⁻³⁴ J·s. Measured 1.054572 × 10⁻³⁴. Difference 0.00048%.

α

α = e² · R0 / (4ε0 · m_p · c² · r_p) = 1/137.0367. Measured 1/137.0360. Difference 0.00048%.

Where the residual sits

The whole residual is the gap between R0 from geometry (1.27348221) and R0 back-computed from measured constants (1.27348831). That is an identified open problem in the geometric derivation of B. It is not a fitted parameter.

Measured inputs to α: m_p and r_p. Exact inputs: e and c. ħ and α are outputs.

All derived quantities