pith. sign in

what is the derivation of the fine structure constant

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: high in recognition cached

Phi-based exponential form for alpha-inverse

The RS derivation employs the exponential form α⁻¹ = 44π × exp(−w₈ ln φ / (44π)) from the ledger reciprocal symmetry and φ self-similarity.

Numerical window: (137.030, 137.039)

The exponential resummation establishes the proved interval (137.030, 137.039) for α⁻¹.

CODATA 137.036 lies inside the proved window

The CODATA 2022 value 137.036 lies inside the RS-derived interval.

What is theorem-grade vs empirical confirmation

The exponential form and interval are theorem-grade in Lean with zero free parameters; agreement with CODATA is empirical confirmation.

Cited Lean anchors

fine_structure_derived and alphaLock_numerical_bounds anchor the phi foundation.

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.