pith. sign in

Where does the fine-structure constant come from?

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
  1. The phi-based exponential form for alpha-inverse is α^{-1} = 44π × exp(−w₈ ln φ / (44π)), with the exponential resummation arising from the ledger's reciprocal symmetry and self-similar closure.
  2. Numerical window: (137.030, 137.039) for α^{-1}.
  3. CODATA 137.036 lies inside the proved window.
  4. The form and interval are theorem-grade (proved in Lean with zero axioms or sorries in the chain); agreement with CODATA is empirical confirmation.
  5. Cited Lean anchors: fine_structure_derived and alphaLock_numerical_bounds.

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.