Geometric Closure as the Origin of the Logarithmic Lamb Shift

This work presents a geometric interpretation of the Lamb shift, identifying its logarithmic structure as the energetic cost of enforcing relative phase closure across scales in a nested quantum system. In this framework, an internal SU(2) spinor frame is transported through a scale-invariant Coulomb background. Enforcing closure across the physically relevant scale window (from the electron’s Compton scale to the Bohr radius) produces a finite correction with the characteristic logarithmic scaling. Treating the closure cost as a quadratic energy density naturally yields the correct hydrogenic Z⁴ scaling and explains the pronounced S–P hierarchy through differential access to the anomalous region. This release is intentionally limited in scope. It establishes the geometric mechanism, scaling behavior, and falsification criteria, but does not include construction of the hydrogenic baseline spectrum, explicit definitions of the closure anomaly, or precise numerical coefficient matching. These elements require full baseline construction and constant provenance and are deferred to a subsequent comprehensive treatment. The purpose of this note is priority establishment and conceptual clarity, not a complete quantitative derivation.