LHFT Lemma — Projectively Accessible Bright-Sector Closure in the Minimal F=1 Hydrogen Block

This deposit contains a localized Atomic-Sector closure step within the framework of Log-Harmonic Field Theory (LHFT). The document focuses on the first observable atomic bottleneck: the minimal F=1 hyperfine sector of hydrogen.The lemma provides a formal derivation of the transition from logarithmic structural shell operators to effective observed hydrogenic regimes. Key contributions include:Recoupling and Drift Dynamics: Derivation of the drift-active s ↔ p channels and the explicit calculation of drift coefficients d1/2 and d3/2 in the F-coupled basis.Bright/Dark Basis Construction: Introduction of a drift-adapted basis that isolates the "bright" combination (directly coupled to the 2s state) from the "dark" combination.Projective Suppression: A demonstration of how the dark sector, while internally present, becomes projectively inaccessible or strongly suppressed in the observable dynamics.Stability Analysis: A numerical stress-test defining a critical stiffness threshold (G_0ᵐⁱⁿ) below which the projective atomic identity "melts" due to loss of energetic separation.This work represents a "no-arbitrary-fit" stage of the LHFT Closure Program, moving from heuristic architecture toward final microscopic sealing of the atomic sector.