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 (G₀^) 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.