Short form
Paper 9 — Gauge Projection for Dark Energy
Closes the missing factor in the dark-energy derivation by identifying √(1+γ²) with the spectral-norm ratio of the Ashtekar-Barbero connection to the spin connection on the Schwarzschild horizon. The paper shows that the relevant connection pieces occupy orthogonal subspaces and that their spectral norms match exactly on the horizon slice used by the framework.