The Holographic Boundary Principle: A Geometric Normalization from Stellar Photospheres to the Cosmic Horizon

It is an operational reality of astrophysics that observers measure two-dimensional decoupling surfaces rather than continuous three-dimensional bulk volumes. In this Letter, we formalize radiative decoupling as a geometric boundary condition. By coupling measurable radiative observables with Newtonian surface gravity, we define a dimensionless boundary relation. Evaluated analytically under standard macroscopic closures, this relation yields an exact geometric capacity, π³/15 ≃ 2.0671, which acts as an upper limit for ideal radiating boundaries. We verify this bound with an independent solar benchmark, and use a kinematic sample of detached eclipsing binaries to demonstrate the strict structural mass-independence of the boundary relation across stellar scales. Projecting the same two-dimensional capacity to the cosmic horizon yields the master equation: Λ R_H² = π³/15 Introducing the holographic principle, we treat the horizon discretization count N as a discrete quantum state parameter. This converts the macroscopic boundary equation into the explicit derivation: G = (4π⁴c³) / (15ℏΛN) equivalently: GΛ = (4π⁴c³) / (15ℏN) locking the microscopic gravitational constant to the macroscopic boundary tension via the horizon information capacity. We further show that the canonical 10¹²⁰ vacuum discrepancy is strictly proportional to the boundary scaling factor N: Δ = (30/π³)N ≃ 0.967N resolving the energy divergence as an area-scaling dimensional artifact. Assuming spatial flatness, the dark energy fraction is geometrically constrained to: Ω_Λ = π³/45 ≃ 0.6890 Finally, modeling the transition from a continuous primordial fluid to a discrete late-time void network using the 3D kissing number k = yields a kinematic stretch mapping: H_0^local = H_0^CMB (13/12) ≃ 73.01 km s⁻¹ Mpc⁻¹ and provides a structural topological interpretation of the ζ(−1) = −1/12 Riemann regularization. The framework resolves prominent cosmological tensions as rigid topological imperatives of spatial boundaries.