Radiative Decoupling as a Boundary Condition: A Geometric Normalization from Stellar Photospheres to the Cosmic Horizon

Astrophysical measurements are operationally anchored in radiative decoupling surfaces, where photons free-stream and boundary observables are directly accessible. We define a dimensionless decoupling-boundary relation from the observables :

X ≡ (LGM / (g R⁴ T_eff⁴)) (ħ³ c² / k_B⁴).

Under the standard macroscopic closures and , the dependence on mass and the gravitational constant cancels identically, and the relation reduces to the constant phase-space capacity

X → π³/15 ≃ 2.0671.

Using independently determined solar inputs we obtain . Evaluating the same relation for 190 detached eclipsing-binary components yields a mass-independent cluster with ⟨X⟩ = 2.0600 and s_X = 0.0027.

Projecting the same 2D normalization to the Hubble horizon gives the master relation

ΛR_H² = π³/15,

implying Ω_Λ = π³/45 ≃ 0.6890 under spatial flatness.

Embedding the constraint in a mini-superspace action reproduces the Friedmann expansion rate and yields the Bekenstein–Hawking scaling N = A_H / l_P².

Finally, modeling late-time discretization as optimal 3D sphere packing (k = 12) gives a kinematic offset

H₀^local = H₀^CMB (13/12).