The Geometric Origin of the Cosmic Coincidence: Horizon-Boundary Power Equivalence and the De Sitter Attractor

The observable universe, treated as a horizon-bounded non-equilibrium dissipative system, satisfies the governing condition C (t) /P (t) = F (t) → 1, where C (t) is the structural power at the cosmological event horizon and P (t) the horizon persistence capacity. Adopting the founding ansatz C (t) = (c⁵/2G) Ω_Λ (t), we show that F → 1 follows from two independent constraints sharing no derivation: the flat-universe closure relation bounds C (t) below c⁵/2G for all finite time, while the positive-definiteness of expansion work bounds P (t) above the invariant floor Pₕorizon = c⁵/2G, so both converge on c⁵/2G and the de Sitter state is a terminal attractor by thermodynamic necessity. The equipartition condition Pₑxpansion = Pₕorizon admits two algebraically exact crossover epochs, z₁ ≈ 0. 632 (q = 0) and z₂ ≈ 0. 028 (q = −1/2), from a quadratic that factors as (2Ωₘ x − Ω_Λ) (Ωₘ x − 2Ω_Λ) = 0. It also gives the dark-energy density ρdark = c³/ (8πG RH² ṘH) = 6. 0 × 10⁻²⁷ kg m⁻³, exact at the crossover where 3Ω_Λ (1 + q) = 1 and within about 1% of the observed value today — a thermodynamic rationale for its scale, not a first-principles determination. The exact solution Ω_Λ (t) = tanh² (3√Ω_Λ₀ H₀ t / 2) shows the framework reproduces the flat-ΛCDM expansion history, with w = −1, rather than modifying it; being ΛCDM-equivalent, it does not by itself resolve the Hubble tension. A single boundary-radius relation recovers both the de Sitter and Schwarzschild radii with the same structural parameters across more than twenty-three orders of magnitude. The governing condition is not specific to cosmology: it operates wherever a far-from-equilibrium interior is served by a near-equilibrium exporting boundary.