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 P_horizon = c⁵/2G, so both converge on c⁵/2G and the de Sitter state is a terminal attractor by thermodynamic necessity. The equipartition condition P_expansion = P_horizon admits two algebraically exact crossover epochs, z₁ ≈ 0.632 (q = 0) and z₂ ≈ 0.028 (q = −1/2), from a quadratic that factors as (2Ω_m x − Ω_Λ)(Ω_m x − 2Ω_Λ) = 0. It also gives the dark-energy density ρ_dark = c³/(8πG R_H² Ṙ_H) = 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.