The Holographic Coefficient: What Three Infrared Cutoffs Require of c_h^2 to Match the Observed Vacuum Density

Holographic dark energy sets the vacuum density by an infrared length rather than an ultraviolet cutoff, through rho = 3 c_h^2 M_pl^2/L^2. This paper evaluates the formula for three candidate lengths, the Hubble radius, the future event horizon, and the particle horizon, using a reduced Planck mass of 2.435 x 10^18 GeV. With c_h^2 = 1 the three give densities 1.46, 1.03, and 0.14 times the observed value of 2.52 x 10^-47 GeV^4; matching observation requires c_h^2 of 0.685, 0.970, and 7.016 respectively. The order of magnitude is genuinely obtained from the infrared scale, but the coefficient remains an input fitted to the answer. The paper is a computation from stated assumptions, not a measurement.