Although gas (g) and liquid (l) phase densities rho and rho(l) can differ by 3 orders of magnitude, from experiment the corresponding vibrational energy relaxation (VER) rate constants are at the same temperature T, strongly correlated. Namely, these rate constants obey the empirical correlation equation k(Tau,rho(l)) = (rho(l)/rho(g))k(Tau,rho(g))G where typically G approximately 0.5-2.0. The rate correlation equation is usually explained by the isolated binary collision (IBC) hypothesis, which yields a theoretical result for G. However, the physical assumptions underlying the IBC hypothesis have often been criticized. Thus we propose a new purely mathematical hypothesis, which yields the correlation equation including a molecular formula for G. This hypothesis is that the relaxing molecule's normalized vibrational force autocorrelation function is rho-independent to order t(2). The hypothesis is checked numerically for three model dihalogen solute/rare gas solvent VER systems. It is found to be obeyed for 280 thermodynamic states, usually within 0.02% to 0.30%. An inertial dynamics mechanism is proposed as a tentative physical explanation for our mathematical hypothesis.