  The thermal state of the intergalactic medium (IGM) at z < 6 constrains the
nature and timing of cosmic reionization events, but its inference from the
Ly-alpha forest is degenerate with the 3-D structure of the IGM on ~100 kpc
scales, where, analogous to the classical Jeans argument, the pressure of the
T~$10^4$ K gas supports it against gravity. We simulate the IGM using smoothed
particle hydrodynamics, and find that, at z < 6, the gas density power spectrum
does not exhibit the expected Jeans filtering cutoff, because dense gas in
collapsed halos dominates the small-scale power masking pressure smoothing
effects. We introduce a new statistic, the real-space Ly-alpha flux,
$F_\mathrm{real}$, which naturally suppresses dense gas, and is thus robust
against the poorly understood physics of galaxy formation, revealing pressure
smoothing in the diffuse IGM. The $F_\mathrm{real}$ power spectrum is
accurately described by a simple fitting function with cutoff at $\lambda_F$,
allowing us to rigorously quantify the filtering scale for the first time: we
find $\lambda_F$ = 79 kpc (comoving) at z=3 for our fiducial thermal model.
This statistic has the added advantage that it directly relates to observations
of correlated Ly-alpha forest absorption in close quasar pairs, recently
proposed as a method to measure the filtering scale. Our results enable one to
quantify the filtering scale in simulations, and ask meaningful questions about
its dependence on reionization and thermal history. Accordingly, the standard
description of the IGM in terms of the amplitude $T_0$ and slope $\gamma$ of
the temperature-density relation $T = T_0\Delta^{\gamma-1}$ should be augmented
with a third filtering scale parameter $\lambda_F$.
