  We investigate the short, medium, and long-range structure of soft disk
configurations for a wide range of area fractions and simulation protocols by
converting the real-space spectrum of volume fraction fluctuations for windows
of width $L$ to the distance $h(L)$ from the window boundary over which
fluctuations occur. Rapidly quenched unjammed configurations exhibit
size-dependent super-Poissonian long-range features that, surprisingly,
approach the totally-random limit even close to jamming. Above and just below
jamming, the spectra exhibit a plateau, $h(L)=h_e$, for $L$ larger than
particle size and smaller than a cutoff $L_c$ beyond which there are long-range
fluctuations. The value of $h_e$ is independent of protocol and characterizes
the putative hyperuniform limit. This behavior is compared with that for
Einstein solids, with and without hyperuniformity-destroying defects. We find
that key structural features of the particle configurations are more evident,
as well as easier and more intuitive to quantify, using the real-space spectrum
of hyperuniformity lengths rather than the spectral density.
