  In this study we analyze {\sl Atmospheric Imaging Assembly (AIA)} and Hi-C
images in order to investigate absolute limits for the finest loop strands. We
develop a model of the occurrence-size distribution function of coronal loop
widths, characterized by a lower limit of widths $w_{min}$, a peak width $w_p$,
a peak occurrence number $n_p$, and a power law slope $a$. Our data analysis
includes automated tracing of curvi-linear features with the OCCULT-2 code,
automated sampling of the cross-sectional widths of coronal loops, and fitting
of the theoretical size distribution to the observed distribution. With
Monte-Carlo simulations and variable pixel sizes $\Delta x$ we derive a first
diagnostic criterion to discriminate whether the loop widths are unresolved
$(w_p/\Delta x \approx 2.5\pm0.2)$, or fully resolved (if $w_p/\Delta x >
2.7$). For images with resolved loop widths we can apply a second diagnostic
criterion that predicts the lower limit of loop widths, $w_{min} \approx 3
(\Delta x_{crit}-0.37")$ as a function of the critical resolution $\Delta
x_{crit}$. We find that the loop widths are marginally resolved in AIA images,
but are fully resolved in Hi-C images, where our model predicts a lower limit
of loop widths at $w_{min} \approx 100$ km and a most frequent (peak) value at
$w_p \approx 300$ km, in agreement with recent results of Brooks et al. This
result agrees with the statistics of photospheric granulation sizes and thus
supports coronal heating mechanisms operating on the macroscopic scale of
photospheric magneto-convection, rather than nanoflare heating models with
unresolved microscopic scales.
