The ALMA Survey of 70 $\mu$m dark High-mass clumps in Early Stages
  (ASHES). I. Pilot Survey: Clump Fragmentation
  (Abridged) ASHES has been designed to systematically characterize the
earliest stages and to constrain theories of high-mass star formation. A total
of 12 massive (>500 $M_{\odot}$), cold (<15 K), 3.6-70 $\mu$m dark prestellar
clump candidates, embedded in IRDCs, were carefully selected in the pilot
survey to be observed with ALMA. We mosaiced each clump (~1 arcmin^2) in dust
and line emission with the 12m/7m/TP arrays at 224 GHz, resulting in ~1.2"
resolution (~4800 AU). As the first paper of the series, we concentrate on the
dust emission to reveal the clump fragmentation. We detect 294 cores, from
which 84 (29%) are categorized as protostellar based on outflow activity or
'warm core' line emission. The remaining 210 (71%) are considered prestellar
core candidates. The number of detected cores is independent of the mass
sensitivity range of the observations. On average, more massive clumps tend to
form more cores. We find a large population of low-mass (<1 M) cores and no
high-mass (>30 $M_{\odot}$) prestellar cores. The most massive prestellar core
has a mass of 11 $M_{\odot}$. From the prestellar CMF, we derive a power law
index of 1.17+-0.1, slightly shallower than Salpeter (1.35). We use the MST
technique to characterize the separation between cores and their spatial
distribution, and derive mass segregation ratios. While there is a range of
core masses and separations detected in the sample, the mean separation and
mass of cores are well explained by thermal fragmentation and are inconsistent
with turbulent Jeans fragmentation. The core spatial distribution is well
described by hierarchical subclustering rather than centrally peaked
clustering. There is no conclusive evidence of mass segregation. We test
several theoretical conditions, and conclude that overall, competitive
accretion and global hierarchical collapse scenarios are favored over the
turbulent core accretion scenario.
