  Fragmentation during the early stages of high-mass star formation is crucial
for understanding the formation of high-mass clusters. We investigated
fragmentation within thirty-nine high-mass star-forming clumps as part of the
Atacama Large Millimeter/submillimeter Array (ALMA) Survey of 70 $\mu$m Dark
High-mass Clumps in Early Stages (ASHES). Considering projection effects, we
have estimated core separations for 839 cores identified from the continuum
emission and found mean values between 0.08 and 0.32 pc within each clump. We
find compatibility of the observed core separations and masses with the thermal
Jeans length and mass, respectively. We also present sub-clump structures
revealed by the 7 m-array continuum emission. Comparison of the Jeans
parameters using clump and sub-clump densities with the separation and masses
of gravitationally bound cores suggests that they can be explained by clump
fragmentation, implying the simultaneous formation of sub-clumps and cores
within rather than a step-by-step hierarchical fragmentation. The number of
cores in each clump positively correlates with the clump surface density and
the number expected from the thermal Jeans fragmentation. We also find that the
higher the fraction of protostellar cores, the larger the dynamic range of the
core mass, implying that the cores are growing in mass as the clump evolves.
The ASHES sample exhibits various fragmentation patterns: aligned, scattered,
clustered, and sub-clustered. Using the Q-parameter, which can help to
distinguish between centrally condensed and subclustered spatial core
distributions, we finally find that in the early evolutionary stages of
high-mass star formation, cores tend to follow a subclustered distribution.
