/usr/lib/x86_64-linux-gnu/libsmumps_ptscotch.so is in libmumps-ptscotch-dev 5.1.2-4.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libsmumps_ptscotch-5.1.2.so
/usr/lib/x86_64-linux-gnu/libsmumps_ptscotch-5.1.2.so