So, after hours of work the SMART-Test successfully runs. It detected no
problems.
I made parallel a few further experiments.
It tested again the checksums on the XFS-Filesystem with a 4.5 GB big file.
The problems occur to stay. The checksum is after a reboot right. The
signature test succeded successfully. For period of one ore two minutes the
checksums stays correct. Then the value changed to a wrong value, stays the
same for one ore two minutes and then the value changed again. The
Signature-Tests then reports always "signature failed".
Then i testet the checksums with the Trisquel-Core-Utils against the
NTFS-Filesystem with the same 4.5 GB big file. There the problems did not
occur. Always the correct checksums where calculated and the Signature Test
always reported that the signature is correct.
So it seems to be Filesystem-specific problem. The problem occurs on XFS and
EXT4, but not on NTFS.
For me that's a workaround for the future.
So it seems to be problem on the GNU/Linux coreutils!?
Greatings,
elayer