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I think I was wrong about stat("/dev/fd/NN") returning the current 
time as mtime for a pipe.  I think to manifest this problem, kinit 
has to initially open() and stat() the profile before printf has 
finished writing to the pipe.  (It will then block reading the data 
from printf, but it already recorded the timestamp, and it doesn't 
stat() again afterwards.)  That's much less likely than the clock 
second rolling over between profile_init and profile_get.

I was able to produce a failure using many repeated invocations of 
KRB5_KDC_PROFILE=<(printf ...) kinit -k -t KDB:, but it took a long 
time.  To produce a failure in just one try, I wrote a simple test 
program:

int
main(int argc, char **argv)
{
    profile_t profile;
    char *str;

    if (profile_init_path(argv[1], &profile) != 0)
        abort();
    if (profile_get_string(profile, "a", "b", NULL, "no", &str) != 0)
        abort();
    printf("%s\n", str);
    profile_release_string(str);
    return 0;
}

and ran it with:

./a.out <(sleep 1; printf "[a]\nb=yes\n")