Taking the ulimit suggestion above, I get the following output:

core file size          (blocks, -c) 0
data seg size           (kbytes, -d) 36864
max nice                        (-e) 0
file size               (blocks, -f) unlimited
pending signals                 (-i) 38912
max locked memory       (kbytes, -l) 32
max memory size         (kbytes, -m) 36864
open files                      (-n) 8192
pipe size            (512 bytes, -p) 8
POSIX message queues     (bytes, -q) 819200
max rt priority                 (-r) 0
stack size              (kbytes, -s) 8192
cpu time               (seconds, -t) 10
max user processes              (-u) 16
virtual memory          (kbytes, -v) 36864
file locks                      (-x) unlimited
[download]

By my reading, then, the program has 36 megabytes of available RAM, and an 8 megabyte stack. Actually more than the hosting-service promised to deliver, and unquestionably more than enough resources to run this program.

And yet... it doesn't run. If it claims to be “out of memory,” all I can say is ... something having to do with cow excrement.

I still don't know the real reason why it cannot allocate memory, but I'm certain that it's not actually “running out of” anything. Something is different between this case and all others... I just can't determine what it is.