Plumbing – Anyone know what this 4 inch pipe on the outside of the house could be

It's not hammer time, it's thermal expansion. As the hot water travels through the pipe, the pipe itself heats up and expands. As this happens, fasteners and any materials in contact with the pipe experience friction and, at times, the pipe moves slightly against that material and causes a poping sound. It's like snapping your fingers. We hear this all the time with other materials in other circumstances if you think about it. The frequency of the poping changes as the pipe heats up. The fix would be to better secure the pipe (not tight, but with an intermediate material) to the studs or block as necessary to keep it from rattling or "poping". If attached to concrete, insulate the pipe with something, anything, to keep it from contacting the concrete.

It an abandoned sewage and vent pipe. It was replaced, and the roof patched where it used to exit. Apparently they never got around to finishing the job, or just figured it wasn't any problem leaving it like it was. As to whether it's safe, since it hasn't fallen yet, it probably won't. But, you could get a ladder and pull on it to make sure. And no, there isn't a structural integrity issue. I'd finish off the basement ceiling to hide it.