What does the LHC physics program have to do with military applications?

Doesn't all of physics have some military implications?

But at least they make everything public knowledge, instead of keeping it secret and only selling it to one nation.

> any physics has military implications.

Fixed that for you. That's been the case since we discovered sticks and stones, but it doesn't mean that CERN is lying when they say they want to focus on non-military areas.

Let's not assume the worst of an institution that's been fairly good for the world so far.

sure, though "have no concern with" comes across to me less like ""we avoid building anything that could be conceivably used as a weapon by anyone", and more as "We're not in that business, but it's not our concern if you manage to stab yourself with it. It's not secret".