Brake piece grinding against fork This brake was installed on a fixed-gear that did not come with any brakes.  The nut on one side rubs against the fork, and over time it rotates and presses the pad against the wheel.

Here is where it is rubbing:

The workaround is to unscrew the break and re-center it, but it wiggles its way back and I'd rather a more permanent solution.

The first thing that occurs to me is to put a washer on the bolt between the brake and the fork, but the bolt is just barely long enough to screw into the nut.  Could I get a washer and a longer nut to handle this?  Would that fix the problem?

The other idea I had was to file down the nut in the photo so it doesn't contact the fork, but that just feels like a bad idea.

[Edit]
As requested, here's a shot that shows the whole brake:
@Adam Rice is almost there, diagram and suggestion included for what to do now...

First, you need a curved 18mm diameter washer between the brake and the fork. Your brake is a Shimano clone, here is how the original Shimano drive works out:



Note that there is no serrated washer between the curved washer and the brake.

Secondly, you need a 27mm long pivot nut on the back. If your existing nut is 18mm then that is a front nut too, but not suited for your fork. If the nut is 12.5mm or shorter then it is for the back brake.

What now?

Visit your local bike shop on a quieter day of the week and ask for help from the workshop with your predicament. Either get the bike booked in (and expect to pay their minimum workshop time booking slot) or buy the 18mm washer + 27mm nut and do it yourself.

All bike shops have a drawer full of such parts, they may charge ~50p per nut/bolt/washer which is not representative of the cost of the bit or their time to find it for you.

If you are buying something else, e.g. treat yourself to a new track pump, then they may be more helpful and do you the washer/nut out of good will.