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However, the factory slipped on one obvious detail: When the the rear brake
bridge was brazed on, he (she) somehow made the distance from the brake
pivot pin to the right seat stay one sixteenth of an inch longer than that
to the left chainstay. (about 1.25 mm).
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I assume you are talking about the brake center bolt hole? If it appears to be off-center by visually comparing to the wheel/tire, there could be several problems. It is very doubtful that the hole is off center in the bridge, or relative to the seat stays at the bridge.
1) The rear wheel dish could be incorrect; IF the frame was completely correct, then that would also be evident at the chain stays. BUT, it the wheel is centered at the chain stays, that is not a guarantee that the wheel is correct. I've seen many mechanics tweek wheels so they seem to sit centered in a frame.
2) The rear drops may not be symmetrical to the plane of the frame; again, just because the wheel may appear to be centered at the chain stays, or straight compared to the front wheel, doesn't mean the frame is correct. The type of check you performed probably wouldn't reveal small frame errors that could easily account for what you see.
3) The rear drops could be positioned incorrectly; the seat stay length, or inaccurate jigging and brazing/welding, could easily cause "wheel lean" at the brake bridge.
It takes someone with competent alignment techniques and experience to find small errors, so it depends on how "right" you want the frame to be vs. the potential cost to get it there. Vertical alignment error in the rear wheel is not very noticible compared to horizontal alignment error, but it depends on how picky you are and how you ride.
T check yourself, I would advise start with a verifiable "golden wheel" that you know to be dished correctly within 0.5mm or so. Then check that the rear drops are parallel. Be sure to install the wheel on the ground with some slight load on the bike before closing the skewer (skewer must not be bent at all), to ensure the axle is completely seated in the arch of the dropout. Observe the position at both the chain stays and brake bolt. My guess is that you'll still find lateral displacement at the brake bolt, and that effectively the chain stay length is off. The simplest way to fix is to file the dropout arch a little. You'd be shocked at the number of very high-end frame makers use this technique to "align" their frames. Since the modern aluminum frames are not very alignable by standard techniques, subtle arrors are taken out by filing. Often you can even see the file marks still in the droppout arch. They usually don't even re-finish the surface, and it's usually painted or clearcoated over.
Just file very conservatively. It doesn't take much material removal at the dropout to make a substantial difference at the wheel circumference. You'll probably be taking something like 0.005" to 0.010" off. It's hard for me to describe in short how to do this or where exactly to file, so if you don't see the process easily in your head, you might want to defer to a framebuilder or good mechanic. If you have a junk bike, a little trial-and-error practice goes a long way.
Jon Schaer
Columbus, OH