C. Cahillane

I have finally decided to check if linearly adding A_pu for uncertainty is okay.  It turns out it's conservative, and we get lower uncertainty bars if we propagate correctly.
The equation for A_pu is:
A_pu = A_pum + A_uim 

We had been propagating uncertainty linearly like this:
σ_|A_pu| = |A_pum| * σ_|A_pum| + |A_uim| * σ_|A_uim|
σ_φ_A_pu = σ_φ_A_pum + σ_φ_A_uim

This is bad.
The correct way to propagate it is quadratically.  I do not yet have a nice write-up of my equations, but they will be included in DCC T1400586 hopefully soon.  There is no mysterious method of uncertainty propagation used, just simple first order Taylor expansion.
The plot below is my comparison of the correct vs. linear uncertainty propagation.
Plot 1 is the comparison including systematic errors in uncertainty.  Plot 2 is statistical uncertainty only.