Role of β (columns) and accuracy (rows) of associated Z_p, for fixed Δ = 2/3. Shown are PDFs (y-axis) of C_f (x-axis), 1000 random data sets, powers p = 1,...,5 for β = 0.0476 (first column), β = 0.17 (second column), β = 1/3 (third column), and β = 2/3 (fourth column). Corresponding exact co-dimensions (red lines) are, from left to right: C = 0.7, C = 0.8, C = 1, and C = 2. Individual rows from top to bottom contain accuracies of 20%, 10%, 5%, 2%, 0.5%, and 0.1%. As can be seen, the larger β, the more severe are the consequences of inaccuracies in the Z_p. Histograms in the upper right (large β, low accuracy of the Z_p) look worst. We note that axis ranges differ among panels, to best capture the shape of each histogram.