the sampled heavy-tail band matrices often reported sharp interior beta_c_estimate values near about 1.69 to 3.71 with vanishing bracket_width, and the top spectral gap ratios were enormous, often in the hundreds or thousands. But the actual detection fraction was almost always 0.0 and only rarely reached about 0.33, while spike overlap stayed tiny at about 0.004 to 0.09, far below the 0.18 detection criterion even when the outlier gap looked dramatic.