At What Scale Is the Cold Spot? Wavelet Response of a Compensated Spot Across Scales and the Scale-Selection Bias in Its Reported Significance

The Cold Spot was found by a wavelet, and wavelets are used at many scales: the spherical Mexican hat's response to the spot peaks at a particular scale, and the spot's reported significance has always been quoted at the scale where it looks largest. This paper computes the response curve and prices the selection. A compensated spot of the published dimensions returns its largest wavelet coefficient at a scale of 9 degrees, with the response falling to half its peak within roughly a factor of 2.2 in scale on either side; the spot is a genuinely scale-selected object, not an artefact of one filter. But the null distribution of the maximum coefficient over eight standard scales is wider than any single scale's: a global three-sigma detection requires a single-scale coefficient of 3.77 sigma, not 3.00. Significances quoted at the best scale without that correction overstate the spot's rarity by the corresponding margin, a correction that applies to every wavelet-found feature in the sky. The study is computed, not measured.