Remark: Why ordinary windowing was insufficient

Without the subtraction in (eq:windowconstruction), a compact temporal window generally has nonzero Fourier value at zero. The predecessor bound ${\Gamma }_{\ell }\le 1$ alone would then not prove integrability against $n(\omega )\lesssim 1/\omega$. We do not import an unproved low-frequency greybody asymptotic to bypass this issue.