= Solution
<Aliasing> occurs because a sampled grid cannot distinguish certain different continuous <Fourier modes>. With spacing $h$, modes $k$ and $k+2\pi m/h$ agree at every sample point. Frequencies above the <Nyquist frequency> can therefore be misidentified as lower frequencies, changing the resolved spectrum and its subsequent diffusion rate.
For the corrected grid, $h=10/128\,\mathrm{cm}$ and the maximum resolved angular wavenumber is approximately $\pi/h\simeq40.2\,\mathrm{cm^{-1}}$. The initial <Gaussian function> has spectral envelope proportional to $e^{-a|k|^2/4}$. At that one-coordinate cutoff the factor is about $e^{-40.4}$, so the omitted high-frequency tail is tiny. Its continuation mismatch at the distant edges is also tiny. \b[Significant aliasing is not expected for this resolved, smooth initial condition.]
The <linear> constant-coefficient <heat equation> only damps existing modes; it does not generate higher frequencies through nonlinear products. An unresolved narrow peak, a sharp edge or a nonlinear source would require a separate resolution assessment. The duplicated-endpoint grid issue described above should not be diagnosed as high-frequency folding.
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