Despite the simplicity of theoretical models of supersonically turbulent, isothermal media, their predictions successfully match the observed gas structure and star formation activity within low-pressure (P/k < 10^5 K cm^-3) molecular clouds in the solar neighbourhood. However, it is unknown if these theories extend to clouds in high-pressure (P/k > 10^7 K cm^-3) environments, like those in the Galaxys inner 200 pc Central Molecular Zone (CMZ) and in the early Universe. Here we present ALMA 3mm dust continuum emission within a cloud, G0.253+0.016, which is immersed in the high-pressure environment of the CMZ. While the log-normal shape and dispersion of its column density PDF is strikingly similar to those of solar neighbourhood clouds, there is one important quantitative difference: its mean column density is 1--2 orders of magnitude higher. Both the similarity and difference in the PDF compared to those derived from solar neighbourhood clouds match predictions of turbulent cloud models given the high-pressure environment of the CMZ. The PDF shows a small deviation from log-normal at high column densities confirming the youth of G0.253+0.016. Its lack of star formation is consistent with the theoretically predicted, environmentally dependent volume density threshold for star formation which is orders of magnitude higher than that derived for solar neighbourhood clouds. Our results provide the first empirical evidence that the current theoretical understanding of molecular cloud structure derived from the solar neighbourhood also holds in high-pressure environments. We therefore suggest that these theories may be applicable to understand star formation in the early Universe.
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