= Solution
Both <Kaluza-Klein theory> and the <brane-world scenario> use a higher-dimensional bulk. Ordinary Kaluza–Klein matter propagates in the compact directions, producing observable massive towers; absence of weak-scale charged modes requires roughly $R^{-1}\gtrsim\mathrm{TeV}$, or \b[$R\lesssim2\times10^{-19}\,\mathrm m$], and traditional constructions often take Planck-size radii. Brane-world matter is localized while gravity explores the bulk, so large flat dimensions can reach the \b[submillimetre order of magnitude] discussed in the 2004 setting. For $n$ flat dimensions, $M_{\mathrm{Pl}}^2\sim M_D^{n+2}(2\pi R)^n$. These are model-dependent scales, not universal maxima: warped gravity-localizing models can have a noncompact extra dimension. The historical large-flat-dimension mechanism is described in https://arxiv.org/abs/hep-ph/9803315.
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