We analytically uncover the emergence of a universal solidlike phase in one-dimensional hard-sphere systems (Tonks gas). The associated pair distribution function $g\left(r\right)$ decays algebraically as ${(r/\xi )}^{-1/2}$, revealing quasi-long-range order. Beyond that correlation length $\xi \sim \ell /{(1-\varphi )}^2$, an exponential decay regime of the form $e^{-r/\xi }$ sets in, where $\ell$ denotes the mean particle spacing and $\varphi$ the packing fraction. We identify the onset of solidlike behavior near ${\varphi }^{*}\simeq 0.8$ at $\xi \approx \ell$, where the crossover point coincides with the third neighbor shell. Our findings establish a clear theoretical framework for emerging crystallization in one dimension and introduce criteria for detecting incipient solid order in constrained geometries.

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• Classical statistical mechanics
• Confinement
• Crystallization
• 1-dimensional systems