Cold freeze out of superheavy nonthermal dark matter

We present a unified framework, the "X miracle", in which dark matter consists of superheavy, nonthermal X particles whose relic abundance is determined not by the conventional weak-scale, semi-relativistic ("hot") freeze-out of WIMPs, but by annihilation or decay occurring within the smallest and earliest gravitationally bound objects. Unlike thermal WIMPs, which decouple at velocities of order 0.3$c$ with relic abundance $\rho_{\infty}$ set by weak-scale interactions, X particles are produced nonthermally with an initial overabundance $\rho_{ini}\gg \rho_{\infty}$. They become nonrelativistic extremely early, redshift to ultra-cold velocities, allowing collapse into compact bound structures characterized by a novel quantum-gravitational scale, $r_X=4\hbar^2/Gm_X^3=10^{-13}m\gg \hbar/m_Xc$, much larger than the Compton wavelength. The framework predicts a particle mass of $10^{12}$GeV and an enhanced cross section of $10^{-21}$m$^3$/s. Overlapping particle wavefunctions in these compact structures drive annihilation or decay into additional radiation, leading to a "cold" freeze-out that converts most of $\rho_{ini}$ into radiation while leaving a relic density $\rho_{\infty}$. Solutions to the Boltzmann equation indicate that an extreme depletion, with only one particle in a billion surviving, yields an additional radiation contribution $\Delta N_{eff}\approx$0.4, which could help alleviate the Hubble tension. For particles of $10^{12}$GeV, the scenario predicts an energy production rate density of $10^{45}$erg Mpc$^{-3}$Yr$^{-1}$ and particle lifetime $10^{16}$years (or coupling $\alpha_X=0.09$), consistent with current UHECR bounds. Early collapse at $10^{-6}$s may release binding energy as high-frequency (100kHz) gravitational waves or ultralight GUT-scale axions. Superheavy sterile neutrinos provide a natural particle physics realization, linking dark matter to neutrino mass and baryogenesis. If gravitational production dominates, this framework favors high-scale inflation and efficient reheating. The "X miracle" thus demonstrates that dark matter need not be weak-scale: gravitational dynamics can control freeze-out and evolution, producing multi-messenger observational signatures in UHECRs, axions, gravitational waves, and small-scale structures.