Recent calculations based on the same HAL QCD Collaboration $N{\mathrm{\Omega }}_{ccc}$ lattice-QCD potential have reached conflicting conclusions on whether the $NN{\mathrm{\Omega }}_{ccc}$ system supports a bound state. The problem is reexamined here with a highly correlated exponential variational method. The near-threshold state is directly evaluated without coupling-constant extrapolation, and the Coulomb interaction is treated through analytically exact matrix elements. Without Coulomb, the variational energy lies below the $d+{\mathrm{\Omega }}_{ccc}$ threshold, indicating a shallow $\left(0\right)1/2^{+}$ $d\text{–}{\mathrm{\Omega }}_{ccc}$ bound state with a binding energy of about 0.025 MeV. The resulting bound state is spatially extended, with $\sqrt{\langle r_{N\mathrm{\Omega }}^2\rangle }\approx 17.5$ fm, consistent with the near-threshold scale ${\kappa }^{-1}\approx 24$ fm (rms $\approx 17$ fm). When Coulomb repulsion is included, the variational energy approaches the threshold from above while the rms separation grows strongly and remains unconverged; no binding signal is found within the explored basis sizes. Complex-scaling calculations likewise yield no $\theta$-stable resonance pole. In the Coulomb-free model, a survey of the nine spin-channel/time-slice combinations finds only the ${}^{3}S_1$, $t/a=16$ case below threshold.

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• Few-body systems
• Nuclear structure & decays