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Extreme giant molecular clouds in the luminous infrared galaxy NGC 3256

(Abridged) We present a cloud decomposition of $^{12}$CO (2--1) observations of the merger and nearest luminous infrared galaxy, NGC 3256. 185 spatially and spectrally resolved clouds are identified across the central $\approx$ 130 kpc$^{2}$ at 90 pc resolution and completeness is estimated. We compare our cloud catalogue from NGC 3256 to ten galaxies observed in the PHANGS-ALMA survey. Distributions in NGC 3256 of cloud velocity dispersions, luminosities, CO-estimated masses, mass surface densities, virial masses, virial parameters, size-linewidth coefficients, and internal turbulent pressures are significantly higher than in the PHANGS-ALMA galaxies. Cloud radii are slightly larger in NGC 3256 and free-fall times are shorter. The distribution of cloud eccentricities in NGC 3256 is indistinguishable from many PHANGS-ALMA galaxies, possibly because the dynamical state of clouds in NGC 3256 is similar to that of nearby spiral galaxies. However, the narrower distribution of virial parameters in NGC 3256 may reflect a narrower range of dynamical states than in PHANGS-ALMA galaxies. No clear picture of cloud alignment is detected, despite the large eccentricities. Correlations between cloud properties point to high external pressures in NGC 3256 keeping clouds bound and collapsing given such high velocity dispersions and star-formation rates. A fit to the cloud mass function gives a high-mass power-law slope of $-2.75^{+0.07}_{-0.01}$, near the average from PHANGS-ALMA galaxies. We also compare our results to a pixel-based analysis of these observations and find molecular-gas properties agree qualitatively, though peak brightness temperatures are somewhat higher and virial parameters and free-fall times are somewhat lower in this cloud-based analysis.