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Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths , densities ). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson-Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (. This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems).

Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres