Not yet reviewed by Pith; the record is open.

We provide strong numerical evidence for a hidden multihyperuniform long-range order (MHLRO) in SiGeSn medium-entropy alloys (MEAs), in which the normalized infinite-wavelength composition fluctuations for all three atomic species are completely suppressed as in a perfect crystalline state. We show this MHLRO naturally leads to the emergence of short-range order (SRO) recently discovered in MEAs, which results in stable lower-energy states compared to alloy models with random or special quasi-random structures (SQSs) possessing no atomic SROs. The MHLRO MEAs approximately realize the Vegard's law, which offers a rule-of-mixture type predictions of the lattice constants and electronic band gap, and thus can be considered as an ideal mixing state. The MHLRO also directly gives rise to enhanced electronic band gaps and superior thermal transport properties at low temperatures compared to random structures and SQSs, which open up novel potential applications in optoelectronics and thermoelectrics. Our analysis of the SiGeSn system leads to the formulation of general organizing principles applicable in other medium- and high-entropy alloys (HEAs), and a highly efficient computational model for rendering realistic large-scale configurations of MEAs and HEAs.