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A unified fundamental understanding of interfacial thermal transport is missing due to the complicated nature of interfaces. Because of the difficulty to grow high-quality interfaces and lack of materials characterization, the experimentally measured thermal boundary conductance (TBC) in the literature are usually not the same as the ideally modelled interfaces. This work provides a systematic study of TBC across the highest-quality (atomically sharp, harmonic-matched, and ultraclean) epitaxial (111) Al||(0001) sapphire interfaces to date. The comparison of measured high TBC with theoretical models shows that elastic phonon transport dominates the interfacial thermal transport and other mechanisms play negligible roles. This is confirmed by a nearly constant transmission coefficient by scaling the TBC with the Al heat capacity and sapphire heat capacity with phonon frequency lower than 10 THz. Finally, the findings in this work will impact applications such as electronics thermal management, thermoelectric energy conversion, and battery safety. The mechanism of thermal transport at solid interfaces depends on many parameters in particular the quality of the interface. Here, the authors compare experimental and calculated thermal boundary conductance across high-quality harmonic-matched epitaxial Al-sapphire interfaces and find that elastic phonon processes dominate the ultra-clean interfaces. [ABSTRACT FROM AUTHOR]