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We examine whether protons and deuterons in the crystal of KHDCO at 300 K are particles or matter waves. The neutron scattering function measured over a broad range of reciprocal space reveals the enhanced diffraction pattern anticipated for antisymmetrized macroscopic states for protons (fermions). These features exclude a statistical distribution of protons and deuterons. Raman spectra are consistent with a mixture of KHCO and KDCO sublattices whose isomorphous structures are independent of the isotope content. We propose a theoretical framework for decoherence-free proton and deuteron states.

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