| Summary: | Charm meson oscillations are observed in a time-dependent analysis of the ratio of D⁰ → K⁺π⁻π⁺π⁻ to D⁰ → K⁻π⁺π⁻π⁺ decay rates, using data corresponding to an integrated luminosity of 3.0 fb^⁻1 recorded by the LHCb experiment. The measurements presented are sensitive to the phase-space averaged ratio of doubly Cabibbo-suppressed to Cabibbo-favored amplitudes rDK3π and the product of the coherence factor RDK3π and a charm mixing parameter y'K3π. The constraints measured are rDK3π=(5.67±0.12)×10^-2, which is the most precise determination to date, and RDK3π . y'K3π=(0.3 ± 1.8) × 10^-3, which provides useful input for determinations of the CP-violating phase γ in B^± → DK^±, D → K∓π^±π^∓π^± decays. The analysis also gives the most precise measurement of the D⁰ → K⁺π⁻π⁺π⁻ branching fraction, and the first observation of D0 - D0 oscillations in this decay mode, with a significance of 8.2 standard deviations.
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