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The interaction of Λ and Σ hyperons (Y) with nucleons (N) is strongly influenced by the coupled-channel dynamics. Due to the small mass difference of the NΛ and NΣ systems, the sizable coupling strength of the NΣ ↔ NΛ processes constitutes a crucial element in the determination of the NΛ interaction. In this letter we present the most precise measurements on the interaction of p pairs, from zero relative momentum up to the opening of the NΣ channel. The correlation function in the relative momentum space for p ⊕ p pairs measured in high-multiplicity triggered pp collisions at √s = 13 TeV at the LHC is reported. The opening of the inelastic NΣ channels is visible in the extracted correlation function as a cusp-like structure occurring at relative momentum k∗ = 289 MeV/c. This represents the first direct experimental observation of the NΣ ↔ NΛ coupled channel in the p system. The correlation function is compared with recent chiral effective field theory calculations, based on different strengths of the NΣ ↔ NΛ transition potential. A weaker coupling, as possibly supported by the present measurement, would require a more repulsive three-body NNΛ interaction for a proper description of the in-medium properties, which has implications on the nuclear equation of state and for the presence of hyperons inside neutron stars.