Do neutrino oscillations violate CP symmetry?
In plain words
If neutrinos and antineutrinos oscillate differently, leptons break the matter-antimatter mirror symmetry called CP. This may link to why the universe contains matter.
Precise statement
Measure the PMNS phase $\delta_{\mathrm{CP}}$ and determine whether $\operatorname{sin}(\delta_{\mathrm{CP}}) \ne 0$ at $\ge 5\sigma$ using $\nu_{\mu} \to \nu_e$ versus anti-nu_mu -> anti-nu_e appearance. Answer: $\delta_{\mathrm{CP}}$ with uncertainty $\sim 10\text{ to }20\ \mathrm{deg}$ and the yes-no CP verdict.
What would settle it
DUNE and Hyper-Kamiokande appearance data over about 10 years, after the mass ordering is fixed.
Status in the literature
Unverified note
The 2025 NOvA plus T2K joint analysis (Nature) excludes CP conservation at about $3\sigma$ only if the ordering is inverted; for normal ordering CP conservation remains allowed.