= Solution
The <lepton mixing matrix> relates <Charged current>[charged-current] <neutrino> <Flavor eigenstate>[flavour fields] to <Mass eigenstates>[mass eigenfields]: $\nu_{\alpha L}=\sum_iU_{\alpha i}\nu_{iL}$. Nondegenerate <masses> then give relative propagation <phases> and <Flavor eigenstate>[flavour] <Neutrino oscillations>[oscillations]. This is the three-massive-neutrino extension of the minimal massless-neutrino Standard Model.
A <Unitary matrix>[unitary] three-by-three <matrix> has nine real parameters: three <rotation> angles and six <phases>. For <Dirac field>[Dirac] leptons, the independent field rephasings remove five <phases>, because one common <phase> acts trivially. Three angles and one physical <CP violation>[Dirac phase] remain. For <Majorana neutrino>[Majorana] <neutrinos> two additional <phases> cannot be removed, but they cancel from ordinary <Neutrino oscillation>[oscillation] <probabilities>.
\b[The <phases> printed in the lower two rows do not give a <unitary matrix> for general $\delta$.] A consistent convention is $U=R_{23}U_{13}(\delta)R_{12}$, where the real <rotations> use the indicated <Mixing angle>[mixing angles] and
$$
\boxed{U_{13}(\delta)=\begin{pmatrix}c_{13}&0&s_{13}e^{-i\delta}\\0&1&0\\-s_{13}e^{i\delta}&0&c_{13}\end{pmatrix}.}
$$
The lower-row <phase> factors in the resulting full <matrix> are $e^{+i\delta}$, opposite to the $e^{-i\delta}$ in $U_{e3}$. For the source's all-minus assignment, the <Scalar field>[scalar] product of the <electron> row with the conjugated <muon> row is $-2i\,s_{23}s_{13}c_{13}\sin\delta$, which is nonzero at $\delta=\pi/2$ and nonzero <Flavour mixing>[mixing]. This supplies an explicit counterexample. The electron-row moduli used below are unaffected by this correction.<Review of Particle Physics by Particle Data Group (2022)>[Neutrino Masses, Mixing, and Oscillations, §14.3 and equation (14.34): opposite signs of the physical phase in the standard matrix]{ref}
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