The first column of the lepton mixing matrix carries two independent magnitude conditions: the trimaximal norm $|U_{e1}{|}^2=2/3$ and the $\mu –\tau$ balance $|U_{\mu 1}|=|U_{\tau 1}|$. We parametrize their violation by ${ϵ}_1\equiv \frac{3}{2}|U_{e1}{|}^2-1$ and ${ϵ}_2\equiv 3(|U_{\tau 1}{|}^2-|U_{\mu 1}{|}^2)$ and show that current data treat the two differently in central value: with the first JUNO measurement included, ${ϵ}_1=+0.014\pm 0.010$ is consistent with zero, while ${ϵ}_2=+0.29_{-0.13}^{+0.07}$ is large but disfavors zero at only $1.5\sigma$ on the profile likelihood of the global fit, the phase that drives it being still poorly measured. This asymmetry selects a specific framework, which we call the $\pi /12$ model. Its neutrino sector is ${\mathrm{TM}}_1$, supplemented by the electron-row condition $|U_{e2}|/|U_{e3}|=2+\sqrt{3}$ that fixes ${\sin }^2{\theta }_{13}=(2-\sqrt{3})/12=0.02233$ and ${\sin }^2{\theta }_{12}=0.31811$. A charged-lepton 2–3 rotation $R_{23}({\theta }_e,\alpha )$ then leaves the electron row exactly invariant and generates ${ϵ}_2=\sin 2{\theta }_e\cos \alpha$. In a concrete $S_4\times C_4\times C_3\times C_2$ realization, the rotation arises from a single additional flavon whose alignment forces $\alpha =0$; a natural rotation angle ${\theta }_e\simeq 2°$ then reproduces the observed departure of ${\theta }_{23}$ from maximal while pinning the $CP$ phase to $\delta =272°\pm 2°$, near-maximal $CP$ violation with ${ϵ}_2=-0.066$. The framework thereby converts the current ${\theta }_{23}–\delta$ measurements into a sharp test: the predicted $\delta$ sits $1.7\sigma$ from the present central value on the same profile likelihood, the predicted ${ϵ}_2$ has the opposite sign to the measured one, and the Hyper-Kamiokande design precision of 20° on $\delta$ resolves the question at the $3\sigma$ level. The neutrino-sector mass predictions are inherited unchanged, $\mathrm{\Sigma }{m}_{\nu }=65.6\mathrm{meV}$ and $m_{\beta \beta }=5.4\mathrm{meV}$, placing the model at the current DESI bound in $\mathrm{\Lambda }$ cold dark matter .

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• Cabibbo–Kobayashi–Maskawa matrix
• Electroweak interaction
• Hypothetical particle physics models
• Particle astrophysics