{
  "abstract": "The first column of the lepton mixing matrix carries two independent magnitude conditions: the trimaximal norm $|U_{e1}|^2=2/3$ and the $μ$--$τ$ balance $|U_{\\mu1}|=|U_{\\tau1}|$. Parameterizing their violation by $\\varepsilon_1\\equiv\\tfrac32|U_{e1}|^2-1$ and $\\varepsilon_2\\equiv3(|U_{\\tau1}|^2-|U_{\\mu1}|^2)$, we show that current data treat the two differently in central value: with the first JUNO measurement included, $\\varepsilon_1=+0.014\\pm0.010$ is consistent with zero, while $\\varepsilon_2=+0.29^{+0.07}_{-0.13}$ is large but disfavors zero at only $1.5σ$ on the profile likelihood of the global fit, since the phase that drives it remains poorly measured. This asymmetry selects a specific framework, the $π/12$ model. Its neutrino sector is $\\mathrm{TM}_1$, supplemented by the electron-row condition $|U_{e2}|/|U_{e3}|=2+\\sqrt3$ that fixes $\\sin^2θ_{13}=(2-\\sqrt3)/12=0.02233$ and $\\sin^2θ_{12}=0.31811$. A charged-lepton 2--3 rotation $R_{23}(θ_e,α)$ leaves the electron row exactly invariant and generates $\\varepsilon_2=\\sin2θ_e\\cosα$. In a concrete $S_4\\times C_4\\times C_3\\times C_2$ realization, a single additional flavon alignment forces $α=0$; a natural angle $θ_e\\simeq2^\\circ$ then reproduces the observed departure of $θ_{23}$ from maximal while pinning $δ=272^\\circ\\pm2^\\circ$, near-maximal CP violation with $\\varepsilon_2=-0.066$. The result is a sharp test: the predicted $δ$ sits $1.7σ$ from the present central value on the same profile likelihood, the predicted $\\varepsilon_2$ has the opposite sign to the measured one, and the Hyper-Kamiokande design precision of $20^\\circ$ on $δ$ resolves the question at the $3σ$ level. The mass predictions are inherited unchanged, $Σm_ν=65.6$ meV and $m_{ββ}=5.4$ meV, placing the model at the current DESI bound in $Λ$CDM.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08394",
  "author_total": 1,
  "authors": [
    {
      "name": "Vernon Barger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8vvmq28qayhng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08394",
  "fulltext_url": null,
  "id": "8vvmq28qayhng",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08394",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.08394",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8vvmq28qayhng.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2608.08394",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08394"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "The $π/12$ model: trimaximal first-column lepton mixing with charged-lepton $μ$--$τ$ breaking",
  "title_text": "The π/12 model: trimaximal first-column lepton mixing with charged-lepton μ--τ breaking",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/8vvmq28qayhng",
  "venue": "arXiv",
  "versions": []
}