The Holographic Circlette: Part 06 — Topological Origin of Large Lepton Mixing and the PMNS Matrix

Audit note. This paper predates the framework's methodology audit of 2026-05-30. Two recharacterisations apply: (i) DRIFT M9: the Koide / Berry phase δ = 2/9 identification that anchors the lepton-sector amplitudes is now read as transcendental ≈ 2/9 via Lindemann--Weierstrass, not as exact rational; the empirical lepton Koide δ = 0.222230 ± 8 × 10⁻⁶ sits 0.89σ from rational 2/9. (ii) §15 item 86 + 2026-05-29 correction: the universal-2/9 ``Berry phase'' framing reads as index density d/N on the lepton-Feshbach codespace rather than as Chern number; the type-split between (A) rational couplings and (B) transcendental phases applies. The PMNS factorisation derivation chain (zero-controlled CNOT dormancy on LQ = 0; k-indexed walk-operator structure; bimaximal zeroth-order θ₁₂) survives at the structural level; the precise amplitude assignments tied to δ = 2/ We project the identical transition operator onto the LQ=0 lepton subspace to evaluate the PMNS neutrino mixing matrix. Because leptons lack colour superposition, the walk operator acts unsuppressed. We derive theta_12~43.7 degrees with theta_13=theta_23=0 at zeroth order (bimaximal ansatz), resolving why lepton mixing angles are large while quark mixing angles are small. 2026-06-20 legacy canon revision: This is a canon-reconciled legacy version. PMNS delta/holonomy status changed The paper retains its historical derivation trail but carries a 2026-06-20 canon revision note identifying current status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.