The Holographic Circlette: Part 09 — Topological Isolation of the Electron and the Factorisation of the PMNS Matrix

Audit note. This paper predates the framework's methodology audit of 2026-05-30. The Koide bit-to-mass alignment (n=0→τ, n=1→ e, n=2→μ) used in the PMNS derivation chain is now read under DRIFT M9: the Koide phase δ = 2/9 is recharacterised as transcendental ≈ 2/9 via Lindemann--Weierstrass on algebraic substrate amplitudes. The bit-ordering identification n = 2G_0 + G_1 from algorithmic depth (anchored at §15 item 81) survives at Proposition tier; the PMNS factorisation chain (CNOT generation-gate analysis, R1-shielding of the electron, virtual colour-bridge loop for θ₁₃, ν_R-defect origin for θ₁₂) is structural and unaffected by the M9 recharacterisation. Readers should treat the specific numerical predictions (θ₂₃ ≈ 38°, θ₁₃ ≈ 6°) at Proposition tier pending the formula-freedom audit at ANCHOR §16.3. We evaluate the quantum walk operator at higher loop orders. The tree-level CNOT gate mixes muon and tau states (theta_23~38 degrees). The electron is topologically shielded by the R1 constraint. Reactor mixing theta_13~6 degrees arises at loop order n>=3 via virtual quark excursions, rigorously proving the PMNS factorisation theorem. 2026-06-20 legacy canon revision: This is a canon-reconciled legacy version. PMNS factorisation 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retains its historical derivation trail but carries a 2026-06-20 canon revision note identifying current status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.