The Holographic Circlette: Part 05 — Neutrino Masses from the Lattice Koide Formula

Audit note. This paper predates the framework's methodology audit of 2026-05-30. Three recharacterisations apply: (i) DRIFT M9: the lepton Koide phase _ = 2/9 and the neutrino phase _ = 3/9 as exact rationals are recharacterised as transcendentals 2/9 and 3/9 respectively, by Lindemann--Weierstrass on algebraic substrate amplitudes; the empirical lepton = 0. 222230 8 10^-6 sits 0. 89 from rational 2/9. (ii) §15 item 86 + correction: the ``universal 2/9 + 1/9 = 3/9'' framing reads as defect-index density d/N on the LQ = 0 codespace, with R_ = 2 from two Dirac paths retained at near-Locked tier (Koide amplitude Q = 2/3 holds to 10^-5) but the precise phase identifications retained at Proposition tier. (iii) §16. 3 search-space accounting: precision-match claims (such as ``1. 6\% agreement with oscillation data'') require formula-free We extend the circlette lattice mass formula to the neutrino sector. The CNOT gate's inactivity for neutrinos (LQ=0, I3=0) predicts Rₙu=1 and deltaₙu=1/3=3/9. The mass-squared ratio matches NuFIT 5. 3 to 1. 6%. Predicted masses: m1~0. 8 meV, m2~8. 7 meV, m3~50. 1 meV, with mass sum ~60 meV (normal ordering). The neutrino Koide ratio is Qₙu=1/2 exactly. v2. 0 (2026-06-12): an in-PDF dated status/erratum note has been added reflecting the June 2026 canon audit (DRIFT/ANCHOR ledger) ; see the paper's status note for the specific corrections, supersessions, or upgrades. 2026-06-20 legacy canon revision: This is a canon-reconciled legacy version. Neutrino/sterile/Majorana 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retains its historical derivation trail but carries a 2026-06-20 canon revision note identifying current status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.