A Geometric Mechanism for the Koide Relation, with a Preregistered Tau-Mass Kill Test

This package preregisters a candidate geometric mechanism for the Koide relation among the charged-lepton masses, Q = (m_e + m_mu + m_tau) / (√m_e + √m_mu + √m_tau)² = 2/3 (Y. Koide, 1981), together with a dated, public kill test for the tau mass. Credit where due: solving Q = 2/3 for the tau mass given the measured electron and muon masses yields m_tau = 1776.96903 MeV — that value and the relation are Koide's, public since 1981, not this author's. This note contributes two things only: (1) a candidate geometric mechanism for why Q = 2/3 would hold exactly — charged leptons as closed circulations on the edge axes of a cube, Q = 2/3 as a 45° ("horn-torus") condition (the equivalence of Q = 2/3 to the 45° angle is Foot's, 1994), and Brannen's phase (2006) read as the cube's projection product 2/9; and (2) a preregistered kill commitment, made before tau-mass measurements reach deciding precision: "If any single measurement with total uncertainty ≤ 0.05 MeV, or the world average at that precision, settles outside [1776.85, 1777.05] MeV, the mechanism is falsified and the author will say so publicly, in this venue. No reinterpretation, no widened band." Current data cannot decide the test (PDG 2024: 1776.93 ± 0.09 MeV; Belle II 2023: 1777.09 ± 0.14 MeV — they straddle the value); Belle II's projected precision will. A dependency-free Python script included in the deposit (verify_tau.py, Python 3 standard library only) reproduces every load-bearing number in the note.