The Neutrino Oscillation Phase as Compton Clock minus de Broglie Offset: the Two Forms of h = E Δt and the Factor-of-Two Error

One completed cycle of a particle's phase carries the action h, and relativity gives that one cycle two forms (Volume II of The Volumes: Geometry of Electromagnetism): a Compton (rest-frame) form, in which one cycle lasts T_C = h/mc², and a de Broglie form, in which the relativity of simultaneity offsets the phase across space, the de Broglie wavelength λ_dB being the length over which that offset equals one Compton period. The derivation uses no charge, so it applies to the neutrino. Treating the three neutrino mass states as three such clocks, the oscillation phase is computed in two ways for a baseline L, a neutrino energy E and two mass states with Δm² = m_b² − m_a². Read with the Compton form alone, comparing each clock's own elapsed proper time at its own arrival, the phase is Δm²c⁴L/ħcE, twice the measured value. Read as the Compton clock minus the de Broglie offset, comparing the clocks at one detection event, it is Δm²c⁴L/2ħcE, the standard formula confirmed by atmospheric, solar, reactor and accelerator experiments. The difference is exactly the phase accumulated between the two states' arrival times, which is what the de Broglie form accounts for. The same result holds for equal energies, equal momenta and Gaussian wave packets. The doubled phase was proposed in the literature and refuted by comparing amplitudes at a common space-time point; applied to kaon and B-meson oscillations it is excluded at 3.5σ. The resolution is not new. What this note adds is that the published error is the Compton form alone and the published correction is the de Broglie form, so the two forms of h = E Δt are precisely the two pieces the correct phase requires. Flavour oscillation is the one place where the difference between two Compton clocks is observed directly. Volume II, Sec. X, summarizes this result; this note gives the full calculation and its checks.