Editing Openai/6908ee36-d3b4-8010-a468-28e0753d08ae (section)

=== If coherence states are equally spaced phases on an internal rotation with frequency ωC=mHc2/ℏ\omega_C=m_Hc^2/\hbarωC=mHc2/ℏ (Compton clock), then a hop is a phase advance δϕ=2π/N\delta\phi=2\pi/Nδϕ=2π/N: ===

τ=δϕωC=TCN.\tau=\frac{\delta\phi}{\omega_C}=\frac{T_C}{N}.τ=ωCδϕ=NTC.
Your choice α=0.0084304\alpha=0.0084304α=0.0084304 is exactly this with N≃1/α≈118.6N\simeq 1/\alpha\approx 118.6N≃1/α≈118.6 states per Compton period. This is a clean HU-native parameterization: once you defend NNN by symmetry or topology (e.g., allowed irreps or winding number in your 4D manifold), τ\tauτ follows without invoking huge energy splittings.