he Solitary Wave of Uido — Revised with Appendices (2025-08-15)

This revision appends concise technical notes to close the loop without external code/data links. Appendix A gives a Planck-scale nondimensionalization of the governing equation with α′=α/c2\alpha'=\alpha/c^2α′=α/c2, β′=β ℏ3G/c5\beta'=\beta\,\hbar^3G/c^5β′=βℏ3G/c5, Γ′=ΓtP\Gamma'=\Gamma t_PΓ′=ΓtP. Appendix B adds the explicit magnetic/coiling energy (α/2)∥∇×ϕ∥2( \alpha/2)\|\nabla\times\boldsymbol\phi\|^2(α/2)∥∇×ϕ∥2 while avoiding double counting via ∣∇ϕ∣2=∣∇×ϕ∣2+∣∇ ⁣⋅ ⁣ϕ∣2|\nabla\boldsymbol\phi|^2=|\nabla\times\boldsymbol\phi|^2+|\nabla\!\cdot\!\boldsymbol\phi|^2∣∇ϕ∣2=∣∇×ϕ∣2+∣∇⋅ϕ∣2. In the hydrogen run, this resolves the missing ~+87 eV and corrects −100.6 eV to ≈−13.61 eV. Appendix C sketches hidden quaternion couplings that yield internal resonance modes (electron/muon/tau scales). Main text unchanged; this is a clean, self-contained preprint.