CPQ Theory: Electron Mass from Marginal Stability of the Matrix

Within CPQ theory, we present a candidate equation for the electron mass that expresses the logarithmic ratio ln(m_P/m_e) in terms of five numbers, none of which is fitted directly to the electron mass. The structure of the equation ln(m_P/m_e) = 27π(α⁻¹ - e^γ)/(128√3) arises from the marginal stability of a toroidal soliton, the topological coefficient of the loop spectrum, and the geometric correction of the torus. Numerical closure requires the identification of the UV saturation coupling αₛₐₜ⁻¹ = e^γ, which we understand in this work as a priority open RG ansatz. The resulting value ≈ 51.75 (experiment: 51.53, agreement 99.6%) shows that the CPQ structure naturally produces the correct order and form of the electron mass. The article analyses in detail the origin of each of the five numbers and precisely identifies where the chain is robust, where it is structurally motivated, and where it is open. Porschová, A. (2026). CPQ Theory — A Unified Framework from Spacetime Quanta to Cosmology (Books I–III). Zenodo. https://doi.org/10.5281/zenodo.18686137 Porschová, A. (2026). CPQ Field Theory — Applications (Books 01–03). Zenodo. https://doi.org/10.5281/zenodo.19100819 Porschová, A. (2026). The Matrix — Parameters and Dynamics: Foundation of CPQ Theory (3.1). Zenodo. https://doi.org/10.5281/zenodo.19431867