Exact Derivation of Stable Particle Masses from the 23-Channel Vacuum Network (TVS23): Integer and Rational Mass Indices for the Electron and Proton

The Standard Model assigns particle masses as empirical parameters with no derivation from first principles. This paper presents a complete, parameter-free derivation of the electron and proton masses within the Structured Vacuum Theory TVS23, in which the vacuum is a discrete dodecahedral network V₂₃ whose structure is entirely determined by the cubic polynomial x³ − x − 1 = 0 and its discriminant |Δ| = 23. The central result is that particle masses are not real-valued fit parameters but exact discrete invariants: the electron mass index M_e = 511 belongs to ℤ, and the proton-to-electron mass ratio M_p/M_e = 22340448/12167 belongs to ℚ. Both are derived from graph-theoretic and topological properties of V₂₃, with no free parameters. The electron index arises from two contributions: the directed complete graph K₂₃ on a single node (506 edges) and the winding invariant p + q = 5 of the trefoil knot T(2,3), which traverses the five inscribed tetrahedra of the dodecahedral cell. The proton index combines an integer topological layer — four longitudinal channels acting on 459 available vertices — with a rational dynamic correction factor (N³ + 1)/N³ = 12168/12167 derived from the nonlinear vacuum field equation with coupling β = 4/N². Experimental CODATA values are interpreted as real-valued projections of these discrete invariants under the map ℚ → ℝ; sub-keV discrepancies reflect the internal uncertainties of continuous least-squares adjustment, not failures of the discrete law. The muon mass is identified at the integer level as 9 × 23 = 207 m_e