From the Fano 2-22 to the Lepton Masses e Lamb Shift - No Free Parameters

We derive six fundamental constants of particle physics from the entangled topology of the Fano 2-22 (Mori-Mukai ID-69) and the PEPS-5D Lagrangian: 1. The inverse fine-structure constant: \(αMPS⁻¹ = lnλₘₐₓ - π = 137.03599916781\) from a circular MPS with bond dimension \(D=45\). 2. The electron anomalous magnetic moment: a closed topological series\[a_eᵍᵉᵒᵐ = R(1 - Δ S/105) + R^2({√T}{χ} · δₜₕ · 24/25) - R^3({χ}{√T} · 24/25),\]where \(R = αMPS/2π\), yielding \(a_eᵍᵉᵒᵐ = 0.001159652137\), agreeing with experiment to \(1.33×10⁻¹⁰\). 3. The electron mass:\[m_eᵖʰʸˢ = m_eᵇᵃʳᵉ + 1/10(m_eᵇᵃʳᵉ(a_e/2 + α^2/2)) = 510998.888\ eV,\]where \(m_eᵇᵃʳᵉ = MPl exp(-[105-2/2 + Δ S/χ(1 - s/χ)])\), differing from the CODATA value \(510998.900\ eV\) by only \(0.012\ eV\) (12 meV). 4. The muon/electron mass ratio:\[_μ/m_e = 4 + 4/3 = 5.333…\] 5. The tau/muon mass ratio:\[_τ/m_μ = √T = 2√2 = 2.8284271247461903\] 6. The Lamb shift in hydrogen:\[Δ ELambᵍᵉᵒᵐ = f_v(A_5 - R\,A_6' - R^2 A_7) = 1057.8193\ MHz,\]where \(f_v = α^5 m_eᵖʰʸˢc^2/h\), \(A_5 = 24/25δₜₕ\), \(A_6' = √T + π/2 - I_0/2\) with \(I_0 = 4/(3π)\), and \(A_7 = 4π + 1\). The difference from the experimental value \(1057.812\ MHz\) is \(7.3\ kHz\), well within the uncertainties of the proton radius puzzle. All quantities are derived from pure geometric and algebraic inputs: the bond dimension \(D=45\) (adjoint of \(SO(10)\)), the Hilbert space dimension \(105\) (adjoint of \(SO(15)\)), the Euler characteristic \(χ=6\), the string tension \(T=8\), the Tsirelson bound \(√T=2√2\), the entanglement deficit \(Δ S = √T - √7\) from the hinge term phase \(π/6\), the Picard-Fuchs threshold correction \(δₜₕ\), and the bosonic string parameters \(24\) and \(25\). No free parameters are introduced. The electron, muon and tau are the first three excitation modes of the same geometric structure. The absence of a fourth charged lepton is explained by the saturation of the Tsirelson bound. The Lamb shift emerges as a three-term topological series — impact, rotation, back-reaction — mirroring the structure of \(a_e\). The complete Python verification code (Derivation_leptons_mass+Lamb_shift_from_PEPS-5D_MPS-Fano_2_22.py) is available at the Zenodo repository associated with this work (DOI: 10.5281/zenodo.20077021).