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: \ (₌ₒ^-1 = _ - = 137. 03599916781\) from a circular MPS with bond dimension \ (D=45\). 2. The electron anomalous magnetic moment: a closed topological seriesₑ^geom = R (1 - S105) + R² (T ₓ₇ 2425) - R³ (T 2425), \ (R = ₌ₒ/2\), yielding \ (aₑ^geom = 0. 001159652137\), agreeing with experiment to \ (1. 3310^-10\). 3. The electron mass: ₑ^phys = mₑ^bare + 110 (mₑ^bare (aₑ2 + ²2) ) = 510998. 888\ eV, \ (mₑ^bare = M₋ (-105-22 + S (1 - s) ) \), differing from the CODATA value \ (510998. 900\ eV\) by only \ (0. 012\ eV\) (12 meV). 4. The muon/electron mass ratio: \₌䂰 = 4 + 43 = 5. 333\ 5. The tau/muon mass ratio: \₌_ = T = 22 = 2. 8284271247461903\ 6. The Lamb shift in hydrogen: \ E₋₀₌₁^geom = fᵥ (A₅ - R\, A₆' - R² A₇) = 1057. 8193\ MHz, \ (fᵥ = ⁵ mₑ^physc²/h\), \ (A₅ = 2425ₓ₇\), \ (A₆' = T + 2 - I₀2\) with \ (I₀ = 4/ (3) \), and \ (A₇ = 4 + 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 \ (=6\), the string tension \ (T=8\), the Tsirelson bound \ (T=22\), the entanglement deficit \ (S = T - 7\) from the hinge term phase \ (/6\), the Picard-Fuchs threshold correction \ (ₓ₇\), 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 \ (aₑ\). The complete Python verification code (Derivationₗeptonsₘass+LambₛhiftfromPEPS-5DMPS-Fano₂₂2. py) is available at the Zenodo repository associated with this work (DOI: 10. 5281/zenodo. 20077021).
Massimiliano Blandino (Fri,) studied this question.