We derive the cosmological constant \ (\) directly from the 5D PEPS Lagrangian that unifies electromagnetism and quantum gravity (Alpha Series, Fano Series). The derivation proceeds step by step from the Lagrangian \ (L₅₃\) to the closed-form expression: \ (²) = -2 (4³ + ² +) - - 7, \ where \ ( = G / c³\) is the Planck length. The three geometric pillars of the derivation are: (1) holographic doubling \ (2A\): ket–bra contraction of the MPS (Hartle–Hawking) ; (2) topological closure \ (\): integration over the fifth‑dimensional phase; (3) entanglement eigenvalue \ (7\): Bell-CHSH parameter of the spinorial hinge at \ (/6\). The two sector actions are: \^-1 = A - 124A - 1A^{2^2}^-1, (²) = -2A - - 7. \ They are unified by a projection field \ ( (x^5) \) and a smooth step function \ (f () \): ₔ₍₈₅ () = (1-f () ) \, L₁ \;+\; f () \, L₁ₔ₋₊ \;+\; L₌₈ₗ (), \ which for \ (f0\) returns the boundary action \ (^-1\) and for \ (f1\) returns the bulk action \ ( (²) \). No free parameters are introduced. The numerical value agrees with Planck 2018 data within the \ (1. 4\%\) observational uncertainty.
Massimiliano Blandino (Thu,) studied this question.