The Frontier of Two-Loop Corrections

In the complete formalism of the Physics of Informational Emergence (PEI), the nodal coupling gPEI g_{\rm PEI} gPEI is derived purely topologically from the postulates of Part I (dim(M3 M^3 M3) = 3, dim(S5u S_5^u S5u) = 5, fractal fiber F=S1info(e5) F = S_1^{\rm info}(e^5) F=S1info(e5)). The muon-lock (α,κ,ξ,Λ \alpha, \kappa, \xi, \Lambda α,κ,ξ,Λ) is fully fixed at one-loop order (Part III, §3). The residual discrepancy of 0.037 % between the topological value gPEItopo=3/160≈0.136931 g_{\rm PEI}^{\rm topo} = \sqrt{3/160} \approx 0.136931 gPEItopo=3/160≈0.136931 and the Fermilab 2023 fitted value is not an error: it constitutes the predicted signature of the two-loop correction term. We rigorously derive the two-loop perturbative closure equation, detail the dimensional calculation, provide the expected numerical value of δ2L \delta_{2L} δ2L, and show that this prediction is falsifiable by an explicit calculation of the diagrams with two insertions on the S5u S_5^u S5u fiber.