Fano 2-22 is the Feynman Graphon: emergence of FLRW spacetime from algebraic construction (NO FREE PARAMETER)

We construct a sequence of weighted regular graphs G_k whose spectral data are derived from the Minkowski period coefficients of the Fano 3-fold 2-22 (Mori-Mukai ID-69). The coefficients factorize as c5 = 24 * 45, c6 = (4/3 * 45) * (45 + 64), and c7 = 24 * (4/3 * 45) * (45 - 10), which we interpret as trace invariants (spectral moments) of the adjacency matrix of a base graph G_45 with 45 vertices and degree 24. The topological volume of the Fano 2-22 cell is V_cell = delta_th, where delta_th = (1/(2 pi)) ln( sqrt(8) / (sqrt(8) - sqrt(7)) ). A regular lattice of such cells filling the 3-sphere of radius R = pi yields a discrete spacetime whose continuum limit is the FLRW 3-sphere. We prove convergence in cut norm of the graph sequence G_k to the limit graphon W(x,y) with rate O(2^{-k}), where W(x,y) = kappa * Phi_VEV^2 * exp(-gamma * d(x,y)), with Delta = 2 sqrt(2) - sqrt(7), kappa = (24/25) * (delta_th / Delta), and gamma = sqrt(pi^4 + 1) * (24/25) * (delta_th / Delta). The graphon is identified with the Feynman propagator of a massive scalar field on S^3, regularized by the cell volume cutoff delta_th. We derive the exact spectral gap via spherical harmonic expansion on S^3, expressing the eigenvalues in terms of Gegenbauer polynomials. Numerical evaluation yields lambda_1 / lambda_0 ≈ 1.99765, which asymptotically tends to 2 as gamma R → infinity, reflecting the isotropy and homogeneity of the emergent spacetime. The construction contains no free parameters and provides a purely geometric realization of spacetime emergence from a discrete combinatorial structure.