We construct a sequence of weighted regular graphs Gₖ 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 G₄5 with 45 vertices and degree 24. The topological volume of the Fano 2-22 cell is Vcell = deltaₜh, where deltaₜh = (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 Gₖ to the limit graphon W (x, y) with rate O (2^-k), where W (x, y) = kappa * PhiVEV² * exp (-gamma * d (x, y) ), with Delta = 2 sqrt (2) - sqrt (7), kappa = (24/25) * (deltaₜh / Delta), and gamma = sqrt (pi⁴ + 1) * (24/25) * (deltaₜh / Delta). The graphon is identified with the Feynman propagator of a massive scalar field on S³, regularized by the cell volume cutoff deltaₜh. We derive the exact spectral gap via spherical harmonic expansion on S³, expressing the eigenvalues in terms of Gegenbauer polynomials. Numerical evaluation yields lambda₁ / lambda₀ ≈ 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.
Massimiliano Blandino (Sat,) studied this question.