> We present a mathematically rigorous derivation showing that continuous spacetime is not fundamental but a strictly downgraded, high-density approximation of a discrete tri-energy event graph. Space and time are defined primitively on the graph; the FLRW metric emerges as a provable asymptotic limit with explicitly computed leading and subleading terms. The full proof is given in Appendix A. Full cosmological equations, perturbation theory, and observational predictions will appear in a companion paper.