Appendix Proof of the Discrete-to-Continuous Transition & First-Principles Derivation of the Electron Mass

This appendix collection presents two core extensions of the Relaton Universe theory. Appendix D derives the absolute electron rest mass from the Planck scale and the symmetry breaking of the Fischer sporadic group Fi24′Fi24′, yielding mec2=3EP⋅π⋅ee−1⋅∣Fi24′∣−1≈0.5111 MeVmec2=3EP⋅π⋅ee−1⋅∣Fi24′∣−1≈0.5111 MeV with a deviation of +0.02%+0.02% from experiment, achieving a zero-parameter derivation of the mass benchmark. Appendix E rigorously proves that continuous time emerges from discrete relaton-pair networks via phase continuity and chaotic ergodicity, while continuous space emerges through the smoothing of the vacuum effect field, and that Einstein's field equations are recovered in the continuum limit—thus providing a microscopic relational-ontology foundation for continuous spacetime.