Background: The Gibbs Energy Redistribution Theory (GERT) program established a thermodynamic ontology for cosmology (Paper~I) and later identified the post-relativistic dissolution boundary of the relativistic ruler in the Hyperdilute Regime (Paper~II). The complementary open question is the onset of relativistic metric legibility in the early Universe. Objective: To determine, within GERT, the emergence boundary of the relativistic metric ruler and define the lower limit of validity of the effective relativistic regime. Methods: We define the metric-emergence parameter , where is the photon mean free path and is the GERT particle horizon. The boundary is set by . We compute using two recombination treatments (Saha equilibrium and Peebles kinetics) and test robustness against the unknown Primordial Cauldron boundary . Results: We obtain , with uncertainty dominated by recombination kinetics (Saha vs.~Peebles). Varying over 25 orders of magnitude changes by less than , showing strong insensitivity to primordial microphysics. Together with Paper~II (), the relativistic GERT domain spans $15.9\pm0.2\alpha=\log_{10}(a)$. Conclusions: The relativistic ruler is an emergent operational regime, not an ontologically unlimited one. GERT now provides a complete domain map with pre-relativistic, relativistic, and post-relativistic sectors. The onset and dissolution boundaries are thermodynamically controlled, giving a symmetric validity structure for Layer 3.