Photon Dispersion and Gamma‑Ray Burst Tests of Emergent Gravity

This is a revised and updated version of the preprint "Photon Dispersion and Gamma‑Ray Burst Tests of Emergent Gravity" (original DOI: 10.5281/zenodo.18877218). The main changes are: 1. The derivation of the modified dispersion relation now explicitly uses the fundamental relation $8\pi G\beta = \tau^2$ from the comprehensive formulation of Chrono‑Grid Dynamics (CGD) [DOI: 10.5281/zenodo.19044164], showing that the Planck scale emerges dynamically as $M_{\text{Pl}} = \sqrt{\beta}/\tau$.2. The predicted time delays are compared with the projected sensitivity of the Cherenkov Telescope Array (CTA), and a detailed estimate for $E \sim 100$ TeV photons is provided.3. References to the companion numerical study of quantum tetrahedra [DOI: 10.5281/zenodo.19014639] have been added, which independently confirm the discrete quantum geometry underlying CGD.4. The discussion now highlights the consistency with current observational limits (Fermi‑LAT) and the testability with next‑generation gamma‑ray observatories. All other results and conclusions remain unchanged. This work is part of a series on Chrono‑Grid Dynamics; related preprints are available at the DOIs listed above.