A Geometric Interpretation of the Speed of Light

This work presents an attempt to reconstruct the numerical value of the speed of light without starting from Maxwell’s equations or assuming c as an input. Instead, the paper treats c as an emergent propagation scale arising from coherence geometry: a universal threshold near \eta_{\rm crit}\approx 1.7, a cosmological asymmetry factor A=\Omega_\Lambda/\Omega_m, a recombination-scale update time \tau_0, and a mesoscopic coherence length \ell_{\rm micro}. These ingredients combine into a velocity-scale expression, c_{\rm RTLI}=A(2\pi\eta_{\rm crit})\frac{\ell_{\rm micro}}{\tau_0}, which numerically approaches the observed value of c at the 10^{-3} level. The paper should be read as a structural reconstruction rather than a replacement for established electrodynamics or relativity. Its main contribution is to explore whether the speed of light can be interpreted as a coherence bandwidth set by relational update time, mesoscopic length scale, and cosmological asymmetry. Version 4 adds a PCA-based appendix suggesting that the reconstructed value arises from organized variance structure within the RTLI framework rather than arbitrary parameter tuning. The work also proposes possible weak-lensing signatures near the coherence threshold \eta\approx 1.7, making the framework potentially testable in COSMOS-class survey environments.