A Non-Circular RTLI Derivation of the Speed of Light: Asymmetry, Coherence, and the Mesoscopic Corridor Scale

This work presents a non-electromagnetic derivation of the speed of light c within the Relational Thermodynamic Layered Index (RTLI) framework. The derivation does not invoke Maxwell’s equations or assume c at any stage. Instead, c emerges from the interaction of four independently defined structural quantities: (i) the universal coherence threshold \eta_{\rm crit} \approx 1.715, identified empirically across exoplanet resonance statistics, SPARC galaxy rotation curves, and CMB variance structure; (ii) the quantum–geometric asymmetry factor A = \Omega_\Lambda/\Omega_m \approx 2.17; (iii) the minimal relational update time \tau_0 = \hbar / E_{\rm corridor}, set by recombination-scale physics; and (iv) a mesoscopic coherence length \ell_{\rm micro}, derived from RTLI corridor geometry. These quantities combine to yield c_{\rm RTLI} = A(2\pi \eta_{\rm crit})\,\frac{\ell_{\rm micro}}{\tau_0}, which reproduces the defined value of c to within \sim 10^{-3} accuracy, without assuming its value as an input. The work further develops testable observational consequences of RTLI coherence geometry. In particular, it predicts small but systematic curvature suppressions and shear asymmetries in weak-lensing environments near the coherence threshold \eta \approx 1.7, providing falsifiable signatures for COSMOS-class surveys. Update. Version 4 introduces an appendix presenting a principal-component (PCA)–based structural validation of the emergent c, demonstrating that the derived speed arises from coherent variance organization rather than parameter tuning.