This technical note refines the mathematical structure of the RTLI coherence index by introducing a precise, distance-only formulation of curvature consistency based on Menger curvature. Building on prior work showing that RTLI acts as a practical proxy for Gromov–Hausdorff (GH) convergence, this note provides explicit definitions for all components of the RTLI functional—correlation length, curvature consistency, local distance variance, and triangle-inequality deviation—using robust, scale-adaptive statistical methods. The central contribution is the formulation of a Menger-curvature-based consistency invariant, \kappa_{\mathrm{cons}}, which measures curvature coherence across a metric space using median-absolute-deviation (MAD) statistics over well-conditioned triplets at the intrinsic scale r = L_c(X). Because Menger curvature is a pure function of distances, this definition is compatible with GH convergence and avoids coordinate-based curvature estimation. The note also states a natural scale-bound conjecture suggesting Hölder-type GH-stability of \kappa_{\mathrm{cons}}, outlines the path toward establishing GH-continuity of the full RTLI index, and clarifies the geometric meaning of the coherence threshold near \eta \approx 1.7. The result is a rigorous, implementable formulation of RTLI that strengthens its role as a computational tool for detecting geometric coherence, screening GH convergence, and analyzing manifold-likeness in discrete metric data.