Logarithmic and Log-Periodic Structure in the Elliptic Spectral Sector of TS5D: Toward a Geometric Interpretation of Mass Residuals

We analyze the elliptic spectral sector of the Five-Dimensional Solitonic Geometry (TS5D)framework using the first admissible Evans modes obtained from a truncated projection hierarchy.We show that the associated elliptic nome q = exp(−πK′/K) follows a logarithmicscaling law with a subleading log-periodic correction.We then investigate whether this structure captures a nontrivial fraction of the residualhierarchy of particle masses beyond the baseline TS5D mass law. A rigid residual modelcombining cumulative logarithmic contributions and log-periodic modulation improves substantiallyover simple baselines and remains partially stable under leave-one-out validation.The present note is deliberately conservative: it does not claim a full spectral closure ofTS5D, nor the computation of new exact Evans modes. Its purpose is to isolate the mostrigorous consequences already accessible from the currently available admissible modes andto identify the most promising geometric correction structure.