Light-Cone Thickness Oscillation: A Testable Perturbative Model of Cosmic Boundary Structure

We propose that the boundary of the cosmological light cone possesses a finite, non-zero effective thickness that exhibits a log-periodic oscillation as a function of redshift. This oscillatory perturbation, expressed analytically as

\delta R(z) = \epsilon_0 (1+z)^\alpha \sin\!\big(\beta \ln(1+z) + \phi\big),

encodes scale-dependent micro-texture of the vacuum and predicts measurable deviations from classical relativistic light-cone geometry. We outline three observational paths—pulsar timing residuals, high-redshift quasar spectral micro-shifts, and gravitational-lens time-delay anomalies—that can test this model within the next decade. Verification would provide direct evidence of structural modulation at the causal boundary of spacetime, offering a new probe into the fine texture of the universe.