Observational Discriminant Between COCM and Alternative Dark Energy Models: A Comparison Using DESI DR2 and Cosmic Chronometer Data

The Concentric Orbital Cosmological Model (COCM) parametrises the Hubble rate as an oscillatory modulation of the ΛCDM background at fixed frequency ωz = 11.1991. This paper extends the comparison of the COCM against alternative dark energy models to include the mirage class, which captures the DESI DR2 phenomenology with a single additional parameter and performance comparable to w₀ waCDM. With n = 14 data points, the COCM and mirage models are statistically indistinguishable at current precision, as measured by reduced χ²r, AIC, BIC, and Bayesian evidence. However, the two models make qualitatively distinct predictions at DESI DR3 precision: the COCM orbital structure predicts a second harmonic at 2ωz in the H(z) power spectrum, absent by construction in the mirage model and in smooth one-parameter parametrisations of w(z). This provides a falsifiable discriminant that can be tested directly with DR3 data.