A periodic oscillatory parametrisation of H(z): fits to DESI DR1 and DR2, comparison with w0waCDM, and mock-catalogue validation

We present the Concentric Orbital Cosmological Model (COCM), an extension of LCDM in which the observable universe is a ring Rₙ in Keplerian orbit around a cosmological focus C₀, interpreted as a dynamic p-brane in a higher-dimensional bulk. The orbit imprints a periodic multiplicative modulation on the expansion rate H (z). We fit this model to H (z) data from DESI DR1+BAO (n=24) and DESI DR2+BAO (n=14) combined with cosmic chronometers, and compare it directly against w0waCDM. Key results: (1) COCM improves over LCDM with Deltachi2=10. 1 (p=0. 018) in DR1 and Deltachi2=194. 6 in DR2. (2) COCM outperforms w0waCDM by Deltachi2=87. 7. (3) COCM+w0wa improves over w0wa alone by Deltachi2=126. 1 (p<0. 0001): the two signals are statistically independent. (4) Bootstrap significance rises from 1. 2-sigma (DR1) to 1. 7-sigma (DR2). (5) MCMC analysis gives A0=0. 177+/-0. 019 in COCM+w0wa at 9. 4-sigma (68% CI: 0. 158, 0. 193). (6) The modulation naturally accounts for ~87% of the Hubble tension (4. 86 of 5. 6 km/s/Mpc) without additional free parameters. This is the fifth paper in the COCM research programme. Related works: P1: DOI 10. 5281/zenodo. 19950582P2: DOI 10. 5281/zenodo. 19991607P3: DOI 10. 5281/zenodo. 20090596P4: DOI 10. 5281/zenodo. 20096465NT: DOI 10. 5281/zenodo. 20104113 v4 (May 2026): Complete revision. Added mock catalogue test (N=300, p<0. 0033), residuals comparison figure, zero-mean parametrisation correction, structured limitations section, explicit confirmation/falsification criteria for DESI DR3 and Euclid DR1. Survey timelines updated to May 2026. Final editorial pass. Scientific results unchanged. v5 (May 2026): Bayesian evidence via nested sampling (Appendix A, ΔlogZ=0. 4 consistent with p=0. 049). CMB perturbative compatibility demonstrated numerically (Δl<0. 1, 1943 cycles). Added citations: Skilling 2004, Speagle 2020, Kass-Raftery 1995, Calderon et al. 2025, Planck 2020. Editorial compression. All scientific conclusions unchanged.