Λ Constant, w Evolving: A Topological Resolution

Mode Identity Theory holds Λ fixed by construction, yet DESI DR2 reports 2. 8-4. 2σ evidence that the dark energy equation of state w evolves with redshift. This paper resolves the tension: the cosmic standing wave Ψ (t) = cos (t/2) modulates the effective expansion history, producing apparent w (z) evolution when observers fit constant-Λ distances with fluid-based templates. Friedmann inversion of the modulated Hubble rate proves wₑff (z) > -1 at all redshifts; the phantom crossing is a CPL template artifact at z ≈ 0. 66. Tested against the full DESI DR2 BAO dataset (13 observables, 7 redshift bins), MIT achieves χ² = 8. 58 with two free parameters versus ΛCDM's χ² = 10. 28 (ΔAIC = -1. 70). The phase offset δ = -1. 06 rad and coupling ε = 0. 263 are locked prior to Euclid DR1. v5 update: full numerical pipeline added: three-model comparison (ΛCDM, MIT, CPL) against DESI DR2 BAO data (13 observables, 7 redshift bins) with χ² = 8. 58 vs ΛCDM's 10. 28; Friedmann inversion derivation now proves wₑff > -1 at all redshifts (no phantom regime), replacing the leading-order inference template; epsilon calibrated from external dataset (Abbott et al. 2024, zero DESI data) with robustness checks across five dataset combinations; information criteria tables (AIC, BIC, AICc) reported at both k = 2 and conservative k = 3 counting; per-bin residual analysis confirms improvement concentrated at z = 0. 3-0. 7 matching predicted modulation profile; wₑff recovery exercise demonstrates CPL template artifact mechanism on synthetic MIT distances; expanded literature context covering topological cosmology, phantom crossing models, Horndeski and IDE distinctions; specific Euclid DR1 predictions table added; prepared for JCAP submission. Core predictions and locked parameters unchanged.