Λ Constant, w Evolving: A Topological Resolution

The Dark Energy Spectroscopic Instrument (DESI) reports mounting evidence (2.8–4.2σ) that the dark energy equation of state w evolves with redshift. Mode Identity Theory (MIT), which derives cosmological observables from topological boundary conditions, appears vulnerable; however, the framework holds Λ fixed by construction. The cosmic standing wave Ψ(t) = cos(t/2) imprints phase-dependent structure on observable geometry. When observers fit distance data using fluid-based models, they recover apparent w(z) evolution—not because dark energy changes, but because the fitting framework cannot capture phase position. The “Phantom Crossing” emerges naturally as an inference artifact, not exotic physics. MIT distinguishes constant Λ (the surface mode) from varying weff (the observer’s inference signature). DESI constrains the phase offset δ ≈ −1.06 rad, placing observers approximately 2.8 Gyr before the geometric turnaround. v3 erratum: the geometric turnaround now at ~16.6 Gyr (not 13.8 Gyr); full cycle ~33 Gyr. Phase offset revised to δ ≈ −1.06 rad. v3 update: reformatted as explicit MIT supplement; condensed abstract and discussion sections; reordered derivation (Mechanism now follows Parameters); added inline citations for CPL parametrization [3,4]; Λ evolution falsification threshold changed from ">5%" to "2σ" for consistency with other criteria. Core derivations and predictions unchanged. v4 notes: direct confrontation with DESI DR2 Table V parameters; tightened falsification target to z_cross = 0.66 ± 0.12; explicit curvature test (d²w/dz² ≠ 0) as CPL differentiator. Target upload before Euclid DR1 (October 2026).