L(6+7), Evolving Dark Energy, and the Hubble Tension: A Unified Internal-Sector Interpretation with Late-Time Dark-Sector Coupling

This preprint develops a publication-grade late-time cosmology synthesis within the L(6+7) framework, connecting DESI DR2 indications of evolving dark energy and the Zhang–Xu–Chen multi-model analysis of the Hubble tension with a unified internal-sector variational description. The paper does not claim that the Hubble tension has already been solved or that dark-energy–matter interaction has been observationally established. Its central claim is narrower and stronger: L(6+7) provides a controlled theoretical container in which ΛCDM, CPL-like dark-energy evolution, scalar-field dark energy, and late-time interacting dark energy can be understood as limiting cases, truncations, or phenomenological closures of a single variational backbone. The paper derives the effective density and pressure of the seven-sector, formulates the modified continuity equation, introduces the regime indicator kappa_7 and the effective bridge w_eff = w_7 − mu/3, and outlines a practical data-facing program for future confrontation with DESI-like reconstructions, coupling diagnostics, and growth-sector observables.