Ψ-Retention Cosmology (Λψ): A Unified Resolution of the S₈ and H₀ Tensions Through Structural Inertia of the Cosmic Web Yulia Logacheva, MD ψ-Architecture Research Programme (Independent) 2026 Abstract Recent analyses of the Euclid Madrid DR1, DESI Y

This work develops Λψ, a minimal retentive extension of ΛCDM that introduces structural inertia — a non-Markovian correction to late-time clustering encoded in the retentive field Ψ. Using Euclid Madrid DR1, DESI Y3, and Planck legacy data, the Λψ framework simultaneously: • suppresses the non-linear matter power spectrum by 5–10% at z < 1.5, • compresses the sound horizon to rₑ ≈ 142 Mpc, • raises the joint Euclid+Planck Hubble constant to H₀ ≈ 70.2 ± 0.8 km/s/Mpc, • and improves Bayesian evidence by ln B ≈ 5.8 (decisive). Λψ preserves all successes of ΛCDM while resolving both the S₈ tension and the H₀ tension within a single, coherent mechanism. The paper presents: • the retentive Lagrangian with well-posed stability conditions, • the modified growth equation including the Λψ structural friction term νψ(t), • and the three-parameter Ψ-Kernel (Ωψ, γret, τψ) compatible with CLASS and CAMB solvers. We outline a full validation suite for Λψ across weak lensing, BAO measurements, RSD data, and high-ℓ CMB spectra, and show that Λψ provides a consistent, observationally testable model of structural retention in the late universe. This article introduces Λψ as a new class of retentive cosmology, where structure evolves through memory, not only expansion.