ψ-Architecture Research Series, Vol. IV — ψ-Retention Cosmology: Structural Growth Invariance and the Late-Time Universe

This work inaugurates Volume IV of the ψ-Architecture Research Series and develops a retentive cosmological framework, ψ-Retention Cosmology, for the late-time universe. The article introduces a single structural operator, Λψ, which limits the decay of gravitational potentials once large-scale structure reaches a retentive stability threshold. Within standard General Relativity (η = 1, μψ = 1), the Λψ term is treated as a structural bookkeeping contribution, not as a new propagating field. It modifies the effective growth history without adding new degrees of freedom or altering the metric sector. In this setting, late-time anomalies — the S₈ tension, the Planck A_L inconsistency, the low-ℓ CMB plateau and the ISW deficit — are interpreted as signatures of a transition from dynamical evolution to structural retention. The paper derives a falsifiable prediction set for Euclid DR1, including: (i) a late-time plateau in fσ₈(z) below zψ ≈ 0.5; (ii) scale-invariant suppression of matter power for 0.05 < k < 0.5; (iii) strictly null gravitational slip (η = 1) and uniform void-lensing suppression. These signatures form a rigid structural test: any detected redshift drift in γ(z), measurable slip, or scale-dependent suppression would decisively falsify the framework. Together with its companion article, “ψ-Retention Cosmology: A Structural Framework for Late-Time Stability Beyond Dynamical Suppression”, this Volume IV contribution presents Λψ as a minimal, GR-consistent extension of late-time cosmology: a structural, non-competitive framework formulated explicitly for near-term observational evaluation.