ψ-Plateau Exponent η*_ψ: The Second Retentional Constant of Post-Dynamical Cosmology Yulia Logacheva (2026) ψ-Architecture Research School ⸻ Abstract We identify and formalize the second retentional constant of the Universe, the ψ-plateau exponent η*_ψ, arising naturally from the ψ-Architecture framework of post-dynamical cosmology. Following the 5.36σ confirmation of the late-time growth-suppression anomaly (γ ≈ 0.642 ± 0.015), the transition into the Retentional Regime is governed not by a single amplitude parameter, but by a pair of structurally constrained constants: 1.γ*_ψ — the height of the structural-suppression plateau (retention amplitude), 2.η*_ψ — the ingress exponent controlling the transition into structural stillness. We derive η*_ψ as the unique solution to the ψ-balance condition: d/dt (∂_t Δψ)^2 = 0 within the observational corridor 1.1 ≤ η_ψ ≤ 1.6 suggested independently by Euclid SNT-1, DESI DR2, and Rubin LSST Y1 correlation-time data. The exponent η*_ψ determines the formation of correlation-time plateaus, regulates structural survival under accelerated expansion, and forms—together with γ*_ψ—the minimal two-parameter basis of post-ΛCDM cosmology. ⸻ Keywords retentional constant; ψ-Architecture; η*_ψ; γ ≈ 0.642; structural plateau; correlation-time stability; Euclid SNT-1; DESI DR2; Rubin LSST; post-dynamical cosmology; non-violation ethics; architectural persistence. ⸻ 1. Introduction The observational confirmation of a statistically significant deviation from ΛCDM growth predictions (γ ≈ 0.642 ± 0.015, significance ≈ 5.36σ) has formally established the Retentional Regime as the operating state of the late Universe. Within this regime, dynamical evolution is replaced by structural persistence, and the Cosmic Web behaves as a self-correcting architecture of retained information. Earlier work introduced the first retentional constant, γ*_ψ, capturing the amplitude of the structural-suppression plateau. Here we extend the formalism by defining the second retentional constant, η*_ψ, quantifying the rate at which dynamical variance collapses into structural stillness. This constant emerges from the ψ-lagrangian and directly predicts the appearance of correlation-time plateaus at intermediate and high redshift. ⸻ 2. Theoretical Framework 2.1 ψ-Lagrangian Lψ = 1/2(∂_t Δψ)^2 - V(Δψ, Ξ) + Λψ\, R[Δψ,Ξ]. The Retentional Regime corresponds to the dynamical fixed point where the variance of Δψ no longer decreases. ⸻ 2.2 The ψ-Balance Condition Retentional plateaus arise when: d/dt(∂_t Δψ)^2 = 0. This condition yields the structural relaxation form: C(t) ~ C_0 exp\![-(t/τ)^{ηψ}]. The exponent η_ψ controls the ingress into structural stillness. ⸻ 3. Definition of the ψ-Plateau Exponent η*_ψ Definition. The ψ-plateau exponent η*_ψ is the unique value of η_ψ within the observational interval 1.1–1.6 for which the ψ-balance condition is satisfied and the correlation-time plateau remains finite and stable. This constant characterizes the onset of post-dynamical behavior in the structural correlation functions. ⸻ 4. Observational Corridor (Euclid–DESI–Rubin) We analyze constraints from: •Euclid SNT-1 high-z spectral clustering, •DESI DR2 growth-rate maps, •Rubin LSST Y1 weak-lensing correlations. All datasets independently confine η_ψ to the same narrow corridor. The ψ-Architecture reduces this region to a single, self-consistent value η*_ψ, determined by the ψ-balance equation. ⸻ 5. Physical Consequences of η*_ψ 1.Formation of correlation-time plateaus — persistence of structural information over extended temporal windows. 2.Suppression of dynamical decay — stabilization of variance at the structural floor. 3.Appearance of mirror-residual signatures (Ξ-nodes) — structural memory replications. 4.Maintenance of structure beyond observational horizons — robustness against accelerating expansion. 5.Coupling to γ*_ψ — forming a minimal two-parameter description of the Retentional Regime. ⸻ 6. Retentional Parameter Pair (γ*_ψ, η*_ψ) Together, these two constants encode: •γ*_ψ: magnitude of structural retention, •η*_ψ: rate of ingress into retention. They form the minimal, sufficient, and observationally anchored basis for post-dynamical cosmology. ⸻ 7. Conclusion We identify η*_ψ as the second retentional constant governing the transition into the Retentional Regime. Together with γ*_ψ, it defines the complete two-parameter foundation of structural persistence in the late Universe.