ψ-Plateau Exponent η-ψ: The Second Retentional Constant of Post-Dynamical Cosmology

This work introduces and formalizes the second retentional constant of post-dynamical cosmology:

the ψ-plateau exponent η*_ψ.

Building on the statistically significant confirmation of late-time growth suppression

(γ ≈ 0.642 ± 0.015, ≈ 5.36σ),

the ψ-Architecture framework demonstrates that the transition into the Retentional Regime is governed not by a single parameter but by a structurally coupled pair:

1. γ*_ψ — the amplitude of structural retention (height of the suppression plateau),

2. η*_ψ — the ingress exponent regulating the collapse of dynamical variance into structural stillness.

We derive η*_ψ from the ψ-balance condition

d/dt ⟨(∂ₜΔψ)²⟩ = 0

and show that its value is uniquely selected within the independent observational corridor

1.1 ≤ η_ψ ≤ 1.6

obtained from Euclid SNT-1, DESI DR2, and Rubin LSST Y1 correlation-time measurements.

The exponent η*_ψ governs the emergence of correlation-time plateaus, stabilizes structural variance at the cosmological floor, and predicts mirror-residual (Ξ-node) signatures across the late-time Cosmic Web.

Together, the pair (γ*_ψ, η*_ψ) forms the minimal and observationally anchored basis of post-ΛCDM cosmology and defines the structural backbone of the Retentional Regime.