GCST Prediction: Positive Correlation between Large-Scale Structure Growth Rate fσ₈(z) and Dark Energy Equation of State w(z)

Global Complexity–Stability Theory (GCST) interprets dark energy as the global manifestation of structural debt D accumulated in regions of low complexity gradient ∇C ≈ 0. The rate of debt accumulation dD/dt ∝ α dC/dt is directly coupled to the growth rate of large-scale structure, quantified by fσ₈(z). GCST predicts a positive correlation between deviations in fσ₈(z) from the ΛCDM expectation and deviations in the dark energy equation of state parameter w(z) from –1. Specifically, epochs or regions with higher-than-ΛCDM fσ₈(z) should exhibit more negative w(z) (stronger acceleration), with the amplitude: where the coefficient k ≈ 0.03–0.08 (derived from current G_cosmo ≈ 0.8 and dissipation efficiency β ≈ 0.2). This prediction is testable with upcoming data from Euclid (weak lensing + galaxy clustering, 2025–2030), DESI (BAO + RSD, already available 2024–2025), and Rubin Observatory (LSST, 2025–2035). Detection of δw(z) ∝ δfσ₈(z) at the level of 3–5σ in z = 0.5–1.5 bins would strongly support GCST over flat ΛCDM. Keywords GCST, dark energy, structure growth, fσ₈, w(z), cosmic acceleration, complexity thermodynamics, structural debt, Euclid, DESI, Rubin Observatory