State-Dependent Climate Feedback Dynamics: Forward Simulation and Hydrological State Space (v2.0)

This release extends the v1.0 λ–κ manifold analysis (DOI: 10.5281/zenodo.19421325) with a complete forward dynamical simulation of the state-dependent energy balance equation: dT/dt = F(t) − λ(T)·T − κ(T) where λ(T) and κ(T) are Gaussian Process estimates from 141 sliding-window regressions on ERA5 radiative forcing and HadCRUT5 temperature anomalies (1880–2025). Key results:- Forward simulation RMSE = 0.20°C over 146 years (bias = −0.07°C)- Empirically constrained κ calibration via direct energy balance inversion- Aggregate feedback function h(T) = λ(T) + κ(T)/T changes sign at T ≈ 0°C, identifying a dynamical bifurcation between destabilising and stabilising regimes- Phase portrait reveals hysteresis loop structure consistent with fractal dimension D ≈ 2.44 of the λ–κ manifold- Maximum Earth Energy Imbalance EEI = 0.32 W m⁻² The theoretical foundation (THEORY_v2.md) introduces the hydrological state space W(t) = (T, p, e, q, CF, ICE, OHC) and derives the thermodynamic basis for v3.0, including the Clausius–Clapeyron saturation dynamics S(t) = e/e_s(T) and state-dependent heat capacity C(W). This work is a continuation of an independently developed research program on state-dependent climate feedback geometry. Is new version of: 10.5281/zenodo.19421325