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 (THEORYᵥ2. 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/eₛ (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
László Tatai (Sun,) studied this question.