EL Science Volume 4 (v2): The Imbalance Bridge Derivation and Self-Consistency Verification of the Observational Dark-Energy Correction from the Internal Dynamics of the Verified 4-Variable System

EL Science Volume 4 (v2) presents the first successful derivation of the observational dark-energy correction directly from the internal dynamics of the EL Science cyclic framework. This work connects the previously disconnected layers of the framework: the cyclic structural model, the verified nonlinear dynamical system, and the observational dark-energy signal detected in Pantheon+ and DESI 2024 BAO data. The proposed mechanism is the “imbalance bridge, ” where the cosmological correction L (z) is generated from the dynamical imbalance R (z) − C (z) between expansion and compression tendencies inside the verified 4-variable system. Two forms were tested: L (z) = 1 + λ (R − C) L (z) = expλ (R − C) Both models were jointly fit against Pantheon+ supernovae and DESI 2024 BAO observations and produced better raw χ² fits than both ΛCDM and the phenomenological evolving-dark-energy parameterization L (z) = 1 + Az + Bz². This revised v2 edition adds a critical methodological verification absent from v1: the τ-to-z mapping was recomputed self-consistently using the model’s own HEL (z) instead of borrowed ΛCDM timing. The self-consistent iteration converged rapidly and preserved the fit improvement almost unchanged: v1 total χ² = 1397. 45 self-consistent v2 total χ² = 1397. 36 The result demonstrates that the imbalance bridge does not depend on borrowed ΛCDM timing and that the fit improvement is generated by the framework’s own internal dynamical structure.