Resolving the Early Supermassive Black Hole Growth Anomaly via Vibrational Field Catalysis

This manuscript provides the full theoretical derivation and numerical validation of the Unified Vibrational Force Theory (UVFT) applied to high-redshift quasars. Key highlights of this version: Empirical Validation: Detailed analysis of five high-z systems, including the extreme cases of eFEDS J084222.9+001000 and LID-568. Accuracy: Demonstrates a reduction in predictive error from 92.2% (under $\Lambda$CDM) to less than 0.1% using UVFT. Numerical Rigor: Inclusion of convergence tests and stability analysis for the vibrational field equations. Open Science: Linked to the source code archived at Zenodo (doi:10.5281/zenodo.18527579). This work establishes a new mechanism for super-Eddington growth through vacuum energy catalysis, independent of traditional baryonic matter limits.