Mathematical Formalism of the Targeted Gradient Repair Mechanism (TGRM) Author: Cody Ryan Jenkins DOI: 10.5281/zenodo.17234762

This record presents Paper 2 in the Targeted Gradient Repair Mechanism (TGRM) research series. Title: Mathematical Formalism of the Targeted Gradient Repair Mechanism (TGRM)Author: Cody Ryan JenkinsDOI: 10.5281/zenodo.17234762 Overview:This paper provides the first mathematical framework for TGRM, supported by simulated results that demonstrate:- Stability bounds- Convergence conditions- Repair Efficiency Ratios (RER)- Layered defense strategies (Dampeners → TGRM → Pruning) Disclaimer:All results are derived from numerical simulations. They are not experimental validations in biological or hardware systems.Purpose of this release: provide a reproducible simulation framework, guide future empirical validation across biology, AI/ML, and robotics, and invite collaboration from labs and engineers. Related Work:Paper 1: Targeted Gradient Repair Mechanism (TGRM): A Principle for Extending Runtime. DOI: 10.5281/zenodo.17219304Paper 2 builds directly on the foundation established in Paper 1. Citation:Jenkins, Cody Ryan. Mathematical Formalism of the Targeted Gradient Repair Mechanism (TGRM): Simulated Results. Zenodo, 2025. DOI: 10.5281/zenodo.17234762