Dual-Gradient Learning Series

Experimental code and results for the Dual-Gradient Learning Series—a collection of six papers extending information geometry through value-perturbation theory and empirical validation. Papers included:- Paper-A: Dual-Gradient Learning (14,400+ runs)- Paper-B: Sub-Additivity Principle (Theory + Evidence)- Paper-C: ρ-Design Methodology (1,230 runs)- Paper-D: Curvature Emergence- Paper-E: Natural Gradient Validation (234 trials)--[NEW] Experiment 4: Approximation Invariance Test for Paper-E All experiments include complete source notebooks, raw data (CSV, JSON), and publication-ready figures. Author: HIDEKI (ORCID: 0009-0002-0019-6608)