Law of Responsiveness (Destructive Learning, MNIST) v1.0

We report an empirical validation of the Law of Responsiveness, the local proportional law within the Grammar of Existence: ΔR ≈ F · gg · ΔΦ, where ΔR is realized change, ΔΦ is potential change, and gg is the system’s generative gain. Using the MNIST benchmark under controlled architecture and optimizer, we test whether proportional coupling holds in dynamic (non-equilibrium) regimes and collapses in equilibrium/destructive-learning regimes. Results: • Dynamic regime — slope ≈ 1.0 ± 0.05 (log–log), R² ≈ 0.95 → Law valid. • Equilibrium/destructive regime — R² ≈ 0.00 → collapse of responsiveness. This confirms that responsiveness—the capacity to convert potential into realized change—is conditionally valid: it only operates during active transformation and vanishes at equilibrium. The accompanying analysis includes per-window metrics, log–log fits, and regime comparison figures. Relation: Supplement to Empirical Test — Law of Existence (Triadic Balance MNIST) v1.0. Together, the two datasets establish the dual validation of local proportionality (Responsiveness) and global conservation (Existence) within the Grammar of Existence framework.