Metabolic Saliency as KL-Divergence Estimator: Information-Geometric Attribution of Systemic Stress in JSE Equity...

The attribution of systemic financial stress to specific market sectors requires metrics that are faithful to the model's computations, statistically consistent, and connected to a physically meaningful measure of directed information flow. This paper addresses all three requirements through information geometry, contributing to SDGs 7, 8, 9, and 17 through an entropic causal chain linking energy infrastructure failure to financial market stress. We conjecture and empirically verify the Entropy-Saliency Equivalence: Metabolic Saliency is an asymptotically unbiased estimator of the local Kullback-Leibler divergence between stressed and resting sector return distributions, with bias decaying at a parametric rate under Gaussian regularity conditions. The finite-sample bias-variance decomposition of the Kraskov-Stögbauer-Grassberger transfer entropy estimator is derived, establishing a minimax-optimal convergence rate. A novel metric, the Spatio-Temporal Information Flux (STIF), quantifies directed inter-sector stress transmission in bits per trading day, providing a bootstrap-calibrated audit trail aligned with the South African Financial Sector Regulation Act and MiFID II. Empirical validation on the JSE canonical panel (87 securities, 2857 trading days, 2015-2026) with Eskom load-shedding stages as exogenous stress injectors confirms the equivalence (R2=0.810, ρ^=0.90), with walk-forward R2=0.789 and placebo R2=0.081 ruling out estimation artefacts. The energy sector is identified as the primary stress transmitter during Stage 4+ Eskom events (STIF rising from 0.14 to 0.43 bits/day, directional asymmetry ratio 4.7). Robustness checks confirm stability across non-Gaussian securities and rolling transfer entropy windows.