Empirical Boundary Analysis of Allostatic Curvature: Where the Stiffening Hypothesis Holds, Where It Breaks, and Why the Break Points Are Theoretically Meaningful

Abstract - The Allostatic Curvature framework proposes that the Fisher information metric along a neural network's trainingtrajectory accumulates as a monotonically non-decreasing Allostatic Load Functional (ALF), and that thetime-constant variance Var (τₛys) of Liquid Neural Networks decays exponentially as a function of this load — thestiffening hypothesis. This paper provides the first systematic empirical boundary analysis of that hypothesis, establishing where the predicted exponential decay is robustly recoverable, where estimation fails, and why thefailure modes are themselves theoretically meaningful. Three pre-registered Monte Carlo experiments on syntheticLNN-analogous data identify a robust publication zone (α ∈ 0. 05, 1. 50, σₙoise 200 under current sampling densities. Four Empirical Boundary Conditions (EBC-1 through EBC-4) are derived. The paper closes with a 14-step implementation protocol for the live MNIST-based LNN validationstudy. This paper completes the SIP-06 four-paper theoretical arc and precisely specifies the conditions underwhich live empirical validation can proceed. allostatic curvature, stiffening hypothesis, Monte Carlo boundary analysis, Fisher information metric, Liquid NeuralNetworks, topological data analysis, persistent homology, adversarial robustness, regime-switching estimation, HATI², GTRS, SIP-06, AI safety, neural manifold, Watanabe singularity theory