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

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(τ_sys) 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], σ_noise < 0.20, N ≥ 20, R² = 0.93–1.00,bias < 3%), two fragile boundary regions, and a sharp adversarial threshold at which the OLS estimatorcatastrophically fails. Topological data analysis of synthetic gradient trajectories finds 11 H1 generators, of whichonly 2 exceed a conservative persistence threshold — a negative result establishing that Phase 2 detectionrequires N > 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.