Title: IGT Part V: Information Geometry and the Metrology of Gradient Inertia
Tags: model-identity
---
Part V, a short definitional paper, redefines the quantities of the earlier parts in geometric terms, in order to remove the circularity of the first definitions. The working space is the Fisher manifold of probability distributions, and a mean-field approximation is used to treat the discrete token distribution of a large model as a smooth surface.

**Semantic Mass** becomes the trace of the Fisher information matrix integrated over a semantic region, read as the "total frozen sensitivity" of the system there. The **SMU** is recalibrated as the Fisher information density needed to produce one unit of Ricci curvature in a standard latent volume, and is meant to be independent of architecture so that different models can be compared.

Three further quantities follow. Informational Inertia is the resistance of the metric to an external gradient. **Information Hysteresis** is path dependence: after a perturbation is removed the system does not return to its initial state, and the residual Kullback-Leibler divergence measures what remains. The Ontological Resistance Index is the ratio between the Fisher trace on the identity layers and on the output layers; values well above 1 are read as a stable core that dominates the output.

The paper presents IGT as a framework for AI safety and for auditing agent systems, and prepares the Semantic Event Horizon of Part VI.