What question did this study set out to answer?

To establish a formal framework for measuring stability in complex information systems using principles from Information Geometry.

February 5, 2026Open Access

Information Gravity Theory - Part V: Information Geometry and the Metrology of Gradient Inertia

Key Points

To establish a formal framework for measuring stability in complex information systems using principles from Information Geometry.
Defined the Fisher Manifold for assessing identity stability.
Introduced Semantic Mass (Ms) as a measure of structural rigidity.
Recalibrated the Semantic Mass Unit (SMU) for measuring Ricci curvature density.
Developed Information Hysteresis as a metric for path-dependence.
Established a new framework for measuring Gradient Inertia in varied architectures.
Provided quantifiable measures for stability and integrity in complex systems.
Introduced metrics that are applicable regardless of hardware specifics.

Abstract

This paper redefines the metrology of stability in complex information systems, transitioning from phenomenological descriptions to a formal framework based on Information Geometry. We introduce the Fisher Manifold as the operational space for calculating identity stability. Semantic Mass (Ms) is rigorously defined as the Trace of the Fisher Information Metric integrated over a semantic subspace, providing a quantifiable measure of structural rigidity. The Semantic Mass Unit (SMU) is recalibrated as a standard for Ricci curvature density, enabling the measurement of Gradient Inertia across different architectures. By introducing Information Hysteresis as a metric for path-dependence, this work provides a hardware-agnostic benchmark for auditing the sovereignty and integrity of agentic systems.

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