Adaptive Stability Geometry (ASG) Page 1 — Title, Scope, and Foundational Framework V1. 0

Introduction and ScopeWe introduce Adaptive Stability Geometry (ASG) — a geometric and variationalframework for analyzing stability, instability, and collapse in adaptive systems acrossarbitrary domains. The central premise of ASG is that system behavior is governed not byisolated variables or domain-specific equations, but by the geometry of an underlyinginstability field defined over a structured state space.ASG is designed as a coordinate-invariant and scale-invariant theory, in which thetransition between stability and collapse is determined by a finite set of dimensionlessgeometric invariants. These invariants are constructed to be independent of physical units,system representation, and underlying implementation, thereby enabling a universal treatmentof adaptive systems.