TIE 2.1-1: Necessary Conditions for Stability in Interacting Systems Prediction Series of the Theory of Imbalance of Energy (TIE v2)

Stable interacting systems are observed across a wide range of physical contexts, yet
the structural requirements that permit such stability are often treated as consequences
of specific interaction laws rather than as necessary conditions. In this work, we derive
minimal constraints that must be satisfied by any interacting system capable of exhibiting
persistent bounded behavior under perturbation. Without assuming any force law, geometric
structure, or explanatory mechanism, we show that unconstrained instantaneous interaction
response is incompatible with robust stability. Stability instead requires finite interaction
response, which necessarily introduces delayed adjustment, bounded correction rates, and
finite predictability horizons. These results are framed as necessary conditions rather than
sufficient explanations and are explicitly falsifiable. The analysis establishes foundational
constraints that any physical theory describing stable interacting systems must satisfy.
Series Position within TIE v2. — This paper forms part of the Theory of Imbalance of Energy
(TIE v2) program, which is organized into synthesis (TIE 2.0), prediction (TIE 2.1), explanation
(TIE 2.2), and constant-emergence (TIE 2.3) series. The present work is the first contribution
to the TIE 2.1 prediction series. It establishes structural necessity conditions for stability that are
required of any physical theory prior to the introduction of explanatory mechanisms, numerical
constants, or ontological commitments.