What question did this study set out to answer?

This work aims to characterize retention as a stable state following the end of external influence.

January 6, 2026Open Access

Retention Without Dynamics: A Lagrangian Model of Post-Event Stability

Key Points

This work aims to characterize retention as a stable state following the end of external influence.
Introduced a variational framework for retention stability.
Formulated a Lagrangian model involving retentional difference.
Derived conditions for self-sustaining retentional states and exit conditions.
Defined retention as an ontologically distinct post-dynamical regime.
Demonstrated neutral stability and hysteresis in the model.
Established the framework without reliance on energy flow or learning.

Abstract

This work introduces a minimal variational framework for describing retention as a physical mode of stability emerging after the cessation of external dynamics. A Lagrangian model is formulated in terms of a retentional difference and an autonomous retentional node evolving in pseudo-time. The study derives strict threshold conditions for self-sustaining retentional states, demonstrates neutral stability and hysteresis, and defines operational exit conditions without invoking energy flow, learning, or dissipative dynamics. The framework establishes retention as an ontologically distinct post-dynamical regime, providing a foundational basis for the physics and philosophy of persistence.

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