What question did this study set out to answer?

June 1, 2026Open Access

NT22: Derivation of the Fundamental Mode from the DBI Action

Key Points

This note aims to derive the fundamental oscillatory mode of the COCM ring trajectory using the DBI action.
Derivation of the linearised equation of motion for the mode.
Minimisation of the effective equilibrium energy at fixed amplitude over positive integers.
Derivation shows a unique minimum for the closed fundamental oscillatory mode under the DBI action.
The result is conditional based on the kinetic structure of DBI and the scaling of potential curvature.

Abstract

This note derives as the fundamental oscillatory mode of the COCM ring trajectory from the DBI action, closing the Bridge 3 advanced step that presumes without derivation. The derivation proceeds in two steps: (1) the linearised equation of motion for mode yields ; (2) minimisation of the effective equilibrium energy at fixed amplitude over positive integers shows for all , making the unique minimum. The result is Closed* under the DBI action, the potential ansatz , and fixed amplitude . The selection of is conditional on the ansatz: it derives from the kinetic structure of DBI combined with the scaling of the potential curvature, not from DBI alone.

NT22: Derivation of the Fundamental Mode from the DBI Action

Key Points

Abstract

Cite This Study