What question did this study set out to answer?

To explore the geometric derivation of positive back-reaction amplitude delta_y from fundamental principles.

May 28, 2026Open Access

Geometric Origin of Back-Reaction Positivity in the COCM

Puntos clave

To explore the geometric derivation of positive back-reaction amplitude delta_y from fundamental principles.
Derivation of orbital ellipticity from conditions of symmetry breaking due to tension asymmetry.
Analysis based on four geometric hypotheses (G1-G4) regarding effective orbital potential.
Examination of the stability of the displacement mode G3.
Demonstrated that delta_y* > 0 arises from tension asymmetry tau_C0 >> tau_Rn.
Established a connection between the success of delta_y* > 0 and positive orbital ellipticity (e > 0).
Identified an open sub-problem regarding the stability condition of the displacement mode (m_eff^2 > 0).

Resumen

The conditional derivation of orbital ellipticity in NT6 reduces to a single open hypothesis: the back-reaction amplitude deltaᵧ > 0. This note investigates whether deltaᵧ > 0 can be derived from the bulk geometry. The central argument is that the tension asymmetry tauC0 >> tauRn breaks the symmetry deltaᵧ -> -deltaᵧ in the effective orbital potential, generating a negative linear term that displaces the equilibrium from deltaᵧ = 0 to deltaᵧ* > 0. Under four explicit geometric hypotheses G1-G4 (distinct from H1-H3 of NT6), the equilibrium satisfies deltaᵧ* > 0. Under G1-G4, the chain deltaᵧ* > 0 -> J > 0 -> e > 0 is grounded in the bulk geometry. The remaining open sub-problem is G3: the stability of the displacement mode (mₑff² > 0).

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