Reply to: Comment on: Discontinuous codimension-two bifurcation in a Vlasov equation (arXiv:2603.22066)

TL;DR

This paper clarifies that the criticism of the original Vlasov equation bifurcation analysis stems from a definitional discrepancy, and confirms no fundamental conflict exists.

Contribution

It resolves a disagreement by identifying a definitional difference and affirms the original analysis remains valid.

Findings

The criticism is due to a definitional discrepancy.

No conflict exists between the original paper and the comment.

The original bifurcation analysis is upheld.

Abstract

The Comment criticizes the bifurcation analysis performed in the original paper on a Vlasov equation. This criticism can be traced back to a discrepancy in the definition of the paramagnetic phase. Apart from this discrepancy, there is no conflict between the Comment and the original paper.