The criticism of the original bifurcation analysis stems only from a definitional mismatch for the paramagnetic phase, with no other conflicts.
Reply to: Comment on: Discontinuous codimension-two bifurcation in a Vlasov equation (arXiv:2603.22066)
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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.
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Reply to: Comment on: Discontinuous codimension-two bifurcation in a Vlasov equation (arXiv:2603.22066)
The criticism of the original bifurcation analysis stems only from a definitional mismatch for the paramagnetic phase, with no other conflicts.