In charged AdS black holes, the topological number W changes at a boundary membership event τ_a, while the branch response C_par diverges at a separate turning point τ_b, because the two diagnostics track different local structures of the same zero point curve.
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Topological changes and response singularities in black hole thermodynamic branch structure
In charged AdS black holes, the topological number W changes at a boundary membership event τ_a, while the branch response C_par diverges at a separate turning point τ_b, because the two diagnostics track different local structures of the same zero point curve.