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For warm starting states several competing definitions exist, and they disagree on whether the sharp kinks remain.","posed_since":"","precise":"For an initial Gibbs state $\\rho_0 = \\exp(-\\beta H_i)/Z$, compare generalized Loschmidt echoes (the interferometric echo $\\operatorname{tr}(\\rho_0 U(t))$ and fidelity-based echoes) in interacting models. Does any measurable generalization show nonanalyticities at finite $\\beta$ that connect continuously to the pure-state transitions as $\\beta \\to \\infty$? 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