Remark. Rates and hitting times do not survive time reparameterization [ftip-00BP]
Remark. Rates and hitting times do not survive time reparameterization [ftip-00BP]
Two flows can traverse the same curve with arbitrarily different physical clocks. A convergence rate, finite-step budget, or hitting time stated in \(t\) therefore does not transfer through Theorem [ftip-00BN] without quantitative bounds on \(a\) and its integral. If \(\tau _{\max }<\infty \), even the tail and limit of the gradient-flow path are not reached.