Localized-neck and uniform-thread stretching exponents ($L\propto (t^{\ast }-t{)}^{-1/2}\text{ or }(t^{\ast }-t{)}^{-1}$)

A constant-tension slender viscous thread loses the same cross-sectional area along each material element: $A=A_0-Ft/(3\mu )$. Volume conservation gives material stretch $A_0/A$. Near an isolated quadratic minimum of $A_0$, integration over a shrinking material width proportional to $(t^{\ast }-t{)}^{1/2}$ gives total extension exponent $-1/2$. A uniformly thin thread has the same divergent stretch everywhere and exponent $-1$. The localized coefficient is independent of remote endpoints.