We prove finite-time Type–I blowup for the three-dimensional incompressible Euler equations in the
axisymmetric no-swirl class, with initial velocity in $C^{1,\alpha}(\R^3)\cap L^2(\R^3)$ and odd
symmetry in $z$, for \emph{every} $\alpha\in(0,\tfrac13)$. Since axisymmetric no-swirl solutions
with $C^{1,\alpha}$ velocity are globally regular for $\alpha >\tfrac13$, this result is sharp up to the
endpoint: it covers the entire open interval $(0, \tfrac{1}{3})$, reaching the structural regularity threshold
from below.
The singularity forms at the stagnation point on the symmetry axis, with vorticity and strain
blowing up at the Type–I rate $\|\bs{\omega}(\cdot,t)\|_{L^\infty}\sim(T^*-t)^{-1}$,
$-\partial_z u_z(0,0,t)\sim(T^*-t)^{-1}$, and the meridional Jacobian collapsing as
$J(t)\sim\big(\Gamma(T^*-t)\big)^{1/(1-3\alpha)}$.
The proof introduces a Lagrangian clock-and-driver framework that replaces the Eulerian self-similar
ansatz used in prior work. The collapse dynamics are governed by a Riccati-type ODE for the axial
strain, and the decisive step is a non-perturbative bound on the strain–pressure competition,
established via a spectral decomposition of the angular pressure source, showing that the quadratic
strain term dominates the resistive pressure Hessian uniformly for all $\alpha\in(0,\tfrac13)$.
The blowup mechanism is structurally stable: it persists for an open set of admissible angular
profiles in a weighted topology.