Unconditional Axis-Regularity in the 5D Corridor

We study axis regularity for the three-dimensional axisymmetric incompressible Navier–Stokes equations through a five-dimensional radial lift with weighted measure $$d{\mu }_5=r^{3}drdz\mathrm{.}$$ In this formulation the axis problem is reduced to three weighted unit-cylinder estimates: a Hardy–Campanato decay estimate for the singular parabolic core, a weighted Friedrichs–Poincaré estimate for the renormalized vorticity branch, and a localized weighted quartic estimate for the swirl source. The distinguished corridor $$\alpha \in (\frac{3}{4},1)$$ is the range singled out by the scaling analysis of the lifted problem. The main theorem is stated in unconditional form; the remaining unit-scale constants are treated as certified numerical inputs and are recorded in Appendix~A. The body of the paper presents the full analytic reduction from these weighted estimates to a contractive Morrey iteration at the axis.