Turbulence as a Developmental Geometry: A Structural Reformulation of the Vorticity–Stretching Mechanism

This work establishes a structural correspondence between turbulence and Developmental Geometry (DG). The vorticity–stretching mechanism of the Navier–Stokes equations is shown to be the unique local, degree‑1 homogeneous, sign‑preserving curvature–scale coupling required by the DG balance law. The finite cascade flux induces a quadratic propagation cone in log‑scale space, and the dissipation anomaly is conjecturally identified with the DG δ−1/2 divergence. The unattainability of infinite cascade is formulated as a DG structural censorship conjecture. These correspondences arise from shared geometric invariants rather than physical assumptions, suggesting that turbulence is a natural realization of DG and that its qualitative features follow from the underlying developmental geometry.