Strain-Tensor Eigenvalue Decomposition and Intermediate Alignment in 3D Navier–Stokes

A short algebraic note recording the eigenvalue decomposition of the symmetric strain-rate tensor of a divergence-free velocity field and its consequences for the local vortex-stretching term. The intermediate eigenvalue controls the leading contribution once the vorticity direction is aligned with the intermediate eigenvector. All identities are pointwise and unconditional; they do not prove Hypothesis B and leave the supercritical gap open. Files: Strain_Eigenvalue_Breakdown.tex and Strain_Eigenvalue_Breakdown.pdf (AMS-LaTeX source and PDF); StrainEigenvalue.lean (Lean 4 skeleton of the algebraic identities; contains sorry placeholders marking points requiring additional Mathlib eigenvalue infrastructure).