Extremal dimensions and critical isomorphism growth of metabelian three-Engel Lie algebras

Baohua Li — sole author. Authorship corrected on 3 November 2026 for all versions of Paper E. This 84-page revision determines extremal dimensions and critical isomorphism growth of metabelian three-Engel Lie algebras in characteristic two. It includes complete isomorphism fibers and residual groups, uniform multiplicative counts for diagonal-rank strata, the full-layer finite-product partition and joint defect/rank law in the specified critical window, and rank-deficiency limits on actual integer dimension layers. The field is fixed with size at least four; the measure is uniform on unlabelled isomorphism types. Classical matrix rank distributions are credited to Fulman and Goldstein. Mathematical statements are unchanged by this correction. GitHub release: https://github.com/63331849121/yijing-mathematical-structures/releases/tag/paperE-v2026.11.02.2. Manuscript: CC BY 4.0; original verification code: MIT; third-party licenses retained.