Exact Tensor Ranks and Fast CPU Contractions with Wirkung

Wirkung discovers and certifies exact tensor-rank results: rank and border rank 14 for T(1,2,2), and 25 for T(1,2,3); border-rank lower bounds 40 for T(1,2,4), 47 for T(1,3,3), and 45 for T(2,2,3). Independent proof-DAG verification combines border substitution, symmetry reduction, Koszul flattenings and integer projections. Reduced classes share proofs across roots; torus-weight blocks replace dense Koszul matrices. The decompositions yield optimal 14- and 25-product bilinear block algorithms, with certified product-count overhead at most 2.5% and 6.4% for the 41- and 50-product constructions. The product-count correspondence holds for every fixed positive rectangular block shape; over the complex numbers, its limiting form equals border rank. Whole-contraction CPU benchmarks on x86 and Apple M4 demonstrate hardware-dependent selection of transform executors. The record provides the paper, editable vector-figure sources, certificates, independent verifiers, reproducibility code and measurements under component-specific terms. Research evaluation and reproduction are permitted; production licensing is separate.