Independent Verification of the Wang F₂-Certificate for R(⟨3,3,3⟩) ≥ 20
Stefan Beuchert · arXiv (Cornell University) · 2026
Independent replay-verification of Wang's finite-field lower-bound certificatefor 3×3 matrix multiplication rank over F₂. Main result: The Wang F₂-certificate (arXiv:2603.07280, 2026) forR_F₂(⟨3,3,3⟩) ≥ 20 has been fully and independently replay-verified.All 496 entries passed without failure. Runtime: ~3.3 hours. Proof mix:- flatten_matrix: 14 entries- forced_product: 14 entries- backtracking: 238 entries- degenerate: 230 entries Claim scope (guarded):- claim_type: finite_field_lower_bound_certificate- claim: R_F₂(⟨3,3,3⟩) ≥ 20 (F₂-specific only)- anti_claim: not_global_rank_lower_bound This verification does NOT imply:- integer or characteristic-free rank bounds over ℤ/ℚ/ℂ- R(⟨3,3,3⟩) = 22 or = 23- rank-22 exclusion over ℚ or ℂ Background: Bläser proved R(⟨3,3,3⟩) ≥ 20 over arbitrary fieldsby algebraic methods. Wang (arXiv:2603.07280) provides an independent,automated, machine-verifiable F₂-specific certificate with 496 entries.Both results are independent and complementary.R(⟨3,3,3⟩) remains open: 19 ≤ R ≤ 23 (Bläser / Laderman 1976). Stefan Beuchert (ORCID: 0009-0002-3883-5540) Mail:: [email protected] Reference: Wang, arXiv:2603.07280 (2026)License: Creative Commons Attribution 4.0 International