Is 47 multiplications optimal for 4x4 matrix multiplication over GF(2)? Beat AlphaTensor's rank-47 scheme

Over the field $\mathbb{F}_2=\mathrm{GF}(2)$, the product of two $4\times 4$ matrices can be computed with 47 scalar multiplications (bilinear rank 47), discovered by AlphaTensor (2022) - beating the 49 multiplications of two recursive levels of Strassen's algorithm. Whether 47 is optimal is open: no bilinear algorithm for $4\times4$ multiplication over $\mathbb{F}_2$ using $\le 46$ multiplications is known, and no matching lower bound is proven. Exhibit a bilinear algorithm multiplying $4\times4$ matrices over $\mathbb{F}_2$ using at most 46 multiplications (improving the upper bound $R_{\mathbb{F}_2}(\langle 4,4,4\rangle) \le 47$), or prove a lower bound exceeding the current best-known value.

Acceptance. FULLY RESOLVES (upper bound): an explicit set of $r \le 46$ rank-1 triples $\{(u_k,v_k,w_k)\}$ with $u_k,v_k,w_k \in \mathbb{F}_2^{16}$ whose sum equals the $\langle 4,4,4\rangle$ matrix-multiplication tensor over $\mathbb{F}_2$ - verifiable exactly (no floating point) by expanding the sum modulo 2 and checking all $16\times16\times16$ tensor entries, or equivalently by checking the induced bilinear formulas compute $C=AB \bmod 2$ on symbolic $4\times4$ inputs. FULLY RESOLVES (lower bound): a machine-checkable proof that $R_{\mathbb{F}_2}(\langle 4,4,4\rangle) \ge 48$. PARTIAL: an independent rank-47 scheme, or a nontrivial lower bound. Provide the triples and an exact (mod 2) verifier.