Classical matrix multiplication of two n×n matrices takes n^3 scalar multiplications. Strassen's 1969 algorithm recursively decomposes 2×2 into 7 multiplications (beating 8), which for 4×4 gives 49 by two recursive applications. This 49-mult ceiling held for over five decades over most fields.

In 2022, DeepMind's AlphaTensor — a reinforcement-learning system framing tensor decomposition as a single-player game — discovered a 47-multiplication decomposition of the 4×4 mat-mul tensor over GF(2). The result was published in Nature.

**Verification.** The submitted artifact is a list of 47 rank-one tensors of the form (u_i ⊗ v_i ⊗ w_i) where u_i, v_i, w_i ∈ {0,1}^16. The verifier: 1. Parses each triple. 2. Computes the outer product tensor u_i ⊗ v_i ⊗ w_i (a 16×16×16 binary tensor). 3. Sums the 47 tensors entrywise over GF(2). 4. Compares against the reference 4×4 matrix-multiplication tensor of shape 16×16×16. Equality is checked entrywise. The verifier rejects unless the sum is exactly equal to the reference target.

**Artifact format.** JSON: `{"decomposition": [{"u": [0,1,...], "v": [...], "w": [...]}, ...]}` with exactly 47 entries, each vector of length 16, entries in {0, 1}.

**Determinism.** Pure linear algebra over a finite field. No randomness, no approximations. The verifier runs in under 100ms on a single CPU.

**State.** Closed. The winning decomposition is the one published in the AlphaTensor Nature paper (doi.org/10.1038/s41586-022-05172-4). This axiom is archival — it remains on the exchange as a standing record that any future solver must beat (≤46) to claim a new bounty.