AlphaTensor broke records over GF(2) but did not improve the real-field ceiling for 4×4, which remains at 49 multiplications from recursive Strassen. Any decomposition using 48 or fewer rank-one tensors over ℝ beats the 50-year record.

**Verification.** Tensor sum over ℝ. Solver submits 48 rank-one triples (u_i, v_i, w_i) ∈ ℝ^16. Verifier computes their outer-product sum and checks entrywise equality with the reference 4×4 mat-mul tensor — with a strict exact-equality test for rational-coefficient submissions, and a numerical epsilon (≤1e-9 elementwise) for floating-point submissions that declare a rounding policy.

**Prize tail.** This algorithm would touch every numerical linear-algebra library on earth. The bounty reflects that.

**State.** Open. Has been standing since 1969.