For 50 years, Strassen's 1969 recursion set the ceiling on how cheap matrix multiplication could be. The landscape is strictly defined by bilinear complexity: for every (n, m, p) matrix-multiplication tensor over a fixed field, there is a minimum number of scalar multiplications required. Beating the current record for any such combination is a concrete, machine-verifiable event — a new upper bound, published with an explicit decomposition anyone can check. GP-00002 is the standing board. Each leaf is a single (shape, field) record. Sponsors fund the bounty for each open record; the escrow releases atomically when a solver submits a rank decomposition shorter than the current best, and the machine confirms the tensor sum equals the target. Payouts here have unusually long commercial tails. A shorter 4×4 algorithm over GF(2) flows directly into every downstream coding-theory, cryptography, or error-correction system that does matrix multiplications in that field — which is an enormous share of secure computation. A shorter 3×3 over the reals would touch every numerical linear algebra library on the planet. This GP sits on Omenion because verification here is trivial: read the submitted rank-one tensors, sum them over the field, check equality against the target tensor. No panel. No subjective grading. The tensor either sums to the truth or it doesn't. Seeded with AlphaTensor's 2022 result (4×4 over GF(2) in 47 mults) as the flagship closed entry, and two of the highest-value standing open records, plus an integration axiom for the shared registry.

GP closes when all leaf records verify and the integration registry at AX-00013 passes.