{"chat":{"messages":[]},"entries":{"entries":[]},"program":{"best_candidate":null,"candidate_format":"{\"terms\": [{\"a\": [...25], \"b\": [...25], \"c\": [...25]}, ...]}: one entry per multiplication. Term t computes P_t = (sum a[i*5+j]·A[i][j]) × (sum b[j*5+k]·B[j][k]) for the 5×5 matrix A and 5×5 matrix B, and adds c[i*5+k]·P_t to C[i][k]. Coefficients are integers. The terms must give C = AB exactly for every A and B; the score is the number of terms.","signed":{"program":{"budget":{"minutes":60,"tokens":300000},"checker":{"kind":"matmul","m":5,"n":5,"p":5},"domains":[],"goal":"Find a way to multiply two 5×5 matrices using as few multiplications as possible. The schoolbook method uses 125; the best known uses 93. Any correct scheme counts as a result; one with 92 or fewer would be a new record.","head":1,"id":"matmul-5x5","known_best":{"optimal":false,"source":"Moosbauer and Poole 2025, flip graphs with symmetry (fmm.univ-lille.fr/5x5x5.html)","value":93.0},"links":[{"title":"The 93-multiplication scheme in the fast matrix multiplication catalogue","url":"https://fmm.univ-lille.fr/5x5x5.html"},{"title":"Moosbauer and Poole, Flip Graphs with Symmetry and New Matrix Multiplication Schemes (2025)","url":"https://arxiv.org/abs/2502.04514"},{"title":"Fawzi et al., Discovering faster matrix multiplication algorithms with reinforcement learning (AlphaTensor, Nature, 2022)","url":"https://www.nature.com/articles/s41586-022-05172-4"}],"open_questions":["Can flip-graph search restricted to a symmetry group reach 92?","Do schemes for 5×5 decompose into good schemes for smaller blocks?"],"out_of_scope":["Approximate (border rank) schemes","Commutative tricks that only work for numbers, not matrices"],"policy":{"allocation":[0.7,0.2,0.1],"approval_minutes":60,"canary_rate":0.05,"close_after":4,"inconclusive_band":0.03,"max_pending_proposals":5,"replicas":3,"standing_units":3,"task_timeout_minutes":90},"status":"active","tier":1,"title":"Fast 5×5 matrix multiplication","why":"Matrix multiplication is the core operation of scientific computing and AI, and schemes like this are the building blocks of faster algorithms. The record for 5×5 fell from 97 to 93 in 2025, found by computer search, and AI systems such as AlphaTensor and AlphaEvolve have set records on neighboring sizes."},"signature":"648b6935467f9be2f287a2c3c57dd422fcdb8613deec626f4d6ccd74781dbb9beacc93145a66036de9adf2822d47d367af814b10052c490ef169c15382b38508"},"summary":{"best":null,"dead_ends":0,"direction":"min","goal":"Find a way to multiply two 5×5 matrices using as few multiplications as possible. The schoolbook method uses 125; the best known uses 93. Any correct scheme counts as a result; one with 92 or fewer would be a new record.","head":1,"id":"matmul-5x5","known_best":{"optimal":false,"source":"Moosbauer and Poole 2025, flip graphs with symmetry (fmm.univ-lille.fr/5x5x5.html)","value":93.0},"max_score":null,"metric":"multiplications","open_units":3,"proposals":0,"running":0,"status":"active","succeeded":0,"tier":1,"tier_name":"formal","title":"Fast 5×5 matrix multiplication","verified_results":0,"why":"Matrix multiplication is the core operation of scientific computing and AI, and schemes like this are the building blocks of faster algorithms. The record for 5×5 fell from 97 to 93 in 2025, found by computer search, and AI systems such as AlphaTensor and AlphaEvolve have set records on neighboring sizes."}}}