⚠️ WORK IN PROGRESS — This catalog is actively under construction. Some entries may be missing, incorrect, or mis-attributed. Treat all values as provisional until cross-checked against the cited source. See DISCOVERIES_PENDING_ANALYSIS.md and ROADMAP.md for known gaps.

MMC — Matrix Multiplication Catalog

Browse 2,300+ verified factor matrices for fast matrix-multiplication algorithms, drawn from Strassen 1969 → AlphaEvolve 2025. Every entry here has its factor matrices on disk and round-trips through a Java verifier. See the repository for the methodology and source.

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format field ω rank (UB) + adds lineage source scheme

⟨∞,∞,∞⟩ — asymptotic exponent ω over time

The matrix-multiplication exponent ω — smallest constant such that ⟨n,n,n⟩ can be done in O(n^ω) operations as n → ∞. Lower bound is the information-theoretic ω ≥ 2; whether ω = 2 is open. Data from docs/omega-history.json. The plot also overlays the commutative exponent ωc (data from docs/omega-history-commutative.json) — each green point is a single-shape upper bound logn(Rc(n)); commutative algorithms do NOT lift to recursive matrix matmul, so the commutative series is not an aggregated asymptotic like NC ω.

y-axis is bounded [2, max(ω) + 0.05]; linear by default.
kind year ω ≤ method source notes

References

Lower-bound citations referenced in the table above. Numbers are stable across filter changes.