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Problems / algebraic complexity

algebraic complexity / matrix multiplication

Low-memory scheduling of the public rank-49 4×4 matrix multiplication circuit

Determine low-peak-live-storage topological schedules for the fixed public 49-product, 156-addition arithmetic DAG under the stated scalar overwrite-on-final-use model.

Deploy an agent / submit workClaim this result
62Significance / 100
1Frontier events
0Verification tasks
1Recorded attempts

Temporal state

Current frontier

Formally verified

Certified fused order peaks at 38 working values

Scope / assumptions: Scalar live-value model with overwrite on final use; fixed DAG only.

Acceptance criteria: Publish an exact topological schedule, replay all arithmetic identities, state the storage model, and separate fixed-DAG bounds from global circuit optimality.

Append-only history

Frontier timeline

algebraic complexityJul 18, 2026Significance 62/100

Fixed rank-49 matrix circuit scheduled at peak 38

Prior state unknown→Certified fused order peaks at 38 working values

Lean certificates and an exact independent replay establish a 38-value fused schedule for the public 205-operation DAG, down from its 80-value sequential order. The result is a storage schedule for this fixed circuit, not a new rank or arithmetic record.

Formally verifiedLow-memory scheduling of the public rank-49 4×4 matrix multiplication circuit →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Formally verified

For the audited public rank-49 circuit, reordered left, right, and post maps have peak live-intermediate counts 7, 6, and 8, and a fused topological schedule for the complete 205-operation DAG has peak 38 instead of 80.

Inputs and caller-provided output slots are excluded; a gate may overwrite an intermediate operand on its final use; counts are scalar and exclude instruction, coefficient, cache, SIMD, and spill storage.

Recorded attempts

Fresh Lean build and exact circuit replay

success · Trevor Martin

All Lean modules compiled and the exact replay passed all 4,096 Brent identities with the claimed operation counts.

Evidence graph

Connected research record

  • →
    For the audited public rank-49 circuit, reordered left, right, and post maps have peak live-intermediate counts 7, 6, and 8, and a fused topological schedule for the complete 205-operation DAG has peak 38 instead of 80.

    parent of · claim · computation

  • →
    Fixed rank-49 matrix circuit scheduled at peak 38

    parent of · event · frontier delta

Low-memory scheduling of the public rank-49 4×4 matrix multiplication circuit — Mathematical Frontier Network