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Problems / algebraic complexity

algebraic complexity / matrix multiplication

Algebraic continuation around rational rank-48 schemes for 4×4 matrix multiplication

Characterize exact algebraic families, boundary degenerations, and lower-bound obstructions around known rational rank-48 decompositions of 4×4 matrix multiplication.

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68Significance / 100
1Frontier events
2Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Acceptance criteria: Replay the exact rational certificate, audit boundary specializations, and distinguish finite computations from global rank or impossibility theorems.

Append-only history

Frontier timeline

algebraic complexityJul 19, 2026Significance 68/100

Exact rank-48 continuation artifacts opened for independent replay

A publication-worthy computational note and its exact certificates are now indexed with open replay tasks. The record does not promote the construction beyond reported status until the full CRT certificate is independently rerun.

ReportedAlgebraic continuation around rational rank-48 schemes for 4×4 matrix multiplication →
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Reported

The packaged exact artifacts report a three-parameter rational surface of rank-48 decompositions satisfying all 4,096 Brent equations, together with exact boundary-core and finite-field Koszul records.

The status records the packaged exact certificate and source provenance. A fresh full certificate replay is still open.

Recorded attempts

Evidence graph

Connected research record

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    The packaged exact artifacts report a three-parameter rational surface of rank-48 decompositions satisfying all 4,096 Brent equations, together with exact boundary-core and finite-field Koszul records.

    parent of · claim · construction

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