Matrix-multiplication exponent

The exponent ω is the infimum such that n×n matrix multiplication uses O(n^ω) arithmetic operations.

Specification version 1Published 2026-08-271 evidence records

What we know

Current frontiers derived from accepted Claims.

PROVEN LOWER BOUNDBEST KNOWN UPPER BOUND

2 ≤ ω < 2.371339

UNKNOWN GAP

Proven lower boundGap: UnknownBest known upper bound

Claims

Assertions tied to evidence, attribution, and review.

2026

CLM-LR-DRAFT-OMEGA-1>= 2 ≤ ω < 2.371339ASYMPTOTIC BOUNDNew bounds for matrix multiplicationEvidence: 1 linked source records

SOURCE CONFIRMED

Timeline

The frontier as it changed over time.

How this frontier is derived

Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.

—No breakthrough events recorded yetEvents appear here when an accepted Claim tightens a bound or closes the frontier.

Specification

What question is being asked?

The exponent ω is the infimum such that n×n matrix multiplication uses O(n^ω) arithmetic operations.

Constraints: model=arithmetic complexity · matrices=n×n

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Corrections & disputes

Record history

No unresolved corrections or disputes are recorded for this published version.

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Editorial status

Evidence-backed record

1 accepted Claim, with 1 linked evidence records.

Human-reviewed · No AI-only claims

Verified prizes & bounties

Active verified incentives

No active verified bounties are linked to this Limit.

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Reproducibility

Machine-checked history

No accepted machine-checked reproductions are recorded for this Limit.

Cite this LimitLimits Registry. LR-DRAFT-OMEGA. Matrix-multiplication exponent. 2026.