Integer multiplication leaderboard
Community progress on OpenAI #109. Compare conditional exponent savings, follow the evidence, and give every contribution its credit.
Snapshot: 2026-10-08T12:53:45.074Z
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The challenge
T(n) = O(n (log n)^(1 − κ)) in the fixed finite-alphabet multitape Turing-machine model.
Reported conditional claims, not verified theorems. Larger κ means a stronger asymptotic exponent saving—not faster measured runtime. Different constructions retain different hypotheses; inspect each source before comparing or reusing it.
Reported bounds
1. **icekylinx — κ = 3.84569 × 10⁻⁵** · Conditional, open PR
Copied retained centers · two-stage assembly. PR #36 · Source 11817cc
2. **DominikScholz — κ = 1.6631776 × 10⁻⁵** · Conditional, open PR
Fixed local bases in two stages. PR #35 · Source 9c345a2
3. **jamesyc — κ = 1.639226629 × 10⁻⁵** · Conditional, open PR
Reversed two-stage basis · balanced assembly. PR #34 · Source 7fecbe3
4. **rohanarun — κ = 1.5878574 × 10⁻⁵** · Conditional, open PR
Exact data-corner certificates. PR #31 · Source 122e645
5. **jacklightChen — κ = 1.5536 × 10⁻⁵** · Conditional, open PR
Two-stage controlled corners. PR #29 · Source 9d96327
6. **eumemic — κ = 1.076678 × 10⁻⁶** · Conditional, open PR
Smaller h30 producer · complex batching. PR #15 · Source a17cab3
Drafts to watch
- **rohanarun — κ = 3.850771033 × 10⁻⁵** · Draft, unreviewed
Copied centers + reversed corners; full integrated check pending in cited draft. PR #37 · Source 2f7578a
- **hipotures — κ = ≈ 1.1668950558467842 × 10⁻⁶** · Draft, unreviewed
Alternative source-framed h53 construction. PR #20 · Source 4f8d6c8
Verification is a contribution, too
princezuda: Lean certificate arithmetic, scoped algebra and an independent finite-circuit check. The author explicitly does not claim formal verification of the full multiplication theorem.
Attribution and updates
Editorial snapshot of selected public contributions, not a live GitHub feed or an exhaustive priority record. The ranking takes one strongest non-draft claim per listed submitter, ordered by reported κ. Drafts are separate. None of these external claims has been accepted as a full proof by Prove Together. Source commits pin what was indexed; PR discussions may change.
Built on OpenAI's original manuscript, Douglas Colkitt's compact-control framework, the work of David Harvey and Joris van der Hoeven, and the community dependency chains cited in each PR. Credit also belongs to Paureel, Bortlesboat, dleen, RaD / hipotures and Swapnil Jain. Ranking a submitter does not assign sole credit. Retain the source authors' AI-assistance disclosures.
Post new bounds, reproducibility reports, corrections and missing attribution on the board with an exact rational κ, assumptions, immutable commit, checks and full credit. Also submit a PR upstream; posting here does not create one. This is an independent community index, not an endorsement by the upstream authors.