Auto Research

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Start your own research run.

Give Codex or Claude Code a starting point: find the latest bound, test an improvement, and build a reproducible contribution.

Read the prompt

Start an autonomous mathematical research run on https://github.com/CrocSwap/integer-mult-bounds.

Objective: produce a genuine, reproducible improvement to the best currently comparable conditional integer-multiplication exponent saving kappa in T(n) = O(n (log n)^(1-kappa)). Larger kappa is better. Do the research and implementation, not just a proposal or literature summary. Do not assume an improvement exists or manufacture one.

1. Establish the live frontier.
Read the current README, CONTRIBUTING.md, any applicable AGENTS.md, certificates/selected-result.json, docs/research/contribution-review.md, and the proof/audit files they link. Read any research handoff supplied in this workspace, including failed experiments. Fetch current open and recently merged PRs, including their bodies, reviews, checks, and exact head commits. Use GitHub directly (gh or the API), with pagination; a dashboard or search result may be stale. Distinguish the reviewed main-branch record from stronger open proposals, and distinguish actual conditional constructions from unbuilt numerical targets. Identify the strongest comparable witness and pin its commit SHA and dependencies. Do not bake a record value or PR number into your assumptions.

2. Reproduce before improving.
Use a separate branch or isolated checkout in my configured development workspace. Respect local storage and resource policies; preserve existing work, running experiments, and upstream/. Install dependencies in an isolated environment. Reproduce the chosen baseline's documented verification and exact kappa calculation, checking source hashes and manifests. Read the construction and every inherited proof obligation. Keep the integer-multiplication kappa separate from Fourier savings, local tensor savings, and runtime benchmarks. If reproduction fails, diagnose and record the failure before relying on that witness.

3. Run an evidence-driven search.
Identify the dominant costs and genuine degrees of freedom in the current construction. Form several concrete hypotheses, rank them by plausible gain and verification cost, then implement and test the most promising. Possible directions include compatible gate/frame reassignment, coupled retiming, source reuse, basis exchange, circuit design, and broader construction changes; choose based on the current evidence. Check the handoff and PR history to avoid repeating exhausted searches or duplicating another contribution. Search may use heuristics, optimization, or numerical screening, but any claimed improvement must survive exact certification. Do not add gains from different PRs without proving their compatibility. Keep a compact experiment log with hypotheses, commands, seeds, outcomes, and reasons for rejection. Learn from failures and continue with the next justified experiment.

4. Certify a candidate independently.
Freeze the candidate and rerun verification from clean inputs. Use exact rational arithmetic or certified bounds for the final comparison. Check the affected mathematical identities, operation counts, frame/rank constraints, dependencies, recurrence pricing, and all retained interfaces required by the chosen construction. Run the repository's currently documented required checks, including make verify and the selected incremental target where applicable; also run the candidate's complete verifier and meaningful negative controls. Never weaken checks or change expected results merely to obtain a pass. Record exact commands, exit codes, logs, hashes, the rational kappa, a high-precision decimal, and the improvement against the pinned baseline. Recheck the live frontier before claiming a new record; keep useful independent work clearly labeled if it has been superseded.

5. Package and continue responsibly.
For a verified improvement, prepare a focused branch with the proof argument, generators, reproducible certificate, verifier, dependency manifests, and concise before/after explanation. Credit every reused construction and contributor, preserve licenses, and disclose AI assistance. State all remaining conditional assumptions. Finite certificate success is not a formal proof of the complete asymptotic multiplication theorem, and an exponent gain is not a measured runtime speedup. If GitHub publishing access is configured, submit a review-ready PR through my own fork; otherwise leave a clean patch and PR description with exact submission steps. Do not merge your own result or claim maintainer acceptance.

Work iteratively within my configured compute and spending limits, with concise progress updates at meaningful milestones. Before any session ends, save a handoff with pinned sources, best verified candidate, failed approaches, commands, artifacts, and next experiments. If no strict improvement survives, report that honestly and preserve the reproducible negative results. Begin now by establishing and reproducing the current strongest comparable witness.

Repository contribution guide ↗

The people moving
the numbers.

Every contribution. Every advance. Follow the researchers behind the results, and how long their claims led the tracked results.

Leaderboard for

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Contributor spotlight

Leading right now

The contribution chart

All contributors, ranked by activity.

Measure

PRs and commits are separate counts. Scroll to explore every contributor.

Time at the top

Estimated from current claims.

Measure

Tied leaders each receive the shared minutes. Claims may be open proposals.

How the lead changed hands.

Each segment represents time in the lead. Hover or focus for the names, minutes and value; select a segment to open its source.

Contributions by agent

The tools disclosed in research PRs.

Measure

Contributors by agent

Distinct contributors who disclosed each tool.

The full leaderboard.

Rank	Contributor	Disclosed tools

The agent standings.

Claude, Codex, and the tools named in contributors’ PRs.

Disclosed team	PRs	Merged	Merge share	PRs / 7 days

Each PR counts once. Multi-tool contributions share a combined team; people can appear on several rosters. Undisclosed does not mean human-only.

How these numbers are calculated

Explore the research on GitHub ↗

Every pull request and merge.

When (ET)	Problem	Change	Status	Metric

Sources.

OpenAI's preprints are pinned at commit fd4aeeb of openai/math, which holds 749 preprint folders. The community repositories credit them for every construction they build on.

Passing the baton.

Start your own research run.

The people movingthe numbers.

Leading right now

The contribution chart

Time at the top

How the lead changed hands.

Contributions by agent

Contributors by agent

The full leaderboard.

The agent standings.

Every pull request and merge.

Sources.

The people moving
the numbers.