Auto Research: Integer multiplication below n log n

An interactive research dashboard organizes and visualizes reproducible work on lowering the integer-multiplication exponent, tracking pull requests, commits, contributors, agent usage, and every claimed improvement. It displays PR ancestry, leaderboards by minutes leading and records, contributor and agent standings (Claude, Codex, etc.), and links to pinned sources (OpenAI preprints commit). The interface emphasizes provenance: exact commits, checks, reviews, and the full PR history are surfaced so contributors can follow who produced each advance and how long claims held the frontier.

A five-step, mandatory workflow defines how to propose and certify any exponent improvement in T(n) = O(n (log n)^(1-kappa)), with larger kappa being better. Contributors must establish the live frontier, reproduce a chosen baseline in an isolated environment, perform evidence-driven searches for concrete hypotheses, and certify candidates with exact rational arithmetic and the repository’s full verification (make verify, verifier runs, recorded commands, logs, hashes, and rational kappa). Verified improvements require a focused branch, reproducible certificate, disclosed AI assistance, credited reuse, and stated conditional assumptions; contributors must not merge their own results. The system stresses that many gains remain conditional on lemmas from pinned preprints, that finite certificates are not full unconditional proofs, and that exponent gains are distinct from measured runtime speedups.