Flywheel: Sharing Agent-Driven Research as a Version-Controlled Graph

Paradigma argues that AI-assisted research should be shared as a running record that others can check and extend, not only as a finished paper. Its proposal describes Flywheel, a tool it is building that works like a ledger for a research project, in the way git keeps the history of a software project. Each step, the evidence behind it and the directions that failed stay in a graph, so a newcomer, or that newcomer's AI model, can start from the current frontier of a problem, inspect a particular step or branch off with a correction.

Paradigma's worked example concerns the Riemann hypothesis, a famous unsolved conjecture about where the zeros of the zeta function lie. It had OpenAI's Codex import the current state of the art into a Flywheel graph, including the recent result from Anthropic's Claude described in Anthropic's research post. A separate Codex session, running in an internal harness with the graph as context and an internal math-model checkpoint it could call for quick calculations, then produced a result in a different direction. The mathematician Gröchenig showed in 2020 that the hypothesis is equivalent to a particular curve derived from the zeta function passing an infinite family of tests: determinants of matrices built from shifted values of the curve must be nonnegative at every matrix size. Paradigma reports that the harness proved, without assuming the hypothesis, that every 2×2 test passes, by showing that the curve bends downward everywhere on a logarithmic scale, and that it checked the proof in the Lean proof assistant without placeholder steps or custom axioms. Paradigma states that this is not a proof of the hypothesis, that larger matrices remain open and that it is not sure the result is new. Its audit of the run logs credits the decisive steps and corrections to Codex, with the internal checkpoint supplying several correct calculations.

The example is meant to show the publishing model rather than settle the mathematics. Paradigma expects the objection that releasing every partial result will bury reviewers, and answers that the problem belongs to the paper format, which hides the process and makes the reviewer reconstruct it. A graph shows where the argument turns, which steps are formally verified and what the model was given versus what it found. Paradigma leaves the central question open: it does not yet know how to give anyone an incentive to review, though it suggests other people's models could spend compute trying to break a result while the graph records what held. It also calls Flywheel rough around the edges. The proposal and its one example establish a design argument, not evidence that open review of this kind will happen.