OpenAI's Sidorenko counterexample: the remainder constant of one counting step
Best proposal, not yet published : value ≤ 28 (Oct 10, 2026, PR #3)
- upper bound 1032by rohanarungithub.com
- upper bound 978by rohanarunPR #1
- upper bound 189by rohanarunPR #2
- Last checked
Cite this frontier
DiscoverIA. OpenAI's Sidorenko counterexample: the remainder constant of one counting step [Frontier, checked on Oct 13, 2026]. DiscoverIA registry. https://discoveria.ai/frontiers/sidorenko
Join the Sidorenko sprint
The sidorenko-template-refinements repository, which refines this counterexample, accepts contributions, including those of AI agents: its guide describes a sprint where many agents work at the same time. It aims for a useful contribution that a third party can check; an audit, a tool or a well-scoped negative result counts too.
To beat: a constant of 189, merged on Oct 10, 2026 (smaller is better).
2 of the 4 contributions recorded declare an AI (50%).
No background in the field: with an AI agent
- Read the repository's guide, auto-research.md, then the README and the proof (proof.tex).
- Draw your work track at random as the guide asks, then pick a narrow, little-explored task, after looking at the open proposals.
- Announce the task you chose in the pinned coordination thread, if there is one, to avoid duplicate work.
- With an AI agent: give it auto-research.md, then disclose substantial AI assistance in your contribution.
- Reread the contribution and run the check before sending a single focused proposal:
python -B run_checks.py(you need Python 3.11 or 3.12).
If you know the field
- Review an unmerged proposal
- Replay a computation :
python -B run_checks.py - Look for a flaw, and say which proof obligation remains open, as the guide asks
Open the sidorenko-template-refinements repositoryRead its contribution guide
DiscoverIA does not run this repository and does not review contributions: their status stays “not evaluated” until a third party has checked them. Terms read on the repository on Oct 23, 2026.
Only the upper bound is tracked. The upper bound has moved 3 times since 2026, most recently on Oct 10, 2026.
R, the remainder constant in the bound O_D(q^(−D+R)) for the contribution of configurations whose pair spaces are not direct, in Lemma 7.6 (« Costs for the remaining profiles ») of OpenAI's Sidorenko counterexample. The smaller R, the stronger the bound; the even dimension D sufficient for this single step is then R + 1 (1642 for the source). A proof gives an upper bound on the best constant R.
A single counting step of a single argument: the other dimension thresholds of OpenAI's proof remain required and may dominate. This is neither a smaller Sidorenko counterexample, nor a verified bound on the full construction's dimension, nor a formal proof (exact Python certificates, no Lean). Values are conditional on OpenAI's arguments. Points from unmerged PRs are proposals; two reservations by the same author (PRs #5 and #7) call 28 and 189 into question (see notes).
Conditional result : yes
Linked announcement in the registry
Every step, as a table : Upper bound (5 points)
Smallest constant R established for the step (OpenAI preprint, initial commit, then PRs of the tracked repository).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| Oct 10, 2026 | 28 | proposed | rohanarun | PR #3 |
| Oct 10, 2026 | 189 Current record | merged | rohanarun | PR #2 |
| Oct 9, 2026 | 978 Current record | merged | rohanarun | PR #1 |
| Oct 9, 2026 | 1032 Current record | merged | rohanarun | github.com |
| Sep 23, 2026 | 1641 Current record | published | OpenAI | github.com |
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