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OpenAI's Sidorenko counterexample: the remainder constant of one counting step

no lower bound tracked≤ value ≤189lower boundupper bound

Best proposal, not yet published : value ≤ 28 (Oct 10, 2026, PR #3)

010006 Octupdated on Oct 13, 2026Upper bound 1641, Sep 23, 2026, OpenAI, publishedUpper bound 1032, Oct 9, 2026, rohanarun, mergedUpper bound 978, Oct 9, 2026, rohanarun, mergedUpper bound 189, Oct 10, 2026, rohanarun, mergedUpper bound 28, Oct 10, 2026, rohanarun, proposal, not yet published28upper0100027 Sept2 Oct7 Oct12 Octupdated on Oct 13, 2026Upper bound 1641, Sep 23, 2026, OpenAI, publishedUpper bound 1032, Oct 9, 2026, rohanarun, mergedUpper bound 978, Oct 9, 2026, rohanarun, mergedUpper bound 189, Oct 10, 2026, rohanarun, mergedUpper bound 28, Oct 10, 2026, rohanarun, proposal, not yet published28upper bound
Only one side is tracked: there is no space between two bounds to colour.Hover over the points or move through them with the keyboard; a click opens the PR, the commit or the source page.Tap a point to read its source; tap it again to open the PR or the page.
  1. upper bound 1032by rohanarungithub.com
  2. upper bound 978by rohanarunPR #1
  3. upper bound 189by rohanarunPR #2
  4. Last checked
Upper bound · proposal, not yet published · Oct 10, 2026
Exact value : 28
Cut the Sidorenko residual constant from 189 to 28 (even D ≥ 30) · PR #3
by rohanarun
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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/en/frontieres/sidorenko/

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).

Points : Upper bound
DateExact valueNatureAuthorsSource
Oct 10, 202628proposedrohanarunPR #3
Oct 10, 2026189 Current recordmergedrohanarunPR #2
Oct 9, 2026978 Current recordmergedrohanarunPR #1
Oct 9, 20261032 Current recordmergedrohanarungithub.com
Sep 23, 20261641 Current recordpublishedOpenAIgithub.com
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