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Planar unit distances: the final grid of OpenAI's argument

no lower bound tracked≤ value ≤32lower boundupper bound

Best proposal, not yet published : value ≤ 30 (Oct 10, 2026, PR #3)

50100Oct 6updated on Oct 13, 2026Upper bound 100, Sep 23, 2026, OpenAI, publishedUpper bound 36, Oct 9, 2026, rohanarun, mergedUpper bound 32, Oct 10, 2026, rohanarun, mergedUpper bound 30, Oct 10, 2026, rohanarun, proposal, not yet published30upper255075100Sep 27Oct 2Oct 7Oct 12updated on Oct 13, 2026Upper bound 100, Sep 23, 2026, OpenAI, publishedUpper bound 36, Oct 9, 2026, rohanarun, mergedUpper bound 32, Oct 10, 2026, rohanarun, mergedUpper bound 30, Oct 10, 2026, rohanarun, proposal, not yet published30upper 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.What is a bound?
  1. upper bound 100by OpenAIgithub.com
  2. upper bound 36by rohanarungithub.com
  3. upper bound 32by rohanarunPR #2
  4. Last checked
Upper bound · proposal, not yet published · Oct 10, 2026
Exact value : 30
Thirty edges: a joint linear system and bipartite rigidity (6×5, beats 8×4) · PR #3
by rohanarun
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Cite this frontier

DiscoverIA. Planar unit distances: the final grid of OpenAI's argument [Frontier, checked on Oct 13, 2026]. DiscoverIA registry. https://discoveria.ai/frontiers/distances-unite

Propose an improvement No repository or platform says in writing that it accepts contributions for this problem: send a better result or a missing source with the form at the bottom of the page.

Only the upper bound is tracked. The upper bound has moved 2 times since 2026, most recently on Oct 10, 2026.

Number of selected edges in the final algebraic witness (complete grid of N left points by j anchors, N·j edges) of OpenAI's proof of a power saving for planar unit distances, general (rank-two) case; a complete grid with at least this many edges suffices for the conditional conclusion. Smaller = better reduction.

A conditional reduction of one step of the proof: it changes neither OpenAI's 4/3−δ exponent nor supplies an explicit power saving. The source's generic-grid, negligible-height and private-valuation lemmas remain hypotheses. Line cases: 6×4 = 24 edges (one locus is a line) and 4×3 = 12 (same line) are treated separately by the repository; one 8×4 grid covers every case. Points from unmerged PRs are proposals.

Conditional result : yes

Linked announcement in the registry

Every step, as a table : Upper bound (4 points)

Smallest number of edges of the final witness established (OpenAI preprint, initial commit, then PRs of the tracked repository).

Points : Upper bound
DateExact valueNatureAuthorsSource
Oct 10, 202630proposedrohanarunPR #3
Oct 10, 202632 Current recordmergedrohanarunPR #2
Oct 9, 202636 Current recordmergedrohanarungithub.com
Sep 23, 2026100 Current recordpublishedOpenAIgithub.com
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