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)

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.

Sep 23, 2026upper bound 100by OpenAIgithub.com
Oct 9, 2026upper bound 36by rohanarungithub.com
Oct 10, 2026upper bound 32by rohanarunPR #2
Oct 13, 2026Last 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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DiscoverIA. Planar unit distances: the final grid of OpenAI's argument [Frontier, checked on Oct 13, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/distances-unite/

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

Not evaluated describes the scope of the Lean formalization

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
Date	Exact value	Nature	Authors	Source
Oct 10, 2026	`30`	proposed	rohanarun	PR #3
Oct 10, 2026	`32` Current record	merged	rohanarun	PR #2
Oct 9, 2026	`36` Current record	merged	rohanarun	github.com
Sep 23, 2026	`100` Current record	published	OpenAI	github.com

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

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