{"id":"openai-math/The-weak-pinned-planar-distance-theorem","pdf":"https://github.com/openai/math/blob/main/preprints/The-weak-pinned-planar-distance-theorem-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-weak-pinned-planar-distance-theorem-September-23-2026","tags":["discrete-geometry","combinatorics","distinct-distances"],"score":0,"title":"The weak pinned planar distance theorem","domain":"Combinatorics","family":"167","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We prove the weak pinned Erdős distinct-distance conjecture. For every fixed ε > 0, all but $`o(n)`$ points of any n -point planar set determine at least $`n^{1-\\varepsilon}`$ distinct nonzero distances.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Planar distinct distances and unit-distance bounds"}