AI-assisted proof of the deterministic k-server conjecture
Coester, Koutsoupias and Zbysiński report that the work function algorithm is k-competitive on every metric space.
Original report: 2026-09-14Metric embeddings
How faithfully can one distance space be represented in another?
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Understand the topics ↓3 records · Includes focused interests · How we rate progress
OpenAI reports: Planar graph metrics in L₁
The manuscript reports an L₁ embedding with a universal distortion bound for every finite connected planar graph with positive real edge lengths.
Read original source Original manuscript · family 089github.com
Original report: 2026-10-06OpenAI reports: Embedding edit distance in ℓ₁
The manuscript reports matching bounds exp(Θ(√(log d · log log d))) for the least ℓ₁ distortion of unit-cost edit distance on strings of length at most d.
Read original source Original manuscript · family 099github.com
Original report: 2026-10-06Understanding the topics
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How faithfully can one distance space be represented in another? Distortion bounds interact with geometry and algorithm design, but must specify both the source metric and the target space.
This topic groups related mathematical questions across publishers. Each focused problem carries its own baseline and each contribution retains its original source. Results are compared only when their assumptions, optimization target, and computation model agree.
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Background review: 2026-10-11. Selected sources:
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