Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 099-03. Tree Constructions for the l1 Distortion of Binary Edit Distance
Manuscript map · lines 4385–4394
OpenAI@2026-10-07#rem:oai-p-099-03
Authors: OpenAI. Family 099.
Title: Tree Constructions for the l1 Distortion of Binary Edit Distance.
Abstract: We give two independent constructions of binary words of one length at most d whose ordinary edit-distance metrics require ℓ1 distortion ${}exp({}Omega({}sqrt{{}log d{},{}log{}log d}))$ for every sufficiently large d. We also prove a constant-distortion binary conversion for one prescribed input length. Together with the companion upper embedding theorem, these lower bounds determine the order of logarithmic distortion uniformly over finite alphabets with at least two symbols.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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