Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 122-02. A latest-anchor induction with spectrally compact masks for worst-case trace reconstruction
Manuscript map · lines 4825–4834
OpenAI@2026-10-07#rem:oai-p-122-02
Authors: OpenAI. Family 122.
Title: A latest-anchor induction with spectrally compact masks for worst-case trace reconstruction.
Abstract: We give an improved worst-case sample bound for reconstructing a string from independent deletion traces, with its length and retention probability known. For each fixed retention probability, the number of traces is quasipolynomial: the logarithm of the sample budget is $O(({}log n){}3(1+{}log{}log(2n)){}6)$. If the deletion probability is at most $n{}{-{}varepsilon}$ for fixed ε > 0, polynomially many traces suffice. These bounds apply to binary strings and to strings of general symbols observed exactly. They concern sample complexity and do not assert an efficient reconstruction algorithm or matching optimality.
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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