Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 122-03. Quantitative lower bounds for trace reconstruction
Manuscript map · lines 4835–4844
OpenAI@2026-10-07#rem:oai-p-122-03
Authors: OpenAI. Family 122.
Title: Quantitative lower bounds for trace reconstruction.
Abstract: Exact worst-case reconstruction of a binary word from independent deletion traces requires $n{}{{}Omega({}log{}log n)}$ samples for every fixed deletion probability $q{}in(0,1)$, even with unrestricted computation and any fixed positive success probability. This gives a negative answer to the polynomial-sample question for binary trace reconstruction. More generally, when $q{}3{}log n{}to{}infty$, we prove a lower bound of $n{}{c{}log(q{}3{}log n)}$ samples for every fixed $0{}lt c{}lt 1/(4{}log2)$. Here q is the known deletion probability, and all logarithms are natural.
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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