OpenAI · 122-03 · 2026-09-24 · Theoretical computer science
Quantitative lower bounds for trace reconstruction
preprints/quantitative-lower-bounds-for-trace-reconstruction-September-24-2026
Family 122. Superpolynomial lower bounds and quasipolynomial reconstruction from deletion traces.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
At every fixed deletion probability in , reconstructing an arbitrary length- binary string requires independent traces, ruling out polynomial-sample reconstruction. A uniform decoder achieves quasipolynomial sample and running-time bounds for known fixed rational retention probabilities. When the deletion probability is at most for fixed , both bounds become polynomial in the input and parameter encoding.
Exact worst-case reconstruction of a binary word from independent deletion traces requires samples for every fixed deletion probability , 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 , we prove a lower bound of samples for every fixed . Here q is the known deletion probability, and all logarithms are natural.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 122: Quantitative trace-reconstruction bounds with a uniform decoder. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.