OpenAI · 122-02 · 2026-10-05 · Theoretical computer science

A latest-anchor induction with spectrally compact masks for worst-case trace reconstruction

preprints/A-latest-anchor-induction-with-spectrally-compact-masks-for-worst-case-trace-reconstruction-October-5-2026

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 $(0, 1)$ , reconstructing an arbitrary length- $n$ binary string requires $n^{Ω (l o g l o g n)}$ 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 $n^{- ε}$ for fixed $ε > 0$ , both bounds become polynomial in the input and parameter encoding.

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 $O ((lo g n)^{3} (1 + lo g lo g (2 n))^{6})$ . If the deletion probability is at most $n^{- ε}$ 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.

Preprint source and Lean scope

The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.

A Lean scope note is stored for family 122, but it does not name this preprint. It names 122-03. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.