What was already known
Earlier full-trace lower bounds were polynomial. A separate quasipolynomial-sample upper bound and a later uniform decoder concern the opposite direction.
AI involvement
OpenAI is credited as author and attributes its mathematical manuscripts to an internal model. No decisive human-origin repair of the lower-bound construction is disclosed.
OpenAI is credited as author and identifies the internal model as producer of these mathematical manuscripts and proof artifacts.
- Supporting source (github.com) — Quantitative lower-bound theorem, previous bounds and mechanism
- Supporting source (github.com) — Abstract and main decoder scope, including fixed retention and low-deletion regimes
- Supporting source (github.com) — Formalized lower-bound scope and comparator
Importance
Rules out polynomial-sample worst-case reconstruction at every fixed deletion rate.
Limitations
The reported Lean scope covers the sample lower bound. The separate decoder has quasipolynomial samples and bit time for fixed known rational retention probability; its polynomial regime needs deletion probability at most n^(−ε).
Technical verification
The OpenAI Lean scope document maps the complete superpolynomial worst-case sample lower bound, including fixed q and arbitrary fixed positive success probability, to a TraceReconstruction comparator. This rating applies to the lower bound; no corresponding complete formal check of the October decoder is documented here.
Formal checking
Lean formalization linked by the TraceReconstruction comparator and family 122 scope document
- Checker
- OpenAI Lean 4 library and comparator
- Scope
- Superpolynomial sample lower bounds for worst-case binary trace reconstruction at fixed deletion probability, including the quantitative n^{c log(q^3 log n)} regime
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The papers contain model-produced explanations, but no human explanation of the central multiscale lower-bound mechanism was located; Few is the evidence default.
Correction and publication history
Rules out polynomial-sample worst-case reconstruction at every fixed deletion rate.
Read this published revision