What was already known
The classical one-writable-tape simulation uses a square-root space exponent; Williams asked whether that exponent could be reduced by a fixed amount in this model.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Improves the one-tape time-to-space exponent from 1/2 to 2/5.
Limitations
The initial tape and read-only symbols must have fixed polylogarithmic-space access; the simulator’s running time is unrestricted, and the result does not cover general multitape machines.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- A fixed deterministic machine with one writable tape can be simulated through a supplied time cap T≥2 in O(T^(2/5) polylog(T+2)) work-space bits while preserving its finite-control and halting outcome.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision