What was already known
Pak, Panova, and Vallejo formulated the universal tensor-square conjecture, while the related Saxl conjecture concerns distinguished staircase representations only at triangular degrees. Earlier work supported restricted constituent families.
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
Resolves the universal tensor-square conjecture for every possible symmetric-group degree.
Limitations
The statement excludes n=2,4,9; it does not say a prescribed representation works at every degree.
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
- For every positive integer n outside {2,4,9}, some irreducible complex representation of Sₙ has a tensor square containing every irreducible complex representation of Sₙ.
- 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