What was already known
Earlier work established specified constituent families and asymptotically almost all partitions; the tensor cube was known to cover all constituents. The tensor-square conjecture remained open.
AI involvement
OpenAI credits an internal model with the cyclic-polytabloid manuscript and formal proof. Earlier constituent-family and tensor-cube results are human work.
The source credits an internal OpenAI model with the mathematical manuscript and formal proof; individual-session autonomy is not documented.
- Supporting source (github.com) — How the results were produced; verification-stage caveat
- Supporting source (arxiv.org) — Prior hook and two-row constituent baseline
Importance
The claimed proof settles the staircase tensor-square conjecture for every m.
Limitations
The source reports a matching Lean proof. The broader universal tensor-square theorem is a separate claim, and no human audit of this induction is documented.
Technical verification
The release's Lean scope document says the staircase Kronecker-positivity statement is proved for every m ≥ 1, and the OAI/Saxl main file contains the corresponding theorem. This is a source-reported formal check; the Lean project was not rebuilt here. The comparator file is a target containing sorry, not the proof.
Formal checking
Lean proof of OAI.Saxl.saxl_conjecture and saxl_kronecker_pos in the OAI library, matched to the stated Saxl comparator
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- Every staircase Specht tensor square contains every irreducible of the corresponding symmetric group for m ≥ 1
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the cyclic-polytabloid mechanism is documented. Few is the evidence default, not a finding that mathematicians cannot understand the proof.
Correction and publication history
The claimed proof settles the staircase tensor-square conjecture for every m.
Read this published revision