What was already known
Earlier IID constructions concerned the wired forest on transient graphs or invariant determinantal laws in amenable group settings; Lyons had posed the free-forest factor question for Cayley graphs.
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
Answers the general free uniform spanning-forest factor question without amenability or transience assumptions.
Limitations
The selected claim concerns simple unweighted locally finite graphs and a Borel factor; no finitary coding-radius guarantee is asserted.
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
- On every infinite connected locally finite simple unweighted graph, the free uniform spanning forest is a factor of independent identically distributed vertex labels under one root-free Borel equivariant rule.
- 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