OpenAI reports no bigeodesics in planar first-passage percolation

Planar nearest-neighbor first-passage percolation with iid nonnegative nonatomic edge weights almost surely has no doubly infinite geodesic when the minimum of four independent weights has finite second moment.

Sources for this record

What was already known

Earlier directional coalescence results excluded bigeodesics with prescribed typical end-directions, but did not rule out all bigeodesics simultaneously without limit-shape regularity.

AI involvement AI-led

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 Major

Resolves the planar no-bigeodesics conjecture under the stated moment condition.

Limitations

The moment assumption is retained; this is not the moment-free conjecture. The linked Lean scope checks differentiability of the time-constant norm for Gamma weights, not absence of bigeodesics.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

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

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and Lean-scope mismatch review for non-notifying local inclusion.

Read this published revision