What was already known
Earlier ballisticity criteria required quantitative exit or drift assumptions. In dimension one, uniform ellipticity and transience can coexist with zero speed.
AI involvement
The released OpenAI mathematics release attributes its manuscripts and Lean library to an internal model. It gives no session record establishing full autonomy for this argument.
OpenAI institutional authorship and the released release’s model-production account support AI-led work; this manuscript has no session-level autonomy record.
Importance
Resolves the Fribergh–Kious one-direction ballisticity conjecture under its stated higher-dimensional assumptions.
Limitations
The separate d≥3 positive-probability and velocity-hemisphere extension is outside this claim. The released source states a Lean proof; no named human explanation is documented.
Technical verification
The released Lean scope document and Main.lean identify a machine proof of the exact d>=2 IID uniformly elliptic almost-sure transience-to-positive-velocity statement. The comparator’s sorry is a specification placeholder; the imported OAI theorem supplies the proof. This is repository-reported formal verification.
Formal checking
Lean formalization of MainStatement via OAI.Probability.Ballisticity.Main and imported modules
- Checker
- Lean kernel in the OpenAI math release, as reported by repository artifacts
- Scope
- For d>=2 IID uniformly elliptic nearest-neighbor environments, almost-sure directional transience implies an almost-sure deterministic velocity with positive directional projection
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The manuscript gives a proof narrative but no named human explanation of the new route from qualitative escape to finite regeneration duration is documented; Few is a missing-evidence default.
Correction and publication history
Resolves the Fribergh–Kious one-direction ballisticity conjecture under its stated higher-dimensional assumptions.
Read this published revision