# Random-environment transport assumption audit

Family 220: Directional zero–one laws beyond iid environments and iid ballisticity. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Stochastic transport researchers can record when directional transience implies ballistic velocity under iid uniform ellipticity.

## Applicability and commercial boundary

The dependent-environment zero-one result and iid ballisticity result have different assumptions. A positive asymptotic velocity gives no practical finite-time travel guarantee.

## Initial business decision

Research infrastructure. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Represent the two environment classes separately and inspect effective finite-time estimates.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[A directional zero–one law for finite-range-dependent random environments](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026/directional-zero-one-finite-range.pdf).