# First-passage routing model asymptotic audit

Family 212: Planar first-passage geometry and the absence of bigeodesics. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Routing researchers can distinguish iid planar first-passage geometry from operational networks with correlated travel times.

## Applicability and commercial boundary

Infinite-grid geodesic absence and asymptotic shape smoothness do not supply a finite shortest-path acceleration or cover non-iid traffic.

## Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Test whether an actual stochastic routing model meets independence and moment assumptions before using any shape approximation.

## 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

[No bigeodesics in planar first-passage percolation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/No-bigeodesics-in-planar-first-passage-percolation-September-24-2026/main.pdf).