# Lagrangian equivalence limitation ledger

Family 340: A counterexample to the nearby Lagrangian conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Symplectic researchers can distinguish exact embedded Lagrangian equivalence from Hamiltonian isotopy in the specified high-dimensional cotangent example.

## Applicability and commercial boundary

The unrestricted conjecture counterexample does not rule out its restricted cases or improve an operational mechanics solver.

## Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

## Next verification action

Extract the exact topological/isotopy data for a research proof-dependency record.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[A counterexample to the nearby Lagrangian conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-the-nearby-Lagrangian-conjecture-September-23-2026/paper.pdf).