Without a definitive map can I still walk on the paths without breaking the law?
Yes, you can still walk on the paths without the existence of a defintiive map. However, the point is that if the path was to become obstructed thus preventing you from walking on it, there would be little you could do to ensure the path was re-opened without being able to prove its existence as a public right of way. This is what a definitive map would do.
