A further update:
http://www.theglobeandmail.com/news/politics/turf-...If the Lomonosov Ridge is shown to extend to all three of Canada, Russia and Denmark (Greenland) as well as the North Pole, that would seem to constitute the scientific basis for all three to claim the North Pole. From the first article:
"Rob Huebert, an Arctic expert at the University of Calgary, will be watching to see if Canada stretches its claim past the North Pole. The geologic justification – an undersea mountain range called the Lomonosov Ridge that stretches north from Ellesmere Island – is there, he said."
Then how much of the Lomonosov Ridge to claim then does become a political decision for all three countries and, to the extent the claims overlap, they can then negotiate or ask the International Court of Justice for a resolution. The ultimate result could well be that the territories of all three extend to the North Pole, with the North Pole itself becoming a boundary point.
When the Law of the Sea was being negotiated 30-40 years ago, I doubt it was contemplated that any continental shelf extended from one side of any ocean to the other side, although it sounds as though the Soviets could have been aware of the possibility as a result of their secret mapping of the Arctic seabed by submarine.
The bigger legal dispute over the Arctic for Canada as the ice melts could be over the Canadian claim that the Northwest Passage (officially called the Canadian Northwest Passage in Canada) is an inland Canadian waterway, whereas other countries (in particular, the US) consider it to be an international waterway.