Not yet.
Claiming the bottom of the Artic Ocean is a very long term thing. Step one is to stake your claim. Russia will now wait and see what happens. There will be a lot of diplomacy, expert discussions and drinking tea and vodka for a long time. The problem of ownership had presented itself with Antarctica too. That resulted in the Antarctic Treaty which has preserved peace on the South Pole for 50 years now, though there are many resources. I expect a similar scenario at the North Pole. Russia's main objective is to make sure that noone else starts to exploit the Arctic riches and/or encroach on their territory. I do feel it is important that the International Community (most importantly the UN) strongly rejects this course of action.
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They who can give up essential liberty to obtain a little temporary safety, deserve neither liberty nor safety.