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As mentioned prior, wind it fully 1st count your winds till you feel the end.
Obviously, don't force it pass that point.
If worried about over wind, next time count your winds and one less than a full wind should be good.
Run it for a few weeks and keep a little log. Should run for 36 to 40 hours on a full wind, I would think.
Check manuel, for that information. If it continues to be losing & you are out of posible outside interferance like magnetic interferances or power reserves, send it back.
Good choice, Omega bought the Co-axial escapement from Goeoge Daniels and are running with it.
It is more of a marine chronometer design. Should keep time comprable to a Quartz if set correct in therory.
I have not worked on one, if it were my personal watch & out of waranty I would look in side the mechanics of it. BUT, I have bench expirence & don't recommend it.
To repair or service watches, one must be border line for pyscho-ward IMO.
Post your results if it settles down & you tame it, or send er back for adjustments.
If you have'nt read Mark Twain's commentary on his pocket watch, you should.
Everyone with any interest in watches, it should be a mandatory read. Be seated when reading it.
That and Adam & Eve's diaries translated by Mark Twain. My sugested reads for your 50th B-day.
Mike