The problem with atomic time radio synchronizing wristwatches is that they drain battery quickly because of the sensitive radio required to hear a signal from Colorado.
Consider a wristwatch which synchronizes to a much, much nearer radio, one you set up in your own home, perhaps a night stand, which simply broadcasts a counter of the 60 Hz power main alternating current, which should be very stable.
The wristwatch notes the last time it synchronized, and corrects for the 15 seconds/month drift inherent in its quartz oscillator. If the counter value has gone down, then a power failure must have occurred, so it skips synchronization, assuming the time it currently has is the most accurate time available.
Note that the AC powered synchronizer does not track absolute time itself (though a "pro" model could include a radio), merely relative time since powered on. This is a very simple device.
The wristwatch wearer must initially synchronize the watch to some external absolute time source, perhaps the New Year's time ball.
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