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Nothing in your post to indicate anything wrong with the battery. You should be seeing about 14v at the battery terminals when the bike is running. So this implies a fault with either the Alternator or Reg/Rec.
My first check would be to make sure the alternator and rectifier are properly connected to each other and the battery, with all the cables in good condition and most importantly, the connections from alternator to rectifier must be good, clean and firm.
Any sign of melting, burning or charring to the above could well mean that the reg/rec is toast... But not always.
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