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Stat Man
There are very limited circumstances where "you can take points off the scoreboard." You have to refer to the correctable error part of the rules. But even in most cases of correctable error, you don't take points off the scorreboard. You correct the error and resume the game, with all scores that occurred left on the scoreboard. The only time you take them off is if you have erroneously counted a basket or you have erroneously awarded a FT that was made. And all correctable errors must be caught in time to be corrected.
With most things that occur like your six on the court, everything that occurred until it was noticed stands, and the rules violation is penalized at the point it is discovered. So in almost all cases, points will stay on the scoreboard if the refs do it right.
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