Ending the Half

[Simbio]

I don't know if its the offseason rust or what, but I thought I would post this on here to see what kind of response I'd get. This will be based on high school rules:

With :10 seconds left in the half, B committs a live ball foul. At the end of the down, the clock is stopped with :06 seconds left to administer the penalty. The play had ended inbounds. Following the penalty administration, the R winds the clock, the remaining :06 seconds run off before A attempts to snap the ball, and time runs out for the half.

Is the half over, or do we have to run one untimed down? I know how the rule is worded, Rule 3.3.3.A. However, I think that would only apply if during the down where the foul occurred that the time ran out during that down.

Is this correct?