I just came up with a mathematical refinement. So I might have messed up on one or two density calculations. Sorry! I'm eliminating the sub-sub-density; that's one refinement. And I came up with a problem after an experiment, but I've resolved it. The problem was that I realized that even the number after the decimal point needs to be "octified." And the "octified" second number after the decimal point needs to be added to the "octified" first number after the decimal point. I don't expect anybody to understand this...I'm not under any illusions.
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