Okay, so if we store a three-bit 5 as 101 (in columns 0-2) and an additional "non-null" indicating 1 in column 3, we're saying that we have a row that has an association with columns 0, 2 and 3, but not with 1. Since, you know:

> The central component of Pilosa’s data model is a boolean matrix. Each cell in the matrix is a single bit; if the bit is set, it indicates that a relationship exists between that particular row and column.

But why do I want my integers sliced apart into these associations?

So that you can perform very fast range queries on deeply complex filters on those associations