Second-brain topology
The shape of your external memory has a measurable cost.
Topology over volume
Second-brain systems are usually judged by how much they hold. The more useful question is what shape they hold it in. Two note collections of the same size can have wildly different treewidth, and the low-width one is the one you can actually navigate and reason over without holding the whole thing in working memory.
Treewidth is, almost literally, the amount of context you must keep active to make sense of a region. That is why a sprawling but tree-like vault feels manageable while a smaller but densely cross-linked one feels overwhelming: the second has higher width.
The meter applied to memory
The thesis's eighth substrate is cognition, and the claim is the same as for the other seven: the cost of holding a structure is exponential in its treewidth. Your external memory obeys the same law as a tensor network.
Questions
Is a bigger second brain harder to use?
Not necessarily — size is linear, width is the exponent. A large, low-treewidth vault can be easier than a small, high-width one.
How would I lower my vault's treewidth?
By factoring dense clusters into smaller, locally-coherent notes with tree-like links — separating what can be separated, per the shadow–mirror frame.