There's a precise point where your brand and a competitor collapse into the same thing

I work in marketing but my background has always been in maths and the natural sciences. I love it when I can bring these two things together, and this is a really good example of that. To get marketing right in the world of AI you do need to understand some of the underlying mechanisms, otherwise you are doomed to repeat the mistakes that marketing has been making for years. This article is about just one of those things - when you are writing a new blog post or content piece how similar or not should it be to the other pieces you have written? Is repeating yourself good or bad? How much variation should there be?

I've tried to answer that here and this approach is something that I use in my own strategy. Hopefully useful to others.

I wrote before that your brand competes for a drawer rather than renting one. That was the right mechanism, described at the wrong resolution. A new theory published this year gives the actual geometry, and it changes "crowded" from a vague complaint into a specific, predictable event.

The question the original mechanism left open

Superposition explains why a model with limited dimensions ends up representing far more concepts than it has room for: most features are rarely active at once, so they can safely overlap. What that explanation doesn't tell you is where the overlap actually happens, or whether some features get a cleaner allocation of the available space than others. It treats "shares space" as one category. It isn't.

What the new paper actually measures

Ivanov, Oozeer, Raval, Pejovic, Upadhyay and Abdullah (2026) build what they call a frame operator, a matrix that describes how each feature allocates its weight across the model's available directions. Their central finding: once a model is asked to hold more features than it has comfortable room for, something specific happens, not a general fuzziness. Features "collapse onto single eigenspaces, organise into tight frames, and admit discrete classification." That's the technical version of two things that used to be separate becoming, structurally, the same thing.

How I think about this visually to help me make sense to myself :)

Room to spareThree features, three clean directions. Nothing shares space, nothing blurs.

SuperpositionNine features, the same three directions. Two of them land close enough to blur into each other.

Three features in three directions don't need to negotiate. Nine features sharing the same three directions do, and the paper's finding is that this negotiation has a sharp edge, not a gradual one. Below a certain density, everything stays distinct. Above it, specific pairs collapse onto the same direction. Your content either falls on the comfortable side of that edge or the collapsed side. There isn't a well-represented-but-slightly-crowded middle the way "superposition" alone suggests.

This site already makes the same argument, by accident

The nav grid on this site's own homepage assigns a vector count to each section, more for the Archive, fewer for About, as a visual stand-in for how many distinct ideas that section holds. It was built as a design choice in July, before I'd read this paper. It's a coincidence that it happens to illustrate the theory correctly: a section with one clean feature gets one clean line, a section with thirteen overlapping ones gets a tangle. The design didn't know why that was the right metaphor. Now there's a published answer for why it is.

What determines which side of the edge you're on

The paper's practical lever isn't how much content you publish, it's how distinctly your content occupies its own direction relative to everything else already in that part of the space. Two pieces of writing that make the same argument, in the same register, about the same topic, are candidates for the same eigenspace, regardless of how much effort went into either one. The fix was never "write more." It's writing something whose direction doesn't already have eight other things pointing at it.

What to actually check

Before publishing a piece that argues for a position already well covered on your own site or elsewhere, check which existing "direction" it's closest to. If the honest answer is "several," that's not evidence you've found an important topic. It's evidence you're approaching the collapsed side of the edge, and the model is likely to represent your version and the others as one blurred feature rather than as a distinct, retrievable one.

I enjoy chatting about subjects like this, so get in touch if this is interesting to you.

Related reading

• Your brand doesn't get its own space inside an AI model
• AI Visibility Is a Layered Problem