What is the best possible coin?

§ the source

What Eigenslur actually claims

The Eigenslur project starts from something most people have heard but rarely sit with: every word a language model has seen gets turned into a point, a coordinate in a space with a few hundred or a few thousand dimensions. Once something is a point, distance between points means something. Once distance means something, direction means something too. The famous demonstration is king minus man plus woman equals queen. Gender, in that space, isn't a bucket you sort words into. It's a direction you can walk along.

Eigenslur's actual contribution is pointing that same logic at something nobody had bothered to formalize: offensiveness. If contempt clusters as consistently in a model's training data as gender does, it should be extractable as a direction too, and a direction defined over a finite vocabulary has a hard mathematical maximum, a single token that projects further along it than any other. Eigenslur is the name that project gives to that maximum. Worth reading directly rather than through a summary, since the original argument is more careful about the geometry than this page needs to be.

§ the word

What Eigen means

Eigen is German for own or characteristic. In mathematics it shows up as eigenvalue and eigenvector: the vector a transformation does not rotate, only scales. It is the direction that belongs to the system itself, its own truest axis, as opposed to any arbitrary direction you could pick.

Eigen- as a jokey prefix for the maximal, most-extreme version of something was not invented by Eigenslur. It had already been floating around math-adjacent corners of the internet as an inside joke, in much the same way the pseudonymous account eigenrobot has used eigen- as a personal signature for years. What Eigenslur did was take that existing bit and give it a fully worked-out application, a real methodology, and enough visibility that the convention became legible outside niche math-posting circles. This project uses the same convention Eigenslur popularized, not one either project invented, because it already means exactly what is needed here.

Eigen- became a prefix for the extreme, maximal, most-itself version of whatever noun follows it. Not just characteristic anymore, but the theoretical ceiling of. The Eigenslur is not merely an offensive token. It is the most offensive token the method can find, the endpoint of that particular axis.

§ the generalization

The method was never just about slurs

Here's the part of the argument that matters more than the specific axis Eigenslur chose. Once you accept that one property can be a direction, the obvious next question is which other properties are directions, and the honest answer is most of them, as long as the property clusters consistently enough in whatever the model was trained on. Formality is a direction. Sentiment is a direction. Offensiveness, per Eigenslur, is a direction. None of that is specific to language, or to slurs, or to anything else in particular. It's a general fact about finite vector spaces: any direction you can define has an endpoint. A maximum, in the strict sense, the same way a sorted list has a largest element whether or not anyone bothered to check.

Which means the method generalizes to anything you can plausibly represent as a direction. Including, as far as anyone can tell, memecoins.

§ the axis

Memecoins have an axis too

Set language models aside for a second and think about coins.

Every token that has ever traded on a Solana DEX sits somewhere in an enormous, noisy, constantly reshuffling space defined by things like narrative strength, meme density, how well it survives being explained to a stranger in one sentence, how good it looks as a screenshot, how much people want to type the ticker out loud for no financial reason at all. Call the whole bundle social velocity if you need one word for it, though one word is doing a lot of work there.

None of that collapses to a single number, and it was never going to. It's a direction, the same shape as gender was a direction, the same shape as the fuzzier properties researchers keep finding anyway. Coins with high memeability, strong narrative, and real social velocity all point roughly the same way through that space. Coins that are technically sound and mathematically fine and that nobody has ever screenshotted point somewhere else entirely.

And because the space is finite, because there are only so many tickers that have launched or ever will launch with enough liquidity to matter, that direction has an endpoint too. One point, further out than anything that came before it or will come after.

That point is the Eigencoin.

§ the definition

What the Eigencoin actually is

Formally: the Eigencoin is the principal component of the memetic hype space, the single direction that captures more of what makes something spread than any other direction could on its own. If you want the literal term for it, it's the eigenvector of virality. Walk that vector all the way to where it stops, and whatever is standing there is, by construction, the best possible coin that can exist. Not one of the good ones. Not a strong pick. The endpoint.

This is not, directly, a claim about price. Price is downstream of attention, and attention is downstream of this vector. What's being described here is a direction and its endpoint, not a chart. What a chart does after that is just people finding out.

§ related work

What this is actually standing on