This page used to open by saying that nothing here was certified. That was the wrong claim and it had stopped being true: two of these pages draw a certificate straight from the shelf the rest of the site gates, and five of them decide their headline number in exact integer or rational arithmetic. What is true is that nothing here is gated — no number on these pages has a certificate row the build checks, no page here can refuse a deploy, and none of them is covered by make test. That is a fact about ceremony, not about the mathematics, and the two are not the same thing.
So instead of one disclaimer at the door, every card below says what backs its headline number, in the same words the pages use: exact rationals, exact integers, a record from the certificate shelf, or floats. Where it is floats, the page says so beside the number rather than at the bottom.
The elicited geometries look like they hold shapes — a pentagon here, four points on a circle there. So this looks exhaustively, at every triple and quadruple and five-subset of every set from every model, and then runs the identical search on the same numbers with the geometry shuffled out. Almost nothing survives that. What does is not a polygon — and for most of the sets the verdict is not a margin at all but a certificate in whole numbers that no such points exist.
read the hunt →The famous black-hole image is one sky chosen, by an imaging prior, from the infinitely many the data allow. This draws the set instead: 18 skies fitted under deliberately different priors, agreement rendered as ink and disagreement as texture. One slider decides how much of the phase information the picture is allowed to use — and at zero the ring dissolves, because amplitudes alone cannot see where anything is.
open the instrument →A calibration is run forwards and used backwards, and the backwards number always comes off a fitted curve. The fit is an assumption and it is never priced. This computes what the standards allow instead — in closed form, no optimiser, no sampling — under assumptions you can dial one at a time, from monotone only to join the dots, with the parametric fit past the end of the dial.
turn the dial →Their manifolds are found — pulled out of a working model and interpreted. These are stated: a rule, its parameters, and then a drawing. Two of the eight are not illustrations at all but certificates rendered at their own resolution, which is what a proof looks like when you stop reading it and start looking at it.
open the series →Twelve feelings, then the same twelve asked again under six moods — and twelve clock hours carried through the identical pipeline as a control that has no business moving. A mood effect that also moves the clock is not a mood effect. One model’s clock moves anyway.
read the moods →Ask how different two things are, one pair at a time, and you get a table of numbers. A table of distances is a shape — or it is not one, and the difference is decidable in exact integer arithmetic. Every pair is asked both ways round, so the asymmetry is measured rather than averaged away.
compare the three →Goodfire finds circles and colour surfaces by opening the model and decomposing its activations, which needs the weights. This asks from outside instead — every pair, one integer, one row at a time — and then decides exactly what those answers can be. If the circle is real it should survive being asked about; a shape that lives only in the activations was never a shape the model uses.
read the plates →Every other geometry page here asks a model for a table of dissimilarities and decides what shape the answers have. This one asks nothing. The prediction is written first, in the source, and never edited afterwards — which is the only thing that makes “agreed” mean anything.
read the controls →Attention weights are nonnegative and sum to one, which makes a row a point in a simplex — and a bar chart throws that away. Focus is distance from the centre; concentration has contours; temperature is a path. One real row from a tiny GPT, in the room it actually lives in, with the one claim about it that is decided rather than drawn: sharpening must move the point toward a vertex, proved in exact rational arithmetic because consecutive values differ in the fourteenth decimal.
open the instrument →