keys 1 · 2 · 3
keys 1 · 2 · 3
Every point is one real proof, placed by its activation at a chosen layer. Rotate it. Scrub the layer and watch the concept families condense — the depth map, as a moving manifold. Switch the metric to see why raw activations look like a blob but the model's own whitened space pulls the families apart, switch the encoder to watch a general text model fail to separate what the prover separates, and click any point to slice it back to the Lean tokens that produced it.
Whitened is the model's own metric — the label-informed discriminant axes the report's 0.95 / 0.867 readouts actually live in. Raw variance is plain PCA of the activations: a graded blob, silhouette ≈ 0. That contrast is a finding — a proof concept is not a raw cluster you could stumble on; it is linearly separable only in the model's whitened space (rank-fraction ~0.40 — graded, not a hard partition).
In tactic · decision, scrub the layer: the five tactics pull apart from silhouette 0.27 at L8 to 0.34 at L20 — the model committing to its next tactic, deeper in the stack. Flip the encoder to BGE: the same 750 decision states collapse to silhouette 0.056. The general text encoder does not carry the decision; the prover does. That is the report's headline, as geometry you can rotate.
Dynamic replay: the layer morph is a continuous Procrustes-aligned interpolation of the real per-layer activations that came through the sealed substrate capture stack (frame , q-lattice 3·5·7·11). Nothing is simulated — each frame of the animation is a measured layer.