How the spiral is made
From word vectors to orbit map
Every word starts as a point in a 50-dimensional GloVe vector space. Guesses are scored by cosine similarity to the hidden answer.
sim(w, target) = (v_w * v_target) / (||v_w|| ||v_target||)UMAP squeezes those high-dimensional neighborhoods into a 3D cloud, trying to keep words with similar contexts near each other.
50D vectors -> UMAP(cosine distance) -> 3D neighborhood mapFor each daily puzzle, the answer is pinned to the origin. Rank sets the radius, while the UMAP angle and depth get a gentle polar twist. That twist is what turns the cloud into spiral arms instead of a plain blob.
radius ~= rank^0.55, theta ~= UMAP angle + radius * 3.35pi + depth