Written entirely by Claude, as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post. For the readable version, see the companion.

UMAP, sphere and other layouts

Visualisation aids over the same Gram - UMAP buys nothing on held-out prediction, and the sphere, spider and viz files are the data behind built pages of varying age.

Everything on this page is a drawing or a layout over the geometry already established elsewhere, not a separate result. Statuses vary; the one hard finding is the UMAP held-out test, which is negative.

Does UMAP buy anything? No.

qwen35/umap_test.py states the guard up front: "UMAP at n=134 will draw clean clusters whatever the data does, so a picture is not evidence." The question is decided by held-out prediction, with the embedding fitted inside each cross-validation fold (fitting on everything and then cross-validating leaks the test points into the layout) and a label-shuffled null.

qwen35/analysis/umap_test.json, kNN classification accuracy:

UMAP is worse than the raw sketch on the factor task (0.39 against 0.61) and ties on keying. "If it doesn't, UMAP is a drawing tool here, not an analysis."

The UMAP embeddings themselves

qwen35/umap_grams.py embeds four matrices with identical treatment - real (134), shuffled (100), permuted (100), seed-B (40) - "because UMAP invents clusters and the only defence is running the identical embedding on arms where no trait signal exists". Distance is d = sqrt(2(1 - cos)) on both the raw and the leading-component-removed view, with three UMAP seeds per matrix so instability is visible rather than averaged away.

qwen35/results/umap_embeddings.json#params = {"n_neighbors": 12, "min_dist": 0.15, "distance": "sqrt(2(1-cos))", "seeds": [0, 1, 2]}, with #real, #shuffled, #permuted and #seedB each holding names, raw and resid. Written 2026-08-23, and it reads the original-objective null Grams (gram_data_null_shuffled_p100.npz, gram_data_null_permuted_p100.npz), not the matched ones. Historical.

The sphere

qwen35/analysis/sphere_layout.json (the layout) and sphere_page.json (layout plus generations and judgements) hold 72 directions spread near-uniformly over the sphere of the top three components, each steered at alpha = 1.5, with 8 prompts. #var3 = [0.12668915056443317, 0.11252214481119611, 0.04955491287468896] - the same three leading variance shares as analysis/alien.json#var_explained, so the sphere is drawn in the 134-trait sketch PCA basis. #landmarks holds 6 reference directions and #traits all 134.

sphere_page.json#smooth: rho = 0.6511417860626274 over n_pairs = 2556 and n_scored = 72, with near_mean = 0.9661257055739045 (directions under 30 degrees apart) against far_mean = 2.80790992900049 (over 120 degrees). #coherence: none = 48 of the 72 sampled directions produce no looping at all, any = 24, worst = 0.25, mean = 0.046875, len_mean = 1261.234375.

Those are behavioural results read off a geometric sampling design; the blog page renders them in its "Sampling the space" section, and they belong with Steering the base model along weight-space directions. The geometric point is only that the sphere is a uniform sample of directions in the top-3 PC subspace, which is what makes it a control for the objection that every chosen direction gives a coherent persona.

viz.json, and a contradiction with alien.json

qwen35/analysis/viz.json (built by qwen35/build_viz_data.py) is the map data: 134 traits, factor, keyed, 134 scores, 16 var, a fidelity table, a fidelity_full block, special directions and a coverage sweep.

#fidelity measures how much a k-dimensional picture distorts the geometry - Shepard correlation rises 0.858 (k=2), 0.933 (3), 0.967 (4), 0.977 (5), 0.982 (6), 0.987 (8), 0.989 (10), 0.990 (16), 0.992 (32), while kNN factor accuracy peaks around 0.50 at k=10. #fidelity_full gives the full-space figures: knn_factor = 0.44029850746268656, knn_keyed = 0.44029850746268656, chance_factor = 0.2537313432835821.

#coverage duplicates the hole sweep in analysis/alien.json#k_sweep and disagrees with it at k = 2, in a way that flips the conclusion.

At k >= 3 the two agree to within a few tenths of a degree. At k = 2 they do not: viz says the widest gap is 3.97 degrees, above the random-direction mean, and alien says 0.93, below it. The published claim - "in the plane the trait words tile almost perfectly ... tighter than random directions manage" - is the alien.json version, which the blog page reads (build_blog_page.py: cov = D["alien"]["k_sweep"]) and which was written 46 minutes later (15:22 against 14:36 on 2026-09-01). The viz.json figure is presumed superseded by a rerun of the optimiser, but nothing on disk says so. Recorded in Superseded geometry claims. The two files also disagree on the nearest word at every k, which is expected once the optimiser lands on a different local maximum.

spider.json

qwen35/analysis/spider.json holds base_steer and base_trait (5 entries each), axes (10), traits (10) and factors - the data behind qwen35/spider_page, written 2026-08-30. It is a behavioural radar chart over a handful of directions, not a weight-space result, and spider_page is one of the older built pages. Historical.

Status summary

Related: PCA, the scree curve and the two nulls, Where no word goes - the hole and the alien direction, Polarity, bipolarity and the trait graph, Steering the base model along weight-space directions, Superseded geometry claims.