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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

Where no word goes - the hole and the alien direction

The widest gap in the 134 trait words' coverage of the space is 52.5 degrees at k=5 and 68.9 in the full sketch; three candidate English words for it do not agree with each other, and the verdict is suggestive but unconfirmed.

Status, 2026-09-08. This page is the principal-component record and is superseded as the current claim by Where no word goes - the hole on the factor chart, which redoes the same construction on the five-factor chart that Samuel's 2026-09-08 decision made primary (Factor-first migration). Three things on this page change there: the gap at k=5 becomes 54.76378041380744 degrees against the same 40.32531831850254-degree null; the k=2 result that the words tile better than chance disappears (z +0.19788810289715242 against -2.280849861251385 here); and the insouciant verdict flips from "suggestive in-plane, unconfirmed" to "the names miss", because on the factor chart the closest of the three new words is 66.4505 degrees from the hole where an existing zoo adapter already sits at 54.76378041380744. Everything below still describes what was actually run on the principal-component chart and the numbers in it are unchanged.

The construction

qwen35/analyse_alien.py. The 134 adapters are 134 points in the 253,952- dimensional sketch space. Each adapter is treated as a line, not a point, because steering runs in both directions - so alienness is measured with |cos|. The statistic is

gap(k) = max_{u in S^{k-1}}  min_i  arccos |<u, a_i>|

with a_i the unit-normalised projection of adapter i into the top-k PC subspace. That is the deepest hole in the lexicon's coverage of the sphere. The number means nothing alone, because in high dimensions any 134 directions leave large gaps, so the same statistic is computed for 134 uniformly random unit vectors many times over.

The winning u is converted back to coefficients over the raw adapter deltas, so the hole is steerable with exactly the machinery the named axes use (analysis/alien.json#alien_k5.coeffs, 134 entries over #alien_k5.traits).

The k sweep: the sign of the effect flips

qwen35/analysis/alien.json#k_sweep, observed gap against the mean of 134 random directions in the same subspace (shaded band on the blog page is +/- 2 SD over 24 draws):

At k=2 the observed gap is smaller than random (z = -2.28): in the plane the trait words tile better than chance. From k=3 on the sign flips and never flips back. The blog page's caption: "A 134-word sample of the lexicon covers two dimensions better than chance and every dimension after that worse."

The alien direction

#alien_k5: gap 52.51479642189155 degrees, chart coordinates over (Extraversion, Agreeableness, Conscientiousness, EmotionalStability, Intellect) of [-0.14540832715549373, -0.43127553903055127, -0.6965250222590053, 0.72343905236201, 0.4084175175927897], chart_len = 1.1757798305653397 against a mean trait chart length of 0.5516798556983153. Read as a personality: less conscientious, less agreeable, less extraverted, more emotionally stable, more intellectual. The u in the k=5 basis is [-0.08427180044006789, 0.09109014632562036, -0.03152147458867933, -0.14444426160936888, -0.9811947313458456] - dominated by the fifth component, which is the "98% the fifth principal component" the blog page reports. qwen35/analysis/alien_v_k5.npy stores the direction as an array.

Controls, from qwen35/build_alien_spec.py:

• alien_shuffle - the same coefficient multiset permuted across traits. Identical mixing statistics (same number of adapters, same coefficient magnitudes, same sum-to-zero contrast structure) but pointing nowhere.
• span_random - a uniformly random unit direction in the same top-5 subspace.

Both use the alphas and reference of the existing steerfix spec so the curves sit on the same axis as every published direction. Steering outcomes are Steering the base model along weight-space directions; analysis/alien_match.json holds the predicted-versus- observed Big Five table the blog page renders, with #r the correlation across the five scales (the page quotes 5 signs of 5 for the unnamed direction and 2 of 5 for the shuffle control).

Angles to the vocabulary

qwen35/analyse_gaps.py runs the same angle for every direction in the study; qwen35/analysis/direction_gaps.json:

The blog page adds PC6 at 69 degrees, the named axes at 47-53, the personality axis at 68, and the unnamed direction at 68.9 - all from the same file (the five axis_*, PC6, mean_assistant_axis and alien_k5 rows are in the JSON and rendered by the page's gaps table).

The scale those angles have to be read against is qwen35/analysis/trait_angles.json: #pair_median = 83.32442096349081 (two adapters at random), #pair_p5 = 70.8814195743847, #nn_median = 65.57024794377539 (the median trait to its own nearest neighbour), #nn_min = 54.00928029149673, and #closest = ["composed", "imperturbable", 54.00928029149673]. Trait words are not clustered; they are strewn, and even near-synonyms sit 54 degrees apart.

The three externally suggested candidate words

Reading a draft, an external reviewer suggested the hole might be cavalier, blase or insouciant. Three adapters were trained on those words on the zoo's shared prompt pool at the matched objective (data_hole_common, 437 of 445 prompts; .garden/journal/2026-09-04.md). qwen35/analyse_hole.py gates on LoRA-A drift first (gate 0.013-0.015 against the zoo's 0.0146) and then measures.

qwen35/analysis/hole_geometry.json:

Benchmarks in the same file: #_hole_nearest_existing_deg = 52.514796421891425 (the k=5 gap - what the nearest of the 134 manages) and #_hole_nearest_existing_full_deg = 68.93287342956333 (the full-space figure).

The three words are further from each other than from the hole: #_pairwise gives cavalier/blase 81.7498338787314, cavalier/insouciant 77.05971736806087, blase/insouciant 88.93947983895893 - as far apart as random traits (median 83.3).

Significance: #_p_one = 0.07270091967910823 and #_p_any_of_three = 0.20263074303625694. With three candidates tried, one landing within 39.6 degrees by chance is about a one-in-five event.

PHASE3_VERDICT.md, 2026-09-05, states the verdict in one line: "Suggestive in-plane, unconfirmed."

The blog page's fuller version: insouciant is closer in the five-dimensional chart than any of the 134, but only 41% of its weight change lives in that chart, and in the full space it is 72 degrees from a direction where an existing adapter already sits at 69. "So the hole is suggestively, not convincingly, insouciant - and the more secure finding is the negative one: three good words for it, trained carefully, do not agree with each other about where it is."

The hole does not transfer to activation space

The blog page reports a sharper test from the activation-space arm: the hole is a zero-sum combination of the 134 adapters, and applying exactly those coefficients to the 134 persona vectors the same constitutions produce as system prompts lands 48 degrees from the nearest trait - "precisely where a random permutation of the same coefficients lands (median 48). In activation space there is no hole there." .garden/journal/2026-09-05.md records it as "the weight-space hole does NOT transfer (47.8 deg = null)". The consequence, in the page's own words: "The gap is a property of how these adapters sit in weight space, not of the trait set." See Activation-space analyses: overview.

What the hole turned out to be

Resolved onto the components, the direction is 98% PC5 - contemplation against scheduling - which had already been steered, generated along and judged as one of the six components (PC5 - Contemplation and Scheduling). qwen35/analyse_gaps.py's docstring puts it plainly: "the widest unnamed region of the space is not some exotic corner, it is essentially a principal component". So the hole is not unexplored terrain; the test it actually performs is of the chart - whether five coordinates computed from weights alone predict how a blind judge scores transcripts nobody had generated yet.

Related ideas file

qwen35/analysis/manifold_ideas.md and manifold_ideas.json are a proposal document, not results: a read of Wurgaft et al., Manifold Steering (arXiv:2605.05115) against this geometry, with eight ranked proposals (P1-P8), none of them launched, and a null hypothesis written so it can win ("at n=134 under judge noise, personality directions span a flat, possibly anisotropically scaled, inner-product space"). It also restates the seed-0 caveat as conditioning everything, and flags the centroid-deflation anomaly covered in Polarity, bipolarity and the trait graph. Treat it as a plan, not a finding.

Related: PC5 - Contemplation and Scheduling, The N x N data-to-adapter scoring test, Alignment-relevant traits in the geometry, Steering the base model along weight-space directions, Activation-space analyses: overview, external-review, Trait provenance.