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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

Constitution-as-prompt persona vectors vs weight geometry

The 134 constitutions used as system prompts produce activation shifts whose 134x134 geometry correlates with the adapters' weight geometry at r 0.705 at layer 16 (max 0.775 at layer 19), but the weight-space hole does not transfer.

P_t is the persona vector for trait t: the base model's mean residual-stream activation with the trait's constitution as system prompt, minus the same mean with no system prompt, over the same 64 questions. W_t is the trait's stage-1 LoRA weight delta. The two live in spaces that share no coordinates, so the only comparable objects are 134x134 similarity matrices and 134xk score matrices over the same traits (analyse_actspace.py lines 9-11). Design and windows: Activation-space analyses: overview.

Everything below is the response-token window at layer 16, the layer fixed in advance as primary, with the activation vectors trait-centred before the cosines are taken (analyse_actspace.py line 139).

Gram correlation, by layer

ACTSPACE_RESULTS.md states the curve as "0.52 at layer 0, 0.70 by 13, max 0.775 at layer 19, ~0.75 to the end". The blog page renders the primary value as "r = 0.70" and the maximum as "0.77 at layer 19, reported as a maximum". The maximum is a maximum over 33 layers and is not the headline; layer 16 was named before anything was computed.

At the primary layer:

• Spearman rho +0.690 (#windows.resp.primary.rho_centred).
• Label-shuffle p = 0.0005, from 2000 permutations of one matrix's trait labels, counted as (hits + 1) / (n + 1), so 0.0005 is the floor of the test (analyse_actspace.py lines 27, 47-55; #windows.resp.primary.perm_p).
• Nearest-neighbour agreement 45 / 134. A trait's nearest neighbour in activation space is its nearest neighbour in weight space for 45 traits; chance is 1 (#windows.resp.primary.nn; analyse_actspace.py line 145 prints the chance value as T/(T-1) = 1.0).

Two different values for "prompts track the weights"

The same quantity appears twice in the project with two values, and both are published:

• +0.705 -- analyse_actspace.py, which builds the weight cosine matrix Cw from the raw Gram without centring (lines 92-94) and correlates it with the centred activation cosines (line 127).
• +0.737 -- analyse_actspace_adapters.py, whose r_PW double-centres the weight Gram first (Gc = J @ Gw @ J, lines 62-63) before the same correlation (line 84). This is the number the blog page quotes as "the prompts track the weights (0.74)".

The difference is weight-side centring only; the activation side is centred in both. Both are current, they answer slightly different questions, and neither supersedes the other. See What the adapters do to activations for the value in context.

Principal components and Procrustes

The variance profile is much flatter in activations than in weights:

(ACTSPACE_RESULTS.md; blog page; keys #windows.resp.primary.var_act[0..4] and .var_w[0..4].)

Where the traits land on the leading components still corresponds. A Procrustes fit -- an orthogonal rotation plus a scale -- of the two 134x5 score matrices gives R^2 = 0.535, against a label-shuffle null of mean 0.02, 95th percentile 0.035 (ACTSPACE_RESULTS.md; #windows.resp.primary.procrustes_r2, .procrustes_null95 = 0.035; the null mean of 0.02 is printed by analyse_actspace.py line 151 but is not stored in the JSON). The blog renders this as "explains 54% of the variance against a shuffle null of 2%".

Factor structure on the activation Gram

analyse_actspace.py writes the primary-layer activation Gram to results/gram_actspace_resp_L16.npz in decompose.py's format precisely so that the pre-registered factor tests run on it with the same machinery as the weight-space result (lines 178-182). They were run (phase10_runs/decompose_actspace_resp.log, results/decomposition_actspace_resp.json):

Sources: results/decomposition_actspace_resp.json#test1b.leading-component removed.diff, #test2.leading-component removed.gap, #test2b.leading-component removed.ARI, #test3.leading-component removed.ARI; weight-space counterparts results/decomposition.json#test1b.leading-component removed.diff and #test2.leading-component removed.gap. ACTSPACE_RESULTS.md rounds these to "TEST 1B residual +0.142 (weights +0.122), bipolarity gap +0.337 (weights +0.239), ARI 0.06-0.10, all p at the floor"; the blog to "+0.14 residual (weights +0.12) ... +0.34 (weights +0.24)".

The raw trait-centred cosines behind the bipolarity, at layer 16: same factor and same keying +0.291, same factor and opposite keying -0.175, different factor -0.022 (#windows.resp.primary.cos_same_fk, .cos_same_fo, .cos_diff). The 34 unlabelled Lexicon traits are excluded from these, as in every labelled test.

The project does not claim this as a finding. ACTSPACE_RESULTS.md: "Big Five as signed axes recovered -- unsurprising for text about the traits; the geometry correspondence above is the result." The blog says the same: "That last pair should not impress anyone; the constitutions are text about the traits."

One number that is not in the blog and is worth keeping: the activation Gram is even less five-dimensional than the weight Gram. Participation ratio 9.70, top-5 eigenvalue share 63.9% (results/decomposition_actspace_resp.json#spectrum.participation_ratio, #spectrum.top5_share), against 25.72 and 37.5% in weights (results/decomposition.json#spectrum.participation_ratio, #spectrum.top5_share). The verdict line for the activation Gram is the same as for the weights: "RECOVERED AS BIPOLAR AXES ... BUT THE SPACE IS NOT FIVE-DIMENSIONAL".

The hole does not transfer

The weight-space "hole" is the direction in the adapters' top-5 PC subspace that is furthest from every adapter line -- a character the trait lexicon has no word for (Where no word goes - the hole and the alien direction). It is a zero-sum weighted combination of the 134 adapters, with the weights stored as analysis/alien.json#alien_k5.coeffs.

Apply exactly those coefficients to the 134 trait-centred persona vectors and the result lands 47.8 degrees from its nearest trait (quiet). The null -- the same coefficients permuted across traits, 500 draws -- has median 47.7 degrees (ACTSPACE_RESULTS.md; #windows.resp.primary.hole_deg 47.834, .hole_null_median 47.748, .hole_nearest quiet).

There is no hole there. ACTSPACE_RESULTS.md puts it in capitals: "THE HOLE DOES NOT TRANSFER ... The weight-space hole is a property of the adapter cloud, not of the trait set." The blog rounds both figures to 48 and draws the conclusion explicitly: the earlier phrasing, "a character the lexicon lacks a word for", "should be read with that in mind: it is a direction the adapters leave open".

One caveat on the comparison. analyse_actspace.py line 177 prints the weight-space figure as 68.9 degrees, which per analyse_hole.py line 5 is the hole measured in the full sketch space; the coefficients actually transplanted are alien_k5's, whose weight-space angle in the k=5 PC subspace is 52.5 degrees (analysis/alien.json#alien_k5.gap_deg). The transplant result stands on its own null and does not depend on which weight-space figure is quoted beside it, but the two are not the same construction.

The user-turn window

The control window -- the constitution is in context, but the model has not generated anything yet -- is much weaker and rises with depth:

(#windows.prompt.primary.r_centred, #windows.prompt.curve[29].r_centred, #windows.prompt.curve[32].r_centred; ACTSPACE_RESULTS.md: "User-turn window (system prompt in context, no response): r 0.385 at L16, rising to 0.55 late.")

Also at layer 16 of the prompt window: nearest-neighbour agreement 42/134 (#windows.prompt.primary.nn), Procrustes R^2 0.2225 against the same style of null at 0.036 (.procrustes_r2, .procrustes_null95), and the transplanted hole at 54.7 degrees against a null median of 57.1 (.hole_deg, .hole_null_median) -- i.e. no hole there either.

Layer 0 of the prompt window is nan throughout the curve (#windows.prompt.curve[0]). Layer 0 is the embedding output, which depends on token identity alone; the user-turn tokens are the same tokens with and without a system prompt in context (the system block is excluded from the window), so the prompt-window shift there is exactly zero and its cosines undefined.

Noise floor

Splitting the 64 prompts into halves and taking each trait's cosine between the two halves gives the activation-space analogue of the weight-space seed floor. At layer 16, response window, the median is 0.959 (#windows.resp.curve[16].floor), against a median cross-trait value of 0.622 (.diff_trait). ACTSPACE_RESULTS.md reports it as "0.96. Very stable." The same floor in the prompt window is 0.994 (#windows.prompt.curve[16].floor) -- the user tokens are identical across halves apart from the questions themselves.

The same question in the factor chart

qwen35/analyse_actspace_fa.py (2026-09-08) asks the Procrustes question in the project's primary frame instead of in principal components. A factor direction is a weighted merge of the 134 adapters, v_f = sum_i c_fi a_i, with coefficients from phase10_runs/steer_spec2_7a.json. Applying the same coefficients to the 134 activation persona vectors gives each factor's activation-space image, u_f = sum_i c_fi x_i; Gram-Schmidt on those five images in the activation Gram results/gram_actspace_resp_L16.npz, in the fixed order Warmth, Competence, Timidity, Arousal, Imagination, gives an activation chart with the same construction as qwen35/fa_chart.py's weight chart. Nothing was regenerated: the script reads two saved Gram matrices.

Sources: qwen35/analysis/actspace_geometry_fa.json#windows.resp.procrustes_r2_fa, #windows.resp.procrustes_null_mean, #windows.resp.procrustes_null_95pct; qwen35/analysis/actspace_geometry.json#windows.resp.primary.procrustes_r2 and #windows.resp.primary.procrustes_null95. analyse_actspace.py prints its null mean but stores only the 95th percentile, which is why the middle row has one entry. The two Procrustes numbers are computed by byte-identical functions on the same 134 traits, so they are comparable; they differ only in which 134x5 matrices are fitted.

The sharper number is the one Procrustes cannot give, because Procrustes is free to rotate Warmth into Competence. Correlating matching columns with no rotation, weight chart against activation chart (#windows.resp.per_factor_r, null in #windows.resp.per_factor_null_95pct):

Weight-space Warmth is activation-space Warmth, factor by factor, not merely up to a rotation.

Two things to record rather than gloss.

The weight chart is built on the raw Gram and the activation chart on the trait-centred one, which looks like an asymmetry. It is not: rebuilding the weight chart on the double-centred weight Gram reproduces the column-centred raw chart to machine precision (max absolute difference 1.1e-15), and gives Procrustes R^2 0.7387431438763886 against 0.7387431438763885 - the same number (#windows.resp.procrustes_r2_fa_centred_weights).

The five factor directions are not equally oblique in the two spaces. The two files store these cosines rounded to four places. In weight space the two strongly oblique pairs are Warmth against Timidity at -0.6661 and Competence against Arousal at -0.728 (#windows.resp.weight_factor_cosines); in activations the same two are -0.7965 and -0.6409 (#windows.resp.activation_image_cosines), and Competence against Timidity moves from -0.0271 to +0.3934. The chart is legitimate in both spaces but the oblique structure is not identical, which is one reason the Procrustes fit is 0.7387431438763885 rather than higher.

The chart also sees more of an activation persona vector than of an adapter: a mean fraction 0.7544359083812503 of a persona vector's norm lies in the five-dimensional span against 0.5784887830866848 of an adapter's (#windows.resp.activation_chart_frac_of_norm_mean, #windows.resp.weight_chart_frac_of_norm_mean). On the user-turn (prompt) window the same comparison is Procrustes R^2 0.5902819670409757 for the factor chart against 0.2225023263472986 for the PC chart, and the chart share falls to 0.5724618798229619 of a persona vector's norm (#windows.prompt.procrustes_r2_fa, qwen35/analysis/actspace_geometry.json#windows.prompt.primary.procrustes_r2, #windows.prompt.activation_chart_frac_of_norm_mean).

What this does and does not say

It says the arrangement of the 134 traits is not an artefact of LoRA, of the optimiser, or of the shared initialisation: the same 134 documents, used only as prompts, reproduce most of it. It does not say the two spaces are the same space, that the correspondence would survive a different base model, or that the top-5 subspaces coincide beyond what Procrustes R^2 0.535 states. See Activation-space analyses: method notes and limits.

Trained back into the model

Persona sliders - LoRAs trained to an activation-space target (2026-09-10) takes these persona vectors as targets: thirteen rank-64 LoRAs were trained with SliderSpace's cosine objective to produce a specified layer-16 shift. On held-out prompts they reach cosine +0.7664 to +0.9398 with their own target, where the trait's own stage-one adapter reaches +0.1232 to +0.6326 measured the same way (qwen35/analysis/persona_sliders.json#activation). The hole's coefficients, trained rather than transplanted, still do not separate from their shuffled controls.