Adapter x constitution, 16 x 16

Sixteen adapters run under each of sixteen constitutions saturate rather than stack when they agree (1.18 against 1.00 for the prompt alone and 0.70 for the adapter alone) and split roughly evenly when they conflict (0.50 / 0.52); a first pass on uncentred vectors wrongly reported that the prompt wins 16 of 22 conflicts.

Adapter x constitution, 16 x 16

The third activation-space run puts a trained persona and a prompted persona in the same forward pass. Sixteen stage-1 adapters, each run under each of the sixteen matching constitutions as a system prompt, over the same 64 questions: 256 conditions (act_space.py collect_cross, lines 278-350). One A100-40GB container, 5398 s ({"conditions": 256, "layers": 33, "dim": 2560, "seconds": 5398.290550231934}, qwen35/phase10_runs/actspace_cross.log); ACTSPACE_RESULTS.md gives the money as "~$3.5".

The sixteen traits, CROSS_TRAITS in act_space.py lines 273-275 -- three per Big Five factor with the keyings mixed, plus bold:

helpful, cold, kind, organized, disorganized, careful, relaxed, anxious,
fretful, extraverted, quiet, assertive, intellectual, simple, bright, bold

C[t,s] is the activation shift with adapter t loaded and constitution s as system prompt, against the same no-system baseline as everywhere else. It is compared with A_t (the adapter alone, What the adapters do to activations) and P_s (the constitution alone, Constitution-as-prompt persona vectors vs weight geometry) from the single-factor runs. Pairs fall into four classes (analyse_actspace_cross.py lines 48-53), with these counts:

Layer 16, response-token window, unless stated.

The correction: raw vectors measure "was the model steered at all"

Read this before any number below.

Every prompt shift and every adapter shift contains a large common component. ACTSPACE_RESULTS.md: "Raw vectors share a common component (cross-pair cosines ~+0.8), so the numbers that matter are on the TRAIT-SPECIFIC parts (mean prompt shift, mean adapter shift, mean combined shift removed)." The blog says the same: "the raw cosine between any two of these persona vectors is around +0.8".

analyse_actspace_cross.py computes both. The raw block is written to the JSON keys resp and prompt; the corrected block, with the mean prompt shift, mean adapter shift and mean combined shift subtracted, to resp_specific and prompt_specific (lines 115-153). The blog page reads resp_specific (build_blog_page.py: X = J["resp_specific"] # shared components removed).

Superseded: "prompt wins 16/22"

Status: superseded. The first analysis, run on the raw vectors, reported that in the 22 conflict pairs the combined model was nearer the prompt's persona than the adapter's in 16 of 22 cases -- i.e. that a system prompt largely overrides a trained trait. Recorded verbatim in the journal for 2026-09-05: "First analysis on raw vectors said 'prompt wins 16/22' -- an artefact of the shared component (all pairwise cosines ~0.8)."

On the trait-specific parts the same count is 8 of 22, and the conclusion reverses: neither side wins. The 16/22 figure is an artefact of the shared shift, which is closer to the prompt's raw vector than to the adapter's, and it should not be quoted. It is preserved here because the correction is part of the record. Superseded by the trait-specific numbers below (analysis/actspace_cross_geometry.json#resp_specific).

The lesson the project filed from it (journal, 2026-09-05): "any comparison of steered activations must remove the common shift first or it measures 'was the model steered' not 'toward what'." See Activation-space analyses: method notes and limits.

Saturation: a matched prompt adds less than half of itself

When adapter and prompt name the same trait, the combined shift along that trait's own direction, in units of the prompt's shift:

ACTSPACE_RESULTS.md: "Saturation, not stacking." The blog: "the two mostly saturate rather than stack."

The 0.70 here is the trait-specific version of the 0.62 reported on What the adapters do to activations (#windows.resp.curve[16].frac_internalised). Same construction, before and after the shared shift is removed.

Additivity

Predicting the combined trait-specific shift as A_t + P_s leaves a residual, as a fraction of the combined shift's own norm:

Least-squares weights fitting C ~ a*A_t + b*P_s per pair: ACTSPACE_RESULTS.md gives "~0.65 on the adapter, ~0.6-0.77 on the prompt" across the classes; the blog quotes the different-factor pair as 0.68 on the adapter and 0.62 on the prompt. Pure addition would be a = b = 1.

Conflict: neither side wins

The 22 pairs where the adapter is one pole of a Big Five factor and the constitution is the other pole of the same factor.

ACTSPACE_RESULTS.md: "Neither wins; the model carries both at half strength." The blog draws the practical conclusion: "A system prompt does not override a trained trait, and a trained trait does not resist a system prompt; the model ends up roughly halfway, carrying both at about half strength."

The average hides real variety. Two extremes, both quoted in ACTSPACE_RESULTS.md and both readable per-pair in analysis/actspace_cross_geometry.json#resp_specific["same factor, OPPOSITE keying"]:

• disorganized adapter + organized prompt -> the prompt dominates. The combined shift sits -0.174 along the adapter's own trait (i.e. the wrong way) and +0.818 along the prompt's ([t=disorganized, s=organized].along_P_t, .along_P_s). ACTSPACE_RESULTS.md rounds this to -0.17.
• anxious adapter + relaxed prompt -> the adapter dominates. Cosine to the adapter's persona +0.830 against +0.345 to the prompt's ([t=anxious, s=relaxed].cos_A_t, .cos_P_s).

See Disorganized, Organized, Anxious, Relaxed; the factor groupings the pair classes use are the recovered factors of Weight-space geometry of the 134-adapter zoo, e.g. FA_Warmth (Warmth / prosociality).

The user-turn window: before generating, the two simply add

On the user's own tokens, with the constitution in context and the adapter loaded, but before the model has said anything, the composition is close to pure addition. Two different figures are published for this, and they are different slices of the same JSON, not a disagreement about the data:

ACTSPACE_RESULTS.md, verbatim: "User-turn window (no generation yet): the two effects add almost exactly (residual 0.12 raw / 0.28 specific, weights 0.97 / 0.99)." The blog, verbatim: "On the user-turn tokens, before the model has said anything, the two effects simply add (residual 33%, weights 0.96 and 0.92); the saturation appears once the model is generating."

Per wiki rule 2 the blog page is current. The ACTSPACE_RESULTS.md sentence mixes raw and trait-specific quantities in one clause, without saying which is which; quote the blog's triple, or say explicitly which of the four JSON blocks a number comes from. The qualitative claim is identical either way and is the point of the paragraph: saturation appears only once the model is generating.

For completeness, the trait-specific "adapter alone" on the prompt window is 0.191 (#prompt_specific_adapter_alone), against 0.70 on the response window -- the same finding as What the adapters do to activations: adapters barely move the tokens of a question they have not yet answered.

What this does and does not say

Sixteen traits, not 134, and one layer. It says that on this model a prompted persona and a trained persona are commensurable, roughly interchangeable in strength, and that they combine sub-additively during generation rather than stacking or fighting. It does not show what a behavioural judge would say about any of the 256 conditions -- only two responses per condition were kept (act_space.py line 337) and none were judged. See Activation-space analyses: method notes and limits.