Do the recovered factors map onto the Big Five?

Three of the five factors recover cleanly; Extraversion and Emotional Stability come out as withdrawal and arousal, a roughly 45-degree rotation of the same plane.

Do the recovered factors map onto the Big Five?

Samuel asked on 2026-09-07 at 15:29 UTC (transcript 981fa3b5-8a9b-405e-9e84-70cc615d9873.jsonl, line 12978): "to what extent do you think the factors we found map onto the big five axis?" The answer is at line 13013 (2026-09-07T15:30:58Z); verbatim text in wiki/raw/explainer-big-five-mapping.md.

Answer in one line: partly — three of the five cleanly, and the other two present but rotated.

The numbers come from the k = 5 oblimin solution on the centred correlation matrix (qwen35/results/fa_qwen35.json), with Goldberg's markers as +1/0/-1 targets.

What maps

Agreeableness, Conscientiousness and Intellect each come out as one factor whose top loaders are overwhelmingly that factor's markers, with the right poles opposed: agreeable, pleasant and trustful against rude; conscientious and neat against negligent and sloppy; imaginative and creative against unimaginative and simple. Competence leans slightly into Intellect — unintellectual and unintelligent load with sloppy — "which is a blend the human literature also sees at the edges of C."

What does not, and how

Extraversion and Emotional Stability do not appear as separate axes. Their markers occupy the same two-dimensional plane, but the rotation the weights prefer runs diagonally through it:

• one factor is low E and low ES together — fearful, timid, insecure, nervous, bashful, anxious — which is withdrawal;
• the other is high E against high ES — extraverted, talkative against unexcitable, relaxed, withdrawn — which is activation.

"That is roughly the 45-degree rotation from Big Five E/N to a valence-arousal-style pair. So the plane is recovered; the axes within it are not the human ones."

This is also why the signed-separation and bipolarity tests pass for all five factors while the unsupervised rotation lands on the marker axes for only three: those tests are label-based and only need the markers to be organised.

How to weigh the congruences

0.55 to 0.66 is well below the 0.85 to 0.95 that factor-replication work treats as "the same factor". Two things depress it independently of any real mismatch: the targets are idealised +1/0/-1 vectors, and 34 of the 134 variables are lexicon words that the target scores as 0 but that load freely. Against that, "a random 5-factor rotation would give congruences near 0.1 to 0.2, and the top-loader tables are unambiguous for A, C and I."

The conclusion offered:

"the Big Five's content is recoverable from the weight geometry; its axis system is recovered for A, C and I and rotated for E and ES."

The caveat on the number of factors

Parallel analysis at the reference N gives 9, and the k = 9 solution (which drives the steering directions) splits E across three factors and A and I across two each, with best congruences 0.28 to 0.64. "Five is the theory-driven choice; the data alone say the common variance has more than five components, and the extra ones are subdivisions of E, A and I rather than anything outside the Big Five." See How to read the elbow (scree) figure for the related count of eleven components above the structureless null in the PCA.

Two checks the answer asked for before this becomes a claim in the post

1. Whether the E/ES rotation is stable across the second seed. The 15 seed-1 traits include 3 per factor, so the plane can be checked but not the rotation; that needs the 40. See The seed floor.
2. Whether the same rotation appears in the activation-space factoring — "a one-line change to the analysis" that would say whether it is the model's organisation or an artefact of how these particular adapters trained.

Neither had been done as of 2026-09-07.

Status

status: current. The congruence values were checked against qwen35/results/fa_qwen35.json, whose targets.labels are ordered [E, A, C, ES, I, Eval]. The file's solutions.centred_k5.congruence_oblimin rows give 0.6555 with A, 0.5744 with C, 0.4049 ES and 0.3380 E, 0.5389 E and -0.3483 ES, and 0.6823 with I — so every figure in the table above matches the file, except that the transcript rounded the Intellect congruence down to "about 0.6" where the file says 0.6823. Use the file value.