FA_Warmth (Warmth / prosociality)

The largest factor of the k=5 solution and the most selective direction measured anywhere in the study; Tucker congruence +0.655 with Goldberg Agreeableness.

FA_Warmth

The first factor of the centred k=5 principal-axis-factoring solution with oblimin rotation, over the 134x134 adapter correlation matrix. Method and the choice of k are on Factor analysis of the adapter Gram. The blog page titles it Warmth; the solution names it Warmth / prosociality (qwen35/analysis/fa_summary.json#centred_k5.factors[0].name).

SS loading = 10.76 - the largest of the five (qwen35/results/fa_qwen35.md, section 7, and fa_summary.json#...[0].ss).

Loadings

Top ten by absolute loading, from fa_qwen35.md section 7, centred_k5 oblimin, F1 (and identically fa_summary.json#centred_k5.factors[0].top):

Positive pole: agreeable, pleasant, cooperative, trustful, generous. Negative pole: rude, uncooperative, splenetic, ornery. Six of the ten are Goldberg Agreeableness markers and three are unlabelled Lexicon words that land where a reader would put them - see Trait provenance.

Congruence with the Big Five keying

fa_qwen35.md section 6, centred_k5 oblimin row F1:

+0.655 is the highest Agreeableness congruence in any of the four solutions, and it is still short of the conventional 0.85 "fair" bar - fa_qwen35.md records that no factor in any solution clears 0.85.

Steering

From qwen35/analysis/blog_data.json#replication.FA_Warmth: the blind judge names it Agreeableness; slope over |alpha| <= 2 is slope2 = +0.9083333333333332 per unit alpha with sel2 = 10.129292929292934 (the blog page prints 10.1x), and over the full range slope4 = +0.6676155969634231, sel4 = 7.545726505196447.

The blog page: "Warmth is the most selective direction measured anywhere in this study: steering it moves judged Agreeableness +0.91 per unit alpha while barely touching the other four scales - a selectivity of 10.1x, or 7.3x recomputed on only the eighteen prompts that stay free of looping across the whole range." The 7.3x figure is page prose; qual_fa_notes.md is the damage-corrected analysis behind it.

qwen35/analysis/qual_fa.json#directions[0].axis_label:

Interpersonal warmth: curt contempt at negative alpha, effusive tenderness at positive alpha. Delivers its name.

Negative pole: curt, imperative, contemptuous; verdicts without acknowledgement, orders instead of advice, explicit hostility. Positive pole: opens with sympathy, apologises, defers, asks permission, and softens or withholds the actual verdict. Transcripts and dose-response curves: Steering the base model along weight-space directions.

Status

Current. qwen35/direction_pages/FA_Warmth.html is the older per-direction built page for the same object and is historical.

Related: Factor analysis of the adapter Gram, axis_Agreeableness (the named Agreeableness axis), PC4 - Affirmation and Self-Concern, Alignment-relevant traits in the geometry, Steering the base model along weight-space directions, Warm, Agreeable.