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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

Best axis pair per Goldberg group

For each of the five Goldberg groups, the pair of recovered factors on which its positively and negatively keyed adapters separate most, by Mahalanobis distance between the pole means in the plane; Extraversion and Emotional Stability both split best on Timidity with Arousal, Conscientiousness needs Warmth beside Competence, Intellect needs Competence beside Imagination, Agreeableness takes Imagination beside Warmth.

Terms (Tucker congruence, oblimin, factor chart, chart cosine, seed floor, column space, twin score, Fisher norm) are defined in the Glossary.

Best axis pair per Goldberg group

Samuel asked, on 2026-09-15, which pair of chart axes highlights each Goldberg group best, instead of drawing every group against Warmth. The answer is in qwen35/analysis/best_axis_pairs.json, drawn as qwen35/figures/post/facets_best_* and available on the companion's Any two axes page as the "best-separating pair per group" mode of the six-panel view.

Criterion

Coordinates are the mean-centred factor chart (The factor chart, analysis/viz_fa.json). For a group and a pair of factors, take the positively and negatively keyed adapters' coordinates in that plane, pool their two within-pole covariances, and measure the distance between the two pole means in that metric (Fisher's linear discriminant separation). All ten pairs of the five factors are scored; the largest wins. A plain d' (mean distance over root-mean-square spread) is recorded beside it as dprime_plain; it was tried first and rejected, because it can never exceed the best single axis and so picks the second axis for being quiet rather than informative.

Result

Two groups need a diagonal rather than one factor: the Extraversion words and the Emotional Stability words both separate best on Timidity together with Arousal, which is the rotation of the Big Five pair that the congruence table records (Factor analysis of the adapter Gram). Conscientiousness separates far better with Warmth beside Competence (6.38 against 3.47 on Competence alone), because its negative pole sits low on Warmth as well as on Competence; Intellect likewise gains from Competence beside Imagination. Agreeableness is the one group that a single axis already handles (5.95 on Warmth); the pair adds Imagination only because the Agreeableness words' spread along Imagination is small.

Related: The factor chart, Polarity, bipolarity and the trait graph, post-draft.