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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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.
What has been done to the PCs but not to the factors
A row-by-row audit of every analysis the wiki records for the principal components against whether the same exists for the five factor-analytic factors and for the five Big Five keying axes; two gaps were filled on 2026-09-08 and four remain open.
Samuel asked on 2026-09-08 whether the factor analysis carries less supporting analysis than the PCA. It did. This page is the audit: every analysis the wiki records, against the three families of named directions it could be applied to - the principal components of the adapter cloud (PC1-PC6, PCA, the scree curve and the two nulls), the five factor-analytic factors of the k=5 oblimin solution (Factor analysis of the adapter Gram), and the five Big Five keying axes, which are not extracted from the data at all but defined a priori as the mean of a factor's positively keyed markers minus its negatively keyed ones (axis_Extraversion (the named Extraversion axis) and its four siblings).
Read the third column with that difference in mind: several analyses are meaningless for the keying axes because there is nothing to recover - the axis is its own definition.
| analysis | principal components | factor-analytic factors | Big Five keying axes |
|---|---|---|---|
| scree / retained count against the null arms | yes - 11 PCs above shuffled, 0 above permuted, analysis/scree_null_matched.json#n_above_structureless, #n_above_null (PCA, the scree curve and the two nulls) |
yes, added 2026-09-08 - 0 factors retained on shuffled, 8 on permuted, no Big Five congruence in either (Factor analysis of the null arms) | not applicable - the axes are not extracted, so there is no count to null |
| parallel analysis / how many to keep | yes, same source as the row above | yes (Factor analysis of the adapter Gram, results/fa_qwen35.json#n_factors) |
not applicable - there are five by construction |
| steering the base model and blind judging | yes, PC1-PC6 (Steering the base model along weight-space directions, PC1 - Flooding and Composure and siblings) | yes, the five named factors (FA_Warmth (Warmth / prosociality) and siblings) plus the nine fa* columns of the k=9 solution |
yes, all five axes (Steering the base model along weight-space directions) |
| qualitative read of the steered transcripts | yes, PC4-PC6 (analysis/qual_fa.json, Qualitative reads and adjudications) |
yes, the five factors, same file | no |
| cross-seed replication, matrix level | yes - the whole Gram replicates at Pearson 0.9966 (Cross-seed geometry); the PCs inherit it, no per-PC statement | same: inherited, no per-factor statement | same |
| cross-seed replication, per direction | attempted 2026-09-08 and uninformative - 0.998 for every direction against 0.979 for a random merge (Per-direction seed stability, and why the check is uninformative) | same attempt, same verdict | same attempt, same verdict |
| factor analysis re-run at the second seed, congruence against seed 0 | not applicable | open - needs a 40 x 40 within-arm Gram; the matched-objective one does not exist on disk (Per-direction seed stability, and why the check is uninformative) | not applicable |
| activation-space Procrustes | yes - analysis/actspace_geometry.json#windows.resp.primary.procrustes_r2 = 0.5352210111769643 against a shuffle null of #procrustes_null95 = 0.03525949291018074, fitted on PC score matrices (Constitution-as-prompt persona vectors vs weight geometry, Activation-space analyses: overview) |
yes, added 2026-09-08 - the same fit in the factor chart gives analysis/actspace_geometry_fa.json Procrustes R^2 0.7387431438763885, higher than the PC number (Constitution-as-prompt persona vectors vs weight geometry, Factor-first migration) |
no |
| the hole and the alien direction | yes - the hole was found in the top-5 PC subspace (52.5 degrees at k=5, analyse_hole.py docstring, Where no word goes - the hole and the alien direction), and the unnamed direction is 98% PC5 (PC5 - Contemplation and Scheduling) |
yes, added 2026-09-08 by the concurrent factor-first migration - analysis/alien_fa.json and analysis/hole_geometry_fa.json redo the search in the five-dimensional factor chart, written up as Where no word goes - the hole on the factor chart; Where no word goes - the hole and the alien direction remains the PC version |
not a search space, but the axes are placed in the same chart |
| sphere sweep of unchosen directions | yes - the 72 Fibonacci-lattice directions that were steered and judged were sampled on the sphere of the top three PCs (The sphere sweep — 72 directions nobody chose) | partly, 2026-09-08 - analysis/sphere_layout_fa.json places 72 sphere directions on a factor-chart sphere (#chart = "fa", axes Warmth, Competence, Timidity) and that page is being written up by the concurrent session; the judged sweep on disk is the PC one |
the five axes appear as landmarks in both layouts, not swept |
| stage two: does the structure survive the second training stage | yes - centred spectra compared, analysis/stage2_structure.json#spectrum (Structure of the stage-two adapter space) |
yes - Tucker congruence between the two stages' oblimin loadings, #factor_congruence_stage1_vs_stage2.best_matching |
no - the axes were not re-derived or steered in stage two |
| additivity of mixtures | no - never run on PC mixtures | no - never run on factor mixtures | yes - ten matched-norm mixtures of the five axes (Additivity of the Big Five steering axes) |
| nearest-adjective angle for the direction itself | yes - analysis/direction_gaps.json holds PC1-6 |
yes, added 2026-09-08 - analysis/direction_gaps_fa.json adds the five FA_* directions beside the axes and alien_k5 |
yes, in both files |
| identified with a Big Five factor by congruence | yes - each PC's cosine with each axis (PC1 - Flooding and Composure to PC6 - Feeling and Deliberation) | yes - Tucker congruence with the keying targets (Factor analysis of the adapter Gram) | by construction |
| named / described from behaviour | yes, PC1-PC6 | yes, the five factors; the nine k=9 factors are unnamed (Factor analysis of the adapter Gram) | yes |
What was filled on 2026-09-08
- Factor analysis on the null arms. Factor analysis of the null arms. The shuffled arm retains zero factors; the permuted arm retains eight but scores at chance against the Big Five targets, and its factors are the real factors once its adapters are re-identified by the trait they trained on.
- Per-direction seed stability. Per-direction seed stability, and why the check is uninformative. Computed, checked, and found to be a restatement of the matrix-level attenuation rather than evidence about the factors. Recorded so that nobody runs it again or quotes the 0.998.
What remains open
- Factor analysis independently re-run on the seed-1 adapters, with Tucker
congruence back to seed 0. Blocked on a 40 x 40 within-arm Gram for the
matched-objective arm; feasible today with the caveat of the
original-objective arm, whose Gram does exist
(
results/gram_data_null_seedpaired_s40.npz). - A sphere sweep whose 72 directions are sampled in the factor subspace and steered, rather than the existing PC-sampled sweep re-placed on the factor chart.
- Additivity for PC and factor mixtures, which exists only for the keying axes.
- A 100-trait real arm (the Goldberg markers alone, factored out of
results/gram_sweep.npz) so that the null arms' eigenvalues can be read against a real arm with the same number of variables.
Two rows of the table moved while this page was being written: the activation-space Procrustes fit, the nearest-adjective gaps, the hole and the sphere layout were all redone in the factor chart on 2026-09-08 by the factor-first migration (Factor-first migration, The factor chart), which was running in parallel. The table states what is on disk as of 2026-09-08; where a page for a result does not exist yet the JSON file is named instead.
These are also listed on Open questions under "What has not been run"; this page is the map of which instrument has been pointed at which direction, not a claim about which of them would change anything.
Related: Factor analysis of the adapter Gram, Factor analysis of the null arms, Per-direction seed stability, and why the check is uninformative, PCA, the scree curve and the two nulls, Steering the base model along weight-space directions, Open questions.
Sources
qwen35/analysis/fa_nulls.jsonqwen35/analysis/direction_seed_stability.jsonqwen35/analysis/scree_null_matched.jsonqwen35/analysis/alien.jsonqwen35/analysis/actspace_geometry.json#windows.resp.primary.procrustes_r2qwen35/analysis/stage2_structure.json#factor_congruence_stage1_vs_stage2qwen35/analyse_hole.pyqwen35/build_sphere_spec.pyqwen35/analyse_additivity.pyqwen35/analysis/actspace_geometry_fa.jsonqwen35/analysis/alien_fa.jsonqwen35/analysis/hole_geometry_fa.jsonqwen35/analysis/direction_gaps_fa.jsonqwen35/analysis/sphere_layout_fa.json