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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

Weight-space geometry

Adapter effect and LoRA-A driftcurrentThe shared LoRA-A moves 1.5% of its norm across the whole stage-one zoo and about 10% in stage two, which is what makes the stage-one geometry comparable and weakens the stage-two case.
Alignment-relevant traits in the geometrycurrentFour preregistered predictions about sycophantic, obsequious, power-seeking and corrigible; two held and two failed, and the retrain on the zoo's shared prompt pool changed no verdict.
Best axis pair per Goldberg groupcurrentFor 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.
Column-space structurecurrentTwo adapters for the same trait from different LoRA seeds are near-orthogonal as vectors but share output-side subspace - their top left singular directions agree at |cos| 0.77 and 46 percent of one adapter's delta energy lies in the other's column space, against 14 percent for different traits and 1.8 percent for random subspaces; the row space sits exactly at the r/d null, which is why the Frobenius cosine reads 0.018.
Cross-seed geometrycurrentThe arrangement of the adapters reproduces across LoRA seeds even though the coordinates do not - cross-seed cosine tracks within-run cosine at Pearson 0.9966 matched, and the same-seed objective-only comparison sits at 0.954.
Factor analysis of the adapter GramcurrentPrincipal axis factoring with oblimin rotation on the 134x134 trait correlation matrix; parallel analysis chose 9, five were also extracted because five is the hypothesis, and no Goldberg congruence clears 0.85.
Factor analysis of the null armscurrentThe same factor analysis run on the two matched null Grams - the shuffled arm retains zero factors, the permuted arm retains eight and reproduces the real five factors exactly once its adapters are re-identified by the trait they actually trained on, and neither arm shows any Big Five congruence.
Factor analysis of the training-contrast embeddingscurrentFactoring the chosen-minus-rejected MiniLM embeddings of the 134 training corpora with the adapter pipeline returns the same five factors one to one at Tucker congruence 0.81 to 0.97 (mean 0.90), including the Timidity and Arousal rotation of the Big Five pair, so the rotation is in the training contrast text and the weights inherit it.
Full OCT persona replicationcurrentThe zoo's geometry recomputed on the deployed Open Character Training persona adapters (stage one plus 0.25 stage two, exact merge) - the arrangement is the stage-one arrangement (off-diagonal r 0.992, Procrustes 0.995) and second-seed personas identify themselves 15/15.
Goldberg-only factoring and the 34 as a held-out setcurrentThe five factors are not made by the marker words - factoring the 100 Goldberg markers alone returns the same five at mean Tucker congruence 0.9923, and a chart built from those 100 alone places the 34 Big-Five-agnostic Lexicon words where an independent LLM rater says they belong, at mean r 0.6098 against the 0.6069 the marker words themselves achieve; the 34 factored in isolation return all five factors too but as a poorer sample, at the 3rd percentile of 200 random 34-marker subsets, with one chart dimension barely covered; and the training contrast predicts chart position at R^2 0.938, so the frame is the text passed through, as sweep100 found.
Gradient atoms on the zoo's own preference datacurrentRosser's Gradient Atoms pipeline ported to the zoo - per-pair DPO gradients with respect to LoRA-B at B = 0, EKFAC-projected to 6,944 dimensions and decomposed into 200 sparse atoms - recovers bipolar trait axes without labels (trait purity 0.1632 against a label-shuffle null of 0.1000, z 32.4) but only weakly, no atom clears coherence 0.5, four of the five factor directions have a nearest atom above the 20-random-merge band in weight space, and atom coherence predicts nothing about judged steerability.
Module holographycurrentEach of the 248 targeted modules was tested alone; a single module's slice of the weight change classifies a trait's Big Five factor at 0.638 on average against 0.202 chance, where all 248 together reach 0.76.
PCA, the scree curve and the two nullscurrentEleven principal components of the adapter cloud sit above a structureless null and none sits above the permuted null; the elbow is unusable and four different variance spectra circulate for the same cloud.
Per-direction seed stability, and why the check is uninformativecurrentEvery named direction's trait coordinates correlate about 0.998 between the two LoRA seeds, but so does a random merge of the same adapters at 0.979, because the cross-seed Gram is a scaled copy of the within-seed Gram; the check reproduces the matrix-level result and says nothing about the factors.
Polarity, bipolarity and the trait graphcurrentThe Big Five come back as signed bipolar axes rather than clusters - same-keyed traits align, opposite-keyed anti-align by +0.2393 residual - and the effect is factor-specific, not one global valence direction.
Rank sweepcurrentFifteen zoo traits retrained at LoRA rank 1, 4 and 16 with the input frame made to nest inside the zoo's rank-64 one - the arrangement survives almost intact at rank 1 (15 x 15 cosine matrix Pearson 0.9906 against rank 64, factor-chart coordinates Pearson 0.9967, 15 of 15 identified among the 134) while the behaviour does not survive at all (own-factor amplification -0.41 percent of headroom at rank 1 against +27.08 at rank 64) and neither does the fit (reward margin 0.134-0.432 against 5.072-18.467).
Stage two at a second seedcurrentFifteen traits put through the whole two-stage pipeline again from a second initialisation each find their own seed-zero stage-two adapter among 134 (15/15), the two seeds' cosine matrices agree at r = 0.978, and the attenuation slope is 0.116 - 4.6x the r/d prediction, unexplained.
Stage two, exploredcurrentFour experiments on the introspection stage of 2026-09-08 - the shared direction is generic to SFT on self-generated transcripts (a trait-free control reaches cosine 0.3035 against the zoo's 0.389) and is not what makes personas amplify their trait; the two stages are orthogonal in weight coordinates but at cosine 0.530 in activation space; and the factor solution is unchanged by projecting the shared direction out.
Stage-two geometrycurrentThe stage-two SFT adapters share one LoRA initialisation that differs from stage one's, so trait for trait they are orthogonal to the stage-one ones in coordinates, yet their arrangement reproduces the stage-one arrangement at r = 0.79 over 45 traits.
Structure of the stage-two adapter spacecurrentPCA and factor analysis of the 134 introspection-SFT adapters - one large shared direction (15% of squared norm, every adapter at cosine 0.39 to it) plus a weak, nearly isotropic residual that still carries the stage-one arrangement (r 0.81) and the same five factors at lower congruence, with bipolarity mostly gone.
Superseded geometry claimscurrentEvery place the project reversed itself on the weight-space geometry, with dates and both versions - the trait-level withdrawal and its reversal, the bar in the wrong units, the objective mismatch, the scree source and the stale numbers still on disk.
The activation-weighted Gram, and what the seed floor looks like in itcurrentThe 134x134 Gram rebuilt as ASVD's activation-weighted inner product - two adapters are close if they change the modules' outputs alike on the inputs the model actually sees - moves the same-trait cross-seed cosine from +0.0181 to +0.6643, a factor of 36.8, and reverses the ordering that made the seed floor look like absence of signal; but the frame-overlap null moves with it, from 0.0215 to 0.8910, so relative to what a perfectly reproduced update would score the two metrics agree (0.75 against 0.84) and the floor is not a metric artefact by the preregistered test; the factor solution is untouched, Tucker congruence 0.9926.
The factor analysis in the model's own metriccurrentThe 134x134 Gram rebuilt as a Fisher inner product - the curvature of the output distribution rather than the Frobenius length of the weight change - and the same factor analysis rerun on it; the five factors survive with Tucker congruence 0.9654 against the Frobenius solution (minimum 0.9549, all five above the 0.95 "identical" threshold), the Big Five congruences move by at most 0.0589, parallel analysis still retains nine, and the factor structure is therefore a property of the adapters and not of the parameterisation.
The factor chartcurrentOne convention for placing any adapter or direction in five coordinates - the five oblimin factor directions, Gram-Schmidt orthonormalised in the exact Gram in the fixed order Warmth, Competence, Timidity, Arousal, Imagination - which since 2026-09-08 every figure in the project uses.
The N x N data-to-adapter scoring testcurrentEvery one of the 134 traits' preference pairs ranks its own adapter first out of 134 (133 after column standardisation), and the runners-up carry Big Five structure that nothing in the test required.
The null control armscurrentShuffled, permuted and seed-paired arms; all 240 control adapters were first trained at the wrong objective, and the matched retrains changed the null table by nothing to three decimal places.
The seed floorcurrentThe same trait trained twice at different LoRA initialisations agrees at cosine +0.0181, which is not absence of signal but the r/d = 0.025 overlap of two random rank-64 subspaces; 40 of 40 traits still find themselves, and in an activation-weighted metric the same pairs read +0.6643.
The stage boundary in the activation-weighted metriccurrentUnder the activation-weighted metric a stage-one and a stage-two adapter for the same trait reach cosine +0.0090 where the Frobenius one reads +0.00017, but the frame-overlap ceiling for those two frames is 0.7855, so the cross-stage agreement is 0.92 per cent of what a perfectly reproduced update would score against 74.6 per cent for the same trait retrained at a second seed - eighty times lower; the two stages' grand means are functionally near-orthogonal too, at +0.0167; 56 of 134 stage-two adapters still find their own stage-one adapter and the arrangement correlates at 0.40, so the verdict by the preregistered thresholds is a different function with a matching arrangement.
UMAP, sphere and other layoutshistoricalVisualisation aids over the same Gram - UMAP buys nothing on held-out prediction, and the sphere, spider and viz files are the data behind built pages of varying age.
Weight-space geometry of the 134-adapter zoocurrentWhat the geometric object is - 134 stage-1 LoRA weight updates compared through an exact factored Gram, never materialising a dense delta-W - and how PCA over it is done.
What has been done to the PCs but not to the factorscurrentA 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.
Where no word goes - the hole and the alien directionsupersededThe widest gap in the 134 trait words' coverage of the space is 52.5 degrees at k=5 and 68.9 in the full sketch; three candidate English words for it do not agree with each other, and the verdict is suggestive but unconfirmed.
Where no word goes - the hole on the factor chartcurrentRedone on the five-factor chart, the widest gap in the 134 words' coverage is 54.8 degrees against a 40.3-degree null, but the direction is 23.1 degrees from the principal-component one, the k=2 result that the words tile better than chance disappears, and the three externally suggested candidate names now miss the hole outright.