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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

Cross-seed geometry

The 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.

The distinction the whole result turns on

PHASE3_VERDICT.md separates two things that the tooling conflated:

• the coordinates failing to correspond across bases, and
• the organisation failing to replicate.

A cross-run cosine of 0.017 establishes the first. It cannot speak to the second, because structure can reproduce in a rotated basis while every corresponding vector reads as orthogonal. The cross-Gram is the wrong instrument for the question the verdict line was answering.

The coordinate result is The seed floor. This page is the arrangement result.

Gram correlation: the attenuation regression

Regressing the cross-seed cosine on the within-run cosine over the same 5,320 pairs (134 seed-0 adapters x 40 seed-1 adapters), from qwen35/analysis/crossseed_arms.json:

PHASE3_VERDICT's 2026-08-22 phrasing of the original figure: "The cross-seed block IS the within-run block times 1/38." The matched arm is the same statement at Pearson 0.9966.

The task brief's "Pearson 0.997 matched, 0.954 objective-only" needs one correction. 0.997 is the matched-arm Gram-correlation Pearson above (0.99663, rounding to 0.997). 0.954 is not a Pearson: it is the mean same-trait cosine between the seed-1 arm at the plain objective and the seed-1 arm at the matched objective - the same seed, the same byte-identical data, only the objective differing. PHASE3_VERDICT.md, 2026-09-03:

The objective effect in isolation (cross_gram_full_data_null_seedpaired_s40_x_data_null_seedpaired_s40_matched.npz, same seed, same data, only the objective differs): same-trait cosine +0.954 (range 0.908-0.981), different-trait +0.043, 40/40 top-1.

That arm has no entry in crossseed_arms.json; the verdict prose and .garden/journal/2026-09-03.md ("Objective alone, same seed and data: +0.954. The seed does everything.") are the only sources on disk.

The factor structure replicates under an independent initialisation

The 40 seed-1 adapters were decomposed among themselves with the statistic that was fixed in decompose.py before any seed-1 data existed. PHASE3_VERDICT.md:

                          raw diff         p     resid diff         p
  seed 0 (phase-5)         +0.1819   0.00010        +0.1086   0.00010
  seed 1 (independent)     +0.1835   0.00010        +0.1037   0.00010
  ratio                       1.01x                    0.96x

The seed-1 row is confirmed in qwen35/results/decomposition_seed1.json (identical in content to decomposition_seedB.json except for the TEST 6 block): #test1b.raw.diff = 0.18349392568239462 and #test1b."leading-component removed".diff = 0.10369243017205296, both at p = 4.999750012499375e-05, over #n_traits = 40.

The seed-0 row (+0.1819 / +0.1086) is the same 40 traits at seed 0 and has no file on disk that this page could find; the whole-zoo results/decomposition.json gives 0.1754293665715867 raw and 0.12160064112672682 residual over 134 traits, which is a different quantity. Cite the verdict for the 40-trait seed-0 row.

Bipolarity likewise (PHASE3_VERDICT): seed-1 same-keyed +0.2290 against opposite-keyed -0.0949, gap +0.3239 raw and +0.2065 residual, p at the permutation floor, with the different-factor gap at -0.0541 - absent, as it is at seed 0. Confirmed: decomposition_seed1.json#test2.raw = {same_polarity 0.229009379848836, opposite_polarity -0.09489210220813149, gap 0.32390148205696745, n_same 130, n_opp 150} and #test2."leading-component removed".gap = 0.20650021328045762.

The seed-1 arm's own spectrum is thinner than the zoo's, as 40 traits should be: decomposition_seed1.json#spectrum.participation_ratio = 16.667783498348978, #spectrum.top5_share = 0.44063526198714653.

PHASE3_VERDICT's summary: "The same traits whose vectors correlate at 0.017 across these two runs reproduce the factor structure to within 1% and 4%. The coordinates are noise. The structure is not." It also flags the test's status honestly: it was not preregistered, and a reader should weigh it accordingly; what protects it is that the statistic was fixed in decompose.py before any seed-1 data existed, the adapters are independent, and it is a replication rather than a reanalysis, with a matched 40-trait control ruling out trait count.

Procrustes

The task brief asks for a Procrustes result here. The only Procrustes fit found on disk for the zoo is in activation space, not across weight-space seeds: analysis/actspace_geometry.json#windows.resp.primary.procrustes_r2, quoted by the blog page as "a Procrustes fit of the 134x5 score matrices explains ...% of the variance against a shuffle null of 2%", and reported by .garden/journal/2026-09-05.md as "Procrustes R^2 0.535 on PC scores". That belongs to Activation-space analyses: overview. No weight-space cross-seed Procrustes fit exists in this repo; the cross-seed arrangement result is carried entirely by the Gram correlation and the replicated decomposition above. Recorded as a gap.

What this licenses

PHASE3_VERDICT.md, "What now stands":

Upheld. Trait-training deltas organise into five bipolar axes aligned with the Big Five: same-keyed traits within a factor align, opposite-keyed traits anti-align, and the effect is factor-specific rather than one global valence direction. Not a data artefact, not a batch effect, not training strength, not reproduced by either null, and replicated under an independent initialisation.

Newly required by the above. The geometry is meaningful only relative to a fixed initialisation. Anything downstream that compares adapters must hold the seed fixed or be re-derived per seed.

The blog page's closing section states the same shape: "Its coordinates are local to one LoRA initialisation ... Its arrangement is not local - it reappears under a second seed, in the stage-two adapters, and when the constitutions are used as prompts rather than as training data, so it is not an artefact of the optimiser or of the initialisation."

The frame-free version of the same claim

The argument on this page is that the arrangement replicates while the coordinates do not, and it makes that case with a correlation between two Gram matrices. A more direct version was measured on 2026-09-09: compare the column spaces of two adapters instead of their coordinates. That statistic never refers to a basis, and it identifies all 40 seed-1 adapters among the 134 seed-0 candidates at mean rank 1.0, the same as the Frobenius cross-Gram, with same-trait cross-seed overlap 0.5846385056208819 against 0.12880060417597922 for different traits at k = 8 (qwen35/analysis/column_space.json#stage1). It also shows which half of the LoRA factorisation is frame-locked: the row space sits at the r/d null across seeds, the column space does not. See Column-space structure.

Related: Column-space structure, The seed floor, Stage two at a second seed, The null control arms, Polarity, bipolarity and the trait graph, Activation-space analyses: overview, Superseded geometry claims.

The 2026-10-30 post

The post (Post: Persona Geology (2026-10-30)) says "a second set of training runs on the same data gives the same factors". No second-seed factor solution exists; the evidence is the 40 seed pairs on this page and the relabelled permuted arm on Factor analysis of the null arms. Recorded as Source contradictions S32.