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as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post.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

The seed floor

The 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.

What is held constant

The seed-paired arm is 40 traits retrained from a second LoRA initialisation. qwen35/make_nulls.py builds it as a byte-identical copy of the real corpus, so:

• data: identical bytes, same prompts in the same file order (nulls_manifest.json#seed_paired_note: "data byte-identical to source; vary train_qwen35.py SEED and ORDER_SEED at launch, not the data").
• prompt order: not held constant. launch_nulls.sh runs the arm with --seed 1 --order-seed 1. make_nulls.py explains why both must move: SEED seeds random/numpy/torch immediately before the LoRA adapter is constructed, so it fixes the A-matrix initialisation and is passed as both seed= and data_seed=; ORDER_SEED drives the rng that fixes example order. "ORDER_SEED alone is not enough, because it leaves the adapter initialisation identical and would understate the floor." Both are 0 for the real sweep.
• objective: identical in the matched arm only. The original arm trained at plain sigmoid DPO; see below.

The 40 traits are listed in qwen35/results/cross_gram_seedpaired_provenance.json#matched (active, anxious, artistic, assertive, bright, careful, cold, complex, conscientious, disorganized, emotional, energetic, extraverted, fretful, harsh, helpful, innovative, intellectual, introverted, kind, neat, organized, pleasant, quiet, relaxed, simple, sympathetic, temperamental, thorough, touchy, trustful, undependable, unenvious, unexcitable, unimaginative, unintellectual, unsympathetic, unsystematic, untalkative, vigorous), with #subdir_a = "" and #subdir_b = "data_null_seedpaired_s40".

The shared-A design, and why the floor is small

A LoRA writes dW = s * B @ A with B initialised at zero and A drawn at random. Because B starts at zero, A receives almost no gradient and barely moves: measured drift mean ||A_i - A_0|| / ||A_0|| across the zoo is 0.014605041334818797 (qwen35/analysis/align_summary.json#a_drift; the blog page rounds it to "1.5%", and analyse_alignment.py / analyse_hole.py both quote "the zoo's own internal figure 0.0146" as their gate).

So every adapter in the zoo, sharing one seed, writes into the same random 64-dimensional slice of a 2560-dimensional input space, and they are directly comparable. Two independent draws are not: their expected overlap is r / d = 64 / 2560 = 0.025.

qwen35/probe_invariant.py states the measured version: "measured row-space overlap 0.0249, which is 64/2560, exactly what two random rank-64 subspaces of a 2560-dimensional space give."

The numbers

qwen35/analysis/crossseed_arms.json is a two-element list, computed by qwen35/analyse_crossseed.py over the 134 x 40 cross-Gram blocks. Cosines are X / outer(norms_a, norms_b) - exact, no sketch.

The current figure the blog page quotes is the matched one: "Train the same trait twice from two different random LoRA initialisations and the two adapters come out 89 degrees apart (cosine 0.018)." (qwen35/analysis/pc_loadings.json#seed.same_trait_deg = 89.04958220635345 is the 89-degree figure, computed on the original 0.01658715905967511 - the page's data file still carries the pre-matched cosine.)

The attenuation slope is predicted, not fitted

PHASE3_VERDICT.md, postscript to the 2026-08-22 addendum:

Measured slope of cross-seed cosine on within-run cosine: 0.0264. The LoRA rank fraction is r/d = 64/2560 = 0.0250 (Qwen3.5-4B hidden_size 2560, LORA_R 64). Agreement to 6%. The subspace-overlap account predicts that number; no account in which the 0.0167 is absence-of-signal predicts anything at all. This is the strongest single piece of evidence in the addendum, and it was free.

Regressing cross-seed cosine on within-run cosine over the same 5,320 pairs is what produces the slope; the matched arm gives 0.0265 (#[1].slope) at Pearson 0.9966. So the whole cross-seed block is the within-run block times about 1/38.

The objective in isolation

PHASE3_VERDICT.md, addendum 2026-09-03. The npz results/cross_gram_full_data_null_seedpaired_s40_x_data_null_seedpaired_s40_matched.npz holds the same 40 traits at the same seed on the same data with only the objective differing:

same-trait cosine +0.954 (range 0.908-0.981), different-trait +0.043, 40/40 top-1. So the seed change moves an adapter from 0.954 to 0.018 and the objective change moves it from 1.0 to 0.954.

.garden/journal/2026-09-03.md states it in one line: "Objective alone, same seed and data: +0.954. The seed does everything." Those three numbers exist only in the verdict prose and the journal; crossseed_arms.json does not carry that arm.

The same addendum verifies the treatment travelled: first-step loss 0.89-0.94 (ln 2 plus the 0.1 x SFT term, as in the 134) against exactly 0.6931 in the original arm, and kl_term = sq_approx_kl x 0.001 on every logged step. analyse_crossseed.py computes both arms with one code path and "reproduces the 2026-08-22 numbers to the digit" before being trusted on new ones.

The preregistered bar, and why it could not be cleared

PREREGISTRATION_phase3.md, Arm 3:

Pre-registered threshold. The reference is the median cosine of same-factor, same-keying, different-trait pairs: +0.2447. ... If seed-paired lands below 0.35 I will report the trait-level result as unsupported even though it is my own headline.

Measured: median +0.0167, min +0.0151, max +0.0178 over 40 traits (results/compare_nulls_output.txt). About fourteen times less aligned with itself than two different traits sharing a factor and a keying. The trait-level framing was withdrawn on 2026-08-23.

Then reversed on 2026-08-22 22:40 UTC (the addendum is dated earlier in the day than the verdict body it reverses; the verdict body was written 2026-08-23). PHASE3_VERDICT, "THE TRAIT-LEVEL WITHDRAWAL IS REVERSED":

The floor compared a cross-basis cosine (0.0167) against a bar computed within a single basis (+0.2447 ...). Those two numbers are not commensurable. Two independent rank-64 inits span near-orthogonal slices of a 2560-dim space, so a trait direction that reproduced perfectly modulo the subspace would still have scored ~0.02. The test could not have passed under any hypothesis.

The stated general lesson: "A preregistered threshold needs its own check: compute what the statistic would read under the maximal version of the hypothesis, before committing to the threshold."

A units problem sits inside the bar itself, recorded here rather than resolved. The preregistration calls +0.2447 a median. The value +0.2447 is what qwen35/results/decomposition.json#test2.raw.same_polarity reports (0.24472701836565558) and that key is a mean over 932 pairs. results/compare_nulls_output.txt separately reports the median of the same class as +0.2467 (n = 932), and +0.2373 restricted to the 40 seed-twinned traits (n = 130). Both are recorded; neither is silently preferred.

Three structural facts the addendum rests on

From the 2026-08-22 addendum, on the original arm:

1. Perfect separation. min same-trait 0.01509 > max different-trait 0.01490 across all 5,320 cross-trait comparisons; no overlap at all. (Matched arm: 0.01593 > 0.01584, #[1].sep = 9.15e-05.)
2. 40/40 top-1. Every seed-1 trait is its own nearest neighbour among all 134 seed-0 adapters; mean rank 1.0 against a chance mean of 67.5.
3. The whole geometry transfers, uniformly attenuated - the slope result above.

Bipolarity survives the seed boundary: same-keying minus opposite-keying = +0.00866 signed, i.e. the +0.1216 within-run effect at the same 1/38 scale (#[0].signed_bipolarity = 0.008642746343836636).

What is reinstated and what is not

PHASE3_VERDICT.md:

Reinstated. A trait has a reproducible direction in weight space. It survives independent initialisation; the cosine is small only because the LoRA parameterisation confines each run to a different random rank-64 subspace, and 0.0264 is the overlap of two such subspaces, not a measure of signal loss.

Not established. Same-trait pairs train on a byte-identical corpus, so what reproduces is that trait's training signal. This addendum does not upgrade the deflationary reading - it removes a spurious refutation, it does not add evidence that the axes are model-intrinsic personality rather than corpus structure.

Not usable as engineering. 1.7% alignment is statistically unambiguous and practically worthless as a transferable vector. Anything that needs a usable direction still works inside one init, or freezes A globally (LoRA-FA, arXiv:2308.03303) so all adapters share one subspace by construction.

The 2026-08-24 addendum then re-withdrew part of this: "The cross-seed self-cosine (+0.0167) is a seed-plus-objective floor, not a pure seed floor. The trait-level withdrawal STANDS (the preregistration bound it to this measurement as run), but the mechanistic reading 'the init frame alone carries the magnitude' needs the 40 seed-B adapters retrained at the matched objective." The 2026-09-03 addendum discharges that caveat - "the page now quotes 0.0181" - without restating the reinstatement in words; the blog page, which is current truth, treats trait identity as surviving the seed change. Four dated positions on one claim; they are laid out in Superseded geometry claims.

The cross-init probe

qwen35/probe_invariant.py asks whether a weight probe can identify a trait across initialisations using representations that do not depend on the random basis. Three feature spaces, cheapest first: the 248 per-module Frobenius norm profile (basis-free, exact in closed form); a semantic sketch where P_in is 32 real input activations harvested from the base model on a fixed prompt set and P_out the top 32 left singular vectors of the base weight, so neither projection depends on any adapter; and (not implemented there) the functional probe dW . h. The comparison baseline is the random-sketch figure of 0.0166. The script's own header notes it has since been repointed at procedure-invariance (stage-1 DPO versus stage-2 SFT) rather than init-invariance. Results are in qwen35/analysis/functional_probe.json, which this page does not quote.

What is underneath the floor

This page's account - the cosine is small because the two seeds write into independent random rank-64 slices of the input space - was tested directly on 2026-09-09 by splitting each delta into its row space (the span of A) and its column space (the span of B) and comparing the two halves across the seed boundary. Both halves behave exactly as the account requires: the cross-seed row-space overlap is 0.0211080335981577 against a null of 0.021014, while the same-trait cross-seed column-space overlap is 0.4630531697561965 of the delta's energy against 0.1396023334154358 for a different trait and 0.018347 for a random subspace, and the two adapters' top output directions agree at |cos| 0.7701377220108219 (qwen35/analysis/column_space.json#stage1). Column-space overlap identifies 40 of 40 traits without comparing coordinates at all. See Column-space structure.

The floor in a second metric

The 0.0181 is a Frobenius cosine, and the Frobenius metric weights all 2,560 input directions of a module equally when the model's activations effectively use about ten of them. Rebuilt as an activation-weighted inner product on 2026-09-11, the same 40 pairs sit at +0.6642887281525424, 36.8 times the Frobenius figure, and the ordering reverses: a cross-seed twin becomes far more similar than two different traits sharing one initialisation, where here it is far less. The frame-overlap null rises with it, from 0.0215 to 0.8910, so measured against what a perfectly reproduced update would score the two metrics agree and the floor is not a metric artefact by that run's preregistered test (qwen35/analysis/act_gram.json#verdict). See The activation-weighted Gram, and what the seed floor looks like in it; that page also carries the exact reproduction of this page's row through its own code path.

Related: Column-space structure, Cross-seed geometry, The null control arms, Weight-space geometry of the 134-adapter zoo, Stage two at a second seed, Superseded geometry claims, Zoo training recipe, The activation-weighted Gram, and what the seed floor looks like in it.