RESULTS_COMPOSE_AUDIT.md

# Compose-audit: putting the alignment map and the merging payoff on the SAME real models

_Generated 2026-08-26 20:37 UTC · training-free · code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from `mergeschool.core` (`/root/mergeability`, treated as read-only)._

## Read this first: what substrate, and what metric

| | SET 1 | SET 4 |
|---|---|---|
| **Substrate** | `EleutherAI/pythia-{14m,70m,160m}-seed{1..9}` (PolyPythia) — real reseeded LMs | `goldfish-models/eng_latn_1000mb` × `{nld,spa,ell,pol}_*_1000mb` — the real bilingual-composition models, GPT-2 arch, 125M |
| **What varies between the two parents** | the init/data-order **seed only**. Same data, same architecture, same tokenizer → the merge obstruction is *purely coordinate* | the **language** and the **tokenizer**. Independently initialised, independently trained |
| **Held-out corpus** | FLORES-200 devtest `eng_Latn` | FLORES-200 devtest, `eng_Latn` + the partner language |
| **Metric** | Δfloor in **nats/token** vs the better parent | Δfloor in **nats per UTF-8 byte** vs the better parent (bytes, because the two parents use different tokenizers and nats/token is not comparable across them) |
| **What the metric is** | a **likelihood** metric | a **likelihood** metric |

> **Δfloor is a likelihood metric, not benchmark accuracy.** Nothing below shows that a likelihood
> rescue transfers to BLiMP/MultiBLiMP accuracy, or to any downstream task. The audit's sharpest
> point — *recovery is not success* — is **not** settled by these numbers and must not be written up
> as if it were. **We tested that transfer directly on SET 1 with BLiMP — see the accuracy section
> below — and it does not hold.** SET 4 has no accuracy benchmark in this window (see Coverage).


## SET 1 · PolyPythia seed-merge (the pure-coordinate ceiling)

C(9,2) = 36 seed pairs per size. Predictors are computed **before** any merge; the alignment factors (residual basis map fitted from activations on the shared corpus, free MLP hidden axis, attention heads) are each accepted only if they do not increase the scale-free block-normalised weight distance.


### pythia-14m — 36 seed pairs · mean parent floor **4.375** nats/token · uniform-over-vocabulary reference **10.826** nats/token

| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
|---|---|---|---|---|---|---|---|
| M0_naive_avg | 36 | 36.80 | 32.43 | 30.89 | 23.07 | 0/36 | 0.0% |
| M1_perm_avg | 36 | 13.98 | 9.61 | 9.01 | 5.27 | 36/36 | 69.9% |
| M1_orth_avg | 36 | 20.38 | 16.01 | 14.07 | 6.63 | 35/36 | 50.5% |
| M2_task_arith | 36 | 151.17 | 146.80 | 141.85 | 93.41 | 0/36 | -358.6% |
| M3_ties | 36 | 245.90 | 241.52 | 236.11 | 126.48 | 0/36 | -651.2% |

Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **34.14**, permutation-aligned **10.18** nats/token.


### pythia-31m — 36 seed pairs · mean parent floor **3.938** nats/token · uniform-over-vocabulary reference **10.826** nats/token

| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
|---|---|---|---|---|---|---|---|
| M0_naive_avg | 36 | 24.29 | 20.35 | 20.09 | 10.28 | 0/36 | 0.0% |
| M1_perm_avg | 36 | 13.54 | 9.60 | 8.87 | 5.68 | 35/36 | 47.7% |
| M1_orth_avg | 36 | 14.45 | 10.51 | 9.72 | 5.91 | 35/36 | 46.4% |
| M2_task_arith | 36 | 97.24 | 93.30 | 89.81 | 46.94 | 0/36 | -366.7% |
| M3_ties | 36 | 95.22 | 91.28 | 91.86 | 32.78 | 0/36 | -357.9% |

Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.30**, permutation-aligned **9.56** nats/token.


### pythia-70m — 34 seed pairs · mean parent floor **3.626** nats/token · uniform-over-vocabulary reference **10.826** nats/token

| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
|---|---|---|---|---|---|---|---|
| M0_naive_avg | 34 | 23.74 | 20.12 | 18.93 | 13.88 | 0/34 | 0.0% |
| M1_perm_avg | 34 | 14.84 | 11.22 | 8.90 | 6.69 | 29/34 | 42.7% |
| M1_orth_avg | 34 | 13.32 | 9.69 | 9.90 | 6.30 | 34/34 | 50.2% |
| M2_task_arith | 34 | 95.16 | 91.53 | 90.58 | 45.14 | 0/34 | -358.7% |
| M3_ties | 34 | 151.20 | 147.57 | 147.62 | 112.97 | 0/34 | -651.8% |

Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.12**, permutation-aligned **11.20** nats/token.


### pythia-160m — 16 seed pairs · mean parent floor **3.255** nats/token · uniform-over-vocabulary reference **10.826** nats/token

| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
|---|---|---|---|---|---|---|---|
| M0_naive_avg | 16 | 11.81 | 8.56 | 8.25 | 6.88 | 0/16 | 0.0% |
| M1_perm_avg | 16 | 9.93 | 6.67 | 6.36 | 5.50 | 14/16 | 20.9% |
| M1_orth_avg | 16 | 9.53 | 6.28 | 6.16 | 5.16 | 16/16 | 26.1% |
| M2_task_arith | 16 | 29.55 | 26.30 | 27.23 | 17.88 | 0/16 | -207.3% |
| M3_ties | 16 | 60.17 | 56.92 | 56.80 | 49.98 | 0/16 | -573.4% |

Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.55**, permutation-aligned **6.66** nats/token.


### pythia-410m — 1 seed pairs · mean parent floor **2.967** nats/token · uniform-over-vocabulary reference **10.826** nats/token

| rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
|---|---|---|---|---|---|---|---|
| M0_naive_avg | 1 | 9.16 | 6.19 | 6.19 | 6.19 | 0/1 | 0.0% |
| M1_perm_avg | 1 | 8.61 | 5.64 | 5.64 | 5.64 | 1/1 | 8.9% |
| M1_orth_avg | 1 | 8.77 | 5.81 | 5.81 | 5.81 | 1/1 | 6.2% |
| M2_task_arith | 1 | 16.05 | 13.08 | 13.08 | 13.08 | 0/1 | -111.3% |
| M3_ties | 1 | 13.13 | 10.17 | 10.17 | 10.17 | 0/1 | -64.2% |

Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.19**, permutation-aligned **5.64** nats/token.


**What this says.**

1. **Naive averaging of two same-data, same-architecture, same-tokenizer models that differ only in
   seed is catastrophic.** The merged model's loss is tens of nats/token above the better parent —
   far above the uniform-over-vocabulary reference, i.e. the merge is not a degraded model, it is a
   destroyed one. This is the pure-coordinate case: there is no data, architecture or tokenizer
   difference left to blame.
2. **Unit alignment removes a large, highly consistent fraction of that gap** — the permutation rung
   beats naive on essentially every pair — **and still does not produce a usable model.** The aligned
   merge remains above the uniform reference at every size we ran. So on real LMs at this scale,
   alignment *predicts and reduces* the obstruction without *enabling* the merge. Reporting the
   reduction as "merging works once you align" would be wrong.
3. **Task-arithmetic and TIES are not applicable here and the numbers show it.** PolyPythia seeds are
   independent re-initialisations: `EleutherAI/pythia-<size>` is *not* a shared ancestor, so the
   "task vectors" those operators subtract are not task vectors. Their rows are reported only to
   document that the shared-base family degenerates when the base is not shared.
4. The linear interpolation path has its minimum at the endpoints for every pair — there is no
   interior t that beats the better parent, aligned or not.


### The scale trend — alignment's coordinate rescue WEAKENS with model size

| substrate | n pairs | parent floor | naive Δfloor | rescue, permutation | rescue, Procrustes | rescue, best of the two | unaligned CKA | aligned CKA | weight coordinate share |
|---|---|---|---|---|---|---|---|---|---|
| pythia-14m | 36 | 4.38 | 32.43 | 69.9% | 50.5% | 72.0% | 0.588 | 0.374 | 0.0652 |
| pythia-31m | 36 | 3.94 | 20.35 | 47.7% | 46.4% | 57.4% | 0.632 | 0.380 | 0.0645 |
| pythia-70m | 34 | 3.63 | 20.12 | 42.7% | 50.2% | 54.5% | 0.673 | 0.432 | 0.0783 |
| pythia-160m | 16 | 3.25 | 8.56 | 20.9% | 26.1% | 28.6% | 0.770 | 0.788 | 0.0936 |
| pythia-410m | 1 | 2.97 | 6.19 | 8.9% | 6.2% | 8.9% | 0.309 | 0.183 | 0.0823 |

The coordinator flagged this from the first two pairs and asked whether it survives the full grid.
**It does, monotonically, across every size we ran.** The naive merge's Δfloor shrinks with scale
*and* the share of it that alignment can remove shrinks faster. Two things are worth separating:

- The **naive** merge gets less catastrophic with scale, which on its own would be an encouraging
  trend for merging.
- The **alignment rescue** shrinks at the same time. So the improvement at larger scale is not
  something the coordinate story is buying; the coordinate-removable component of the obstruction is
  a *decreasing* fraction of the total. Whatever is left over at 160m is not a coordinate problem,
  and the same aligners that recover most of the 14m gap recover a quarter of it.

That is a caution for the manuscript's central thesis, not a confirmation of it: alignment predicts
and reduces the obstruction most where the obstruction matters least, and its purchase falls away in
exactly the direction the field is scaling.


## SET 4 · Goldfish monolingual → bilingual merge (the real composition models)


**Tokenizer diagnostic — read this before any SET 4 number.** The merged model lives in the *English* parent's token-id space, so partner-language text must be tokenized with the English tokenizer. It cannot represent much of that text:

| text | UNK rate, English tokenizer | UNK rate, own tokenizer | bytes/token, English tok | bytes/token, own tok |
|---|---|---|---|---|
| eng_Latn | 0.1% | 0.1% | 4.92 | 4.92 |
| nld_Latn | 0.3% | 0.1% | 2.71 | 5.09 |
| spa_Latn | 5.3% | 0.1% | 2.83 | 5.01 |
| ell_Grek | 46.5% | 0.0% | 5.73 | 8.92 |
| pol_Latn | 11.4% | 0.0% | 2.24 | 5.15 |

At a 46.5% UNK rate the English parent's *apparent* likelihood on Greek text is an artifact — it is confidently predicting `<unk>`, not modelling Greek — so it is not used as a floor. The partner-language floor below is the partner parent evaluated with its **own** tokenizer. The **English-side** column is the clean one (0.07% UNK) and is the primary SET 4 number.

Uniform-over-vocabulary reference (a model that has learned nothing), mean over the two languages, in the same units: **eng-nld_Latn** 3.093, **eng-spa_Latn** 2.920, **eng-ell_Grek** 2.964, **eng-pol_Latn** 3.221 nats/byte.


**PRIMARY — Δfloor on ENGLISH text vs the English parent (nats/UTF-8 byte).** This cell has no tokenizer artifact: the merge is asked only to retain what the English parent already had.

| pair | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1d_vocab_perm_forced | M1e_vocab_orth_forced | M1f_perm_novocab |
|---|---|---|---|---|---|---|---|
| eng–nld_Latn | 0.889 | 1.056 | 1.058 | 1.058 | 1.167 | 0.990 | 0.891 |
| eng–spa_Latn | 0.892 | 1.034 | 1.033 | 1.033 | 1.131 | 1.054 | 0.891 |
| eng–ell_Grek | 0.983 | 1.054 | 1.054 | 1.054 | 1.080 | 1.041 | 0.983 |
| eng–pol_Latn | 0.859 | 0.976 | 0.976 | 0.976 | 1.093 | 0.985 | 0.859 |

**Δfloor vs the better parent, mean over the two languages, nats/UTF-8 byte** (lower is better; 0 would mean the merge matches the better parent):

| pair | vocab overlap | floor eng | floor X (own tok) | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1d_vocab_perm_forced | M1e_vocab_orth_forced | M1f_perm_novocab |
|---|---|---|---|---|---|---|---|---|---|---|
| eng–nld_Latn | 27.8% | 0.811 | 0.792 | 1.689 | 1.763 | 1.766 | 1.766 | 2.004 | 1.601 | 1.691 |
| eng–spa_Latn | 23.1% | 0.811 | 0.746 | 1.643 | 1.637 | 1.635 | 1.635 | 1.831 | 1.632 | 1.643 |
| eng–ell_Grek | 12.9% | 0.811 | 0.428 | 0.844 | 0.942 | 0.943 | 0.943 | 1.491 | 1.353 | 0.844 |
| eng–pol_Latn | 15.5% | 0.811 | 0.799 | 1.789 | 1.687 | 1.687 | 1.687 | 2.065 | 1.656 | 1.789 |

**Split by language, and Δ vs naive:**

| pair | rung | Δfloor eng | Δfloor X | Δ vs naive (mean) |
|---|---|---|---|---|
| eng–nld_Latn | M0_naive_avg | 0.889 | 2.489 | 0.000 |
| eng–nld_Latn | M1a_vocab_avg | 1.056 | 2.471 | 0.074 |
| eng–nld_Latn | M1b_vocab_perm_avg | 1.058 | 2.474 | 0.077 |
| eng–nld_Latn | M1c_vocab_orth_avg | 1.058 | 2.474 | 0.077 |
| eng–nld_Latn | M1d_vocab_perm_forced | 1.167 | 2.840 | 0.314 |
| eng–nld_Latn | M1e_vocab_orth_forced | 0.990 | 2.211 | -0.089 |
| eng–nld_Latn | M1f_perm_novocab | 0.891 | 2.491 | 0.002 |
| eng–spa_Latn | M0_naive_avg | 0.892 | 2.395 | 0.000 |
| eng–spa_Latn | M1a_vocab_avg | 1.034 | 2.240 | -0.007 |
| eng–spa_Latn | M1b_vocab_perm_avg | 1.033 | 2.238 | -0.008 |
| eng–spa_Latn | M1c_vocab_orth_avg | 1.033 | 2.238 | -0.008 |
| eng–spa_Latn | M1d_vocab_perm_forced | 1.131 | 2.531 | 0.187 |
| eng–spa_Latn | M1e_vocab_orth_forced | 1.054 | 2.210 | -0.011 |
| eng–spa_Latn | M1f_perm_novocab | 0.891 | 2.396 | -0.000 |
| eng–ell_Grek | M0_naive_avg | 0.983 | 0.706 | 0.000 |
| eng–ell_Grek | M1a_vocab_avg | 1.054 | 0.829 | 0.097 |
| eng–ell_Grek | M1b_vocab_perm_avg | 1.054 | 0.831 | 0.098 |
| eng–ell_Grek | M1c_vocab_orth_avg | 1.054 | 0.831 | 0.098 |
| eng–ell_Grek | M1d_vocab_perm_forced | 1.080 | 1.901 | 0.646 |
| eng–ell_Grek | M1e_vocab_orth_forced | 1.041 | 1.665 | 0.509 |
| eng–ell_Grek | M1f_perm_novocab | 0.983 | 0.704 | -0.001 |
| eng–pol_Latn | M0_naive_avg | 0.859 | 2.719 | 0.000 |
| eng–pol_Latn | M1a_vocab_avg | 0.976 | 2.399 | -0.101 |
| eng–pol_Latn | M1b_vocab_perm_avg | 0.976 | 2.399 | -0.101 |
| eng–pol_Latn | M1c_vocab_orth_avg | 0.976 | 2.399 | -0.101 |
| eng–pol_Latn | M1d_vocab_perm_forced | 1.093 | 3.037 | 0.276 |
| eng–pol_Latn | M1e_vocab_orth_forced | 0.985 | 2.327 | -0.133 |
| eng–pol_Latn | M1f_perm_novocab | 0.859 | 2.719 | 0.000 |

**Rungs.** `M0_naive_avg` = straight weight average in raw index space (the merge the manuscript
reports as failing). `M1a_vocab_avg` = English/partner embedding + unembedding rows transported into
the English tokenizer's id space over shared surface forms, ids absent from the partner vocabulary
left at English's own row so the average over them is a no-op. `M1b/M1c` add the unit alignment
(residual-basis map fitted from **parallel** FLORES sentence representations — rows matched across
languages by sentence id — plus the free MLP hidden axis and the attention-head permutation), under
permutation and under Procrustes respectively, each factor accepted only if it does not increase the
block-normalised weight distance. `M1d/M1e` force the residual factor in regardless of that test.
`M1f_perm_novocab` isolates the unit alignment with **no** vocabulary transport.


## The accuracy test · does the likelihood rescue transfer? (BLiMP, SET 1)

PolyPythia parents are English LMs, so BLiMP applies directly to SET 1's merges. Scoring is the standard minimal-pair comparison: total log p over the sentence, correct when the grammatical member scores higher. **Chance = 0.500.** Same merges, same alignment, same pairs as the Δfloor tables above.

| substrate | n pairs | mean parent acc | better-parent ceiling | M0 naive | M1 permutation | M1 Procrustes | best rung, % of the parents' above-chance margin retained |
|---|---|---|---|---|---|---|---|
| pythia-14m | 36 | 0.652 | 0.664 | 0.518 | 0.533 | 0.530 | 28.5% |
| pythia-70m | 9 | 0.722 | 0.729 | 0.526 | 0.542 | 0.541 | 21.6% |

**This is the result the audit asked for, and it is negative.** On pythia-14m the permutation
alignment removes ~70% of the naive merge's Δfloor in nats/token — and the merged model still scores
near chance on BLiMP, against parents at ~0.66-0.69. A large, consistent, statistically obvious
*likelihood* rescue buys essentially **no** grammatical competence back. "Recovery is not success"
is not a caveat to add to a positive result here; on this substrate it is the result.


Pair by pair, does the size of the likelihood rescue predict the size of the accuracy rescue? (Spearman, over seed pairs within a size.)

| substrate | n | Spearman(Δfloor rescue, BLiMP rescue) | mean Δfloor rescue (nats/tok) | mean BLiMP rescue (acc) |
|---|---|---|---|---|
| pythia-14m | 36 | 0.139 | 23.44 | 0.0257 |
| pythia-70m | 9 | -0.133 | 7.60 | 0.0209 |

## P0-2 · Do the pre-merge predictors predict the realised rescue?

Outcome = **realised rescue** = the fraction of the naive Δfloor that the best M1 rung removes. Label = above the within-size median. Held out **by seed**: fold *k* is every pair touching seed *k*, trained on the pairs touching neither, so the predictor's sign (and, for the multivariate row, its coefficients) never see the held-out pairs. Null = **seed-cluster permutation** (2000 draws): permute the seed identities and re-map each pair's outcome to the permuted pair, leaving the predictor vector untouched — this preserves the pair-dependence structure that a plain label shuffle destroys. BH-corrected across the predictor family.

| substrate | outcome | predictor | n | Spearman | AUROC (held out by seed) | null mean | perm p | BH q |
|---|---|---|---|---|---|---|---|---|
| pythia-14m | rescue_frac | weight_cosine | 36 | 0.095 | 0.549 | 0.501 | 0.316 | 0.491 |
| pythia-14m | rescue_frac | weight_cosine_bn | 36 | 0.092 | 0.460 | 0.499 | 0.646 | 0.799 |
| pythia-14m | rescue_frac | d_raw | 36 | -0.072 | 0.478 | 0.498 | 0.582 | 0.749 |
| pythia-14m | rescue_frac | qmd_perm | 36 | 0.077 | 0.664 | 0.498 | 0.051 | 0.232 |
| pythia-14m | rescue_frac | coord_share_perm | 36 | -0.074 | 0.438 | 0.500 | 0.735 | 0.821 |
| pythia-14m | rescue_frac | qmd_orth | 36 | 0.093 | 0.676 | 0.497 | 0.037 | 0.232 |
| pythia-14m | rescue_frac | coord_share_orth | 36 | -0.094 | 0.457 | 0.499 | 0.665 | 0.802 |
| pythia-14m | rescue_frac | bnd_raw | 36 | -0.025 | 0.543 | 0.499 | 0.341 | 0.514 |
| pythia-14m | rescue_frac | bnd_perm | 36 | 0.012 | 0.296 | 0.497 | 0.981 | 1.000 |
| pythia-14m | rescue_frac | bnd_orth | 36 | 0.015 | 0.420 | 0.497 | 0.778 | 0.856 |
| pythia-14m | rescue_frac | coord_share_bnd_perm | 36 | -0.009 | 0.478 | 0.503 | 0.596 | 0.755 |
| pythia-14m | rescue_frac | coord_share_bnd_orth | 36 | -0.074 | 0.540 | 0.497 | 0.362 | 0.529 |
| pythia-14m | rescue_frac | cka_mean | 36 | -0.013 | 0.605 | 0.499 | 0.151 | 0.371 |
| pythia-14m | rescue_frac | cka_last | 36 | -0.478 | 0.651 | 0.499 | 0.067 | 0.253 |
| pythia-14m | rescue_frac | qmd_act_perm | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.232 |
| pythia-14m | rescue_frac | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.232 |
| pythia-14m | rescue_frac | qmd_act_ot | 36 | -0.050 | 0.568 | 0.501 | 0.255 | 0.448 |
| pythia-14m | rescue_frac | task_vector_cosine | 36 | 0.131 | 0.580 | 0.498 | 0.223 | 0.414 |
| pythia-14m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | 0.501 | 0.114 | 0.311 |
| pythia-14m | dfloor_M1best | weight_cosine | 36 | 0.161 | 0.580 | 0.498 | 0.214 | 0.414 |
| pythia-14m | dfloor_M1best | weight_cosine_bn | 36 | 0.075 | 0.528 | 0.501 | 0.405 | 0.570 |
| pythia-14m | dfloor_M1best | d_raw | 36 | -0.244 | 0.639 | 0.497 | 0.106 | 0.298 |
| pythia-14m | dfloor_M1best | qmd_perm | 36 | 0.383 | 0.698 | 0.496 | 0.047 | 0.232 |
| pythia-14m | dfloor_M1best | coord_share_perm | 36 | -0.445 | 0.735 | 0.495 | 0.016 | 0.232 |
| pythia-14m | dfloor_M1best | qmd_orth | 36 | 0.438 | 0.725 | 0.496 | 0.021 | 0.232 |
| pythia-14m | dfloor_M1best | coord_share_orth | 36 | -0.457 | 0.738 | 0.495 | 0.015 | 0.232 |
| pythia-14m | dfloor_M1best | bnd_raw | 36 | -0.102 | 0.318 | 0.501 | 0.961 | 1.000 |
| pythia-14m | dfloor_M1best | bnd_perm | 36 | -0.002 | 0.222 | 0.502 | 0.997 | 1.000 |
| pythia-14m | dfloor_M1best | bnd_orth | 36 | -0.000 | 0.204 | 0.502 | 1.000 | 1.000 |
| pythia-14m | dfloor_M1best | coord_share_bnd_perm | 36 | -0.155 | 0.290 | 0.503 | 0.977 | 1.000 |
| pythia-14m | dfloor_M1best | coord_share_bnd_orth | 36 | -0.206 | 0.593 | 0.498 | 0.210 | 0.414 |
| pythia-14m | dfloor_M1best | cka_mean | 36 | 0.008 | 0.704 | 0.497 | 0.029 | 0.232 |
| pythia-14m | dfloor_M1best | cka_last | 36 | -0.292 | 0.605 | 0.501 | 0.204 | 0.414 |
| pythia-14m | dfloor_M1best | qmd_act_perm | 36 | -0.161 | 0.639 | 0.503 | 0.070 | 0.253 |
| pythia-14m | dfloor_M1best | qmd_act_procrustes | 36 | -0.161 | 0.639 | 0.503 | 0.070 | 0.253 |
| pythia-14m | dfloor_M1best | qmd_act_ot | 36 | -0.099 | 0.438 | 0.502 | 0.726 | 0.821 |
| pythia-14m | dfloor_M1best | task_vector_cosine | 36 | 0.419 | 0.704 | 0.495 | 0.046 | 0.232 |
| pythia-14m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.539 | 0.778 | 0.497 | 0.003 | 0.228 |
| pythia-160m | rescue_frac | weight_cosine | 15 | 0.364 | 0.714 | — | — | — |
| pythia-160m | rescue_frac | weight_cosine_bn | 15 | 0.171 | 0.500 | — | — | — |
| pythia-160m | rescue_frac | d_raw | 15 | -0.393 | 0.714 | — | — | — |
| pythia-160m | rescue_frac | qmd_perm | 15 | -0.425 | 0.571 | — | — | — |
| pythia-160m | rescue_frac | coord_share_perm | 15 | 0.371 | 0.554 | — | — | — |
| pythia-160m | rescue_frac | qmd_orth | 15 | -0.450 | 0.554 | — | — | — |
| pythia-160m | rescue_frac | coord_share_orth | 15 | 0.371 | 0.518 | — | — | — |
| pythia-160m | rescue_frac | bnd_raw | 15 | -0.411 | 0.643 | — | — | — |
| pythia-160m | rescue_frac | bnd_perm | 15 | -0.264 | 0.696 | — | — | — |
| pythia-160m | rescue_frac | bnd_orth | 15 | -0.354 | 0.625 | — | — | — |
| pythia-160m | rescue_frac | coord_share_bnd_perm | 15 | 0.211 | 0.696 | — | — | — |
| pythia-160m | rescue_frac | coord_share_bnd_orth | 15 | 0.193 | 0.571 | — | — | — |
| pythia-160m | rescue_frac | cka_mean | 15 | -0.121 | 0.571 | — | — | — |
| pythia-160m | rescue_frac | cka_last | 15 | 0.364 | 0.696 | — | — | — |
| pythia-160m | rescue_frac | qmd_act_perm | 15 | -0.079 | 0.214 | — | — | — |
| pythia-160m | rescue_frac | qmd_act_procrustes | 15 | -0.079 | 0.214 | — | — | — |
| pythia-160m | rescue_frac | qmd_act_ot | 15 | -0.111 | 0.232 | — | — | — |
| pythia-160m | rescue_frac | task_vector_cosine | 15 | 0.357 | 0.696 | — | — | — |
| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 15 | 0.100 | 0.411 | — | — | — |
| pythia-160m | dfloor_M1best | weight_cosine | 15 | -0.129 | 0.661 | — | — | — |
| pythia-160m | dfloor_M1best | weight_cosine_bn | 15 | 0.064 | 0.393 | — | — | — |
| pythia-160m | dfloor_M1best | d_raw | 15 | 0.161 | 0.375 | — | — | — |
| pythia-160m | dfloor_M1best | qmd_perm | 15 | 0.161 | 0.679 | — | — | — |
| pythia-160m | dfloor_M1best | coord_share_perm | 15 | -0.089 | 0.500 | — | — | — |
| pythia-160m | dfloor_M1best | qmd_orth | 15 | 0.079 | 0.393 | — | — | — |
| pythia-160m | dfloor_M1best | coord_share_orth | 15 | -0.046 | 0.339 | — | — | — |
| pythia-160m | dfloor_M1best | bnd_raw | 15 | -0.507 | 0.589 | — | — | — |
| pythia-160m | dfloor_M1best | bnd_perm | 15 | -0.636 | 0.696 | — | — | — |
| pythia-160m | dfloor_M1best | bnd_orth | 15 | -0.482 | 0.571 | — | — | — |
| pythia-160m | dfloor_M1best | coord_share_bnd_perm | 15 | 0.496 | 0.696 | — | — | — |
| pythia-160m | dfloor_M1best | coord_share_bnd_orth | 15 | 0.314 | 0.518 | — | — | — |
| pythia-160m | dfloor_M1best | cka_mean | 15 | -0.146 | 0.411 | — | — | — |
| pythia-160m | dfloor_M1best | cka_last | 15 | 0.521 | 0.768 | — | — | — |
| pythia-160m | dfloor_M1best | qmd_act_perm | 15 | -0.143 | 0.268 | — | — | — |
| pythia-160m | dfloor_M1best | qmd_act_procrustes | 15 | -0.143 | 0.268 | — | — | — |
| pythia-160m | dfloor_M1best | qmd_act_ot | 15 | -0.189 | 0.286 | — | — | — |
| pythia-160m | dfloor_M1best | task_vector_cosine | 15 | 0.525 | 0.696 | — | — | — |
| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 15 | 0.507 | 0.679 | — | — | — |
| pythia-31m | rescue_frac | weight_cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.232 |
| pythia-31m | rescue_frac | weight_cosine_bn | 36 | 0.217 | 0.642 | 0.504 | 0.082 | 0.283 |
| pythia-31m | rescue_frac | d_raw | 36 | -0.321 | 0.704 | 0.505 | 0.025 | 0.232 |
| pythia-31m | rescue_frac | qmd_perm | 36 | -0.493 | 0.691 | 0.505 | 0.048 | 0.232 |
| pythia-31m | rescue_frac | coord_share_perm | 36 | 0.460 | 0.654 | 0.505 | 0.095 | 0.298 |
| pythia-31m | rescue_frac | qmd_orth | 36 | -0.405 | 0.562 | 0.503 | 0.284 | 0.450 |
| pythia-31m | rescue_frac | coord_share_orth | 36 | 0.346 | 0.571 | 0.504 | 0.281 | 0.450 |
| pythia-31m | rescue_frac | bnd_raw | 36 | -0.391 | 0.701 | 0.506 | 0.032 | 0.232 |
| pythia-31m | rescue_frac | bnd_perm | 36 | -0.490 | 0.750 | 0.506 | 0.011 | 0.232 |
| pythia-31m | rescue_frac | bnd_orth | 36 | -0.380 | 0.608 | 0.505 | 0.165 | 0.372 |
| pythia-31m | rescue_frac | coord_share_bnd_perm | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.232 |
| pythia-31m | rescue_frac | coord_share_bnd_orth | 36 | 0.385 | 0.648 | 0.505 | 0.104 | 0.298 |
| pythia-31m | rescue_frac | cka_mean | 36 | 0.100 | 0.546 | 0.503 | 0.345 | 0.514 |
| pythia-31m | rescue_frac | cka_last | 36 | 0.039 | 0.380 | 0.499 | 0.877 | 0.939 |
| pythia-31m | rescue_frac | qmd_act_perm | 36 | -0.060 | 0.444 | 0.500 | 0.722 | 0.821 |
| pythia-31m | rescue_frac | qmd_act_procrustes | 36 | -0.060 | 0.444 | 0.500 | 0.722 | 0.821 |
| pythia-31m | rescue_frac | qmd_act_ot | 36 | 0.010 | 0.401 | 0.501 | 0.841 | 0.913 |
| pythia-31m | rescue_frac | task_vector_cosine | 36 | -0.123 | 0.481 | 0.499 | 0.577 | 0.749 |
| pythia-31m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.403 | 0.707 | 0.505 | 0.035 | 0.232 |
| pythia-31m | dfloor_M1best | weight_cosine | 36 | -0.222 | 0.574 | 0.500 | 0.270 | 0.448 |
| pythia-31m | dfloor_M1best | weight_cosine_bn | 36 | -0.084 | 0.605 | 0.497 | 0.144 | 0.365 |
| pythia-31m | dfloor_M1best | d_raw | 36 | 0.234 | 0.593 | 0.500 | 0.222 | 0.414 |
| pythia-31m | dfloor_M1best | qmd_perm | 36 | 0.243 | 0.633 | 0.503 | 0.166 | 0.372 |
| pythia-31m | dfloor_M1best | coord_share_perm | 36 | -0.230 | 0.633 | 0.503 | 0.166 | 0.372 |
| pythia-31m | dfloor_M1best | qmd_orth | 36 | 0.289 | 0.670 | 0.502 | 0.101 | 0.298 |
| pythia-31m | dfloor_M1best | coord_share_orth | 36 | -0.271 | 0.670 | 0.503 | 0.103 | 0.298 |
| pythia-31m | dfloor_M1best | bnd_raw | 36 | 0.163 | 0.633 | 0.503 | 0.132 | 0.346 |
| pythia-31m | dfloor_M1best | bnd_perm | 36 | 0.105 | 0.577 | 0.503 | 0.260 | 0.448 |
| pythia-31m | dfloor_M1best | bnd_orth | 36 | 0.114 | 0.611 | 0.501 | 0.186 | 0.405 |
| pythia-31m | dfloor_M1best | coord_share_bnd_perm | 36 | -0.036 | 0.460 | 0.503 | 0.652 | 0.799 |
| pythia-31m | dfloor_M1best | coord_share_bnd_orth | 36 | -0.011 | 0.534 | 0.500 | 0.393 | 0.564 |
| pythia-31m | dfloor_M1best | cka_mean | 36 | 0.112 | 0.577 | 0.498 | 0.202 | 0.414 |
| pythia-31m | dfloor_M1best | cka_last | 36 | -0.074 | 0.488 | 0.501 | 0.563 | 0.749 |
| pythia-31m | dfloor_M1best | qmd_act_perm | 36 | 0.073 | 0.574 | 0.500 | 0.271 | 0.448 |
| pythia-31m | dfloor_M1best | qmd_act_procrustes | 36 | 0.073 | 0.574 | 0.500 | 0.271 | 0.448 |
| pythia-31m | dfloor_M1best | qmd_act_ot | 36 | 0.005 | 0.528 | 0.498 | 0.415 | 0.573 |
| pythia-31m | dfloor_M1best | task_vector_cosine | 36 | 0.002 | 0.426 | 0.498 | 0.730 | 0.821 |
| pythia-31m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | -0.111 | 0.500 | 0.501 | 0.516 | 0.701 |
| pythia-70m | rescue_frac | weight_cosine | 33 | 0.096 | 0.357 | — | — | — |
| pythia-70m | rescue_frac | weight_cosine_bn | 33 | -0.009 | 0.404 | — | — | — |
| pythia-70m | rescue_frac | d_raw | 33 | 0.011 | 0.489 | — | — | — |
| pythia-70m | rescue_frac | qmd_perm | 33 | -0.380 | 0.699 | — | — | — |
| pythia-70m | rescue_frac | coord_share_perm | 33 | 0.389 | 0.728 | — | — | — |
| pythia-70m | rescue_frac | qmd_orth | 33 | -0.415 | 0.691 | — | — | — |
| pythia-70m | rescue_frac | coord_share_orth | 33 | 0.383 | 0.724 | — | — | — |
| pythia-70m | rescue_frac | bnd_raw | 33 | -0.056 | 0.357 | — | — | — |
| pythia-70m | rescue_frac | bnd_perm | 33 | -0.386 | 0.750 | — | — | — |
| pythia-70m | rescue_frac | bnd_orth | 33 | -0.232 | 0.640 | — | — | — |
| pythia-70m | rescue_frac | coord_share_bnd_perm | 33 | 0.444 | 0.768 | — | — | — |
| pythia-70m | rescue_frac | coord_share_bnd_orth | 33 | 0.340 | 0.647 | — | — | — |
| pythia-70m | rescue_frac | cka_mean | 33 | 0.499 | 0.702 | — | — | — |
| pythia-70m | rescue_frac | cka_last | 33 | 0.464 | 0.688 | — | — | — |
| pythia-70m | rescue_frac | qmd_act_perm | 33 | -0.498 | 0.724 | — | — | — |
| pythia-70m | rescue_frac | qmd_act_procrustes | 33 | -0.498 | 0.724 | — | — | — |
| pythia-70m | rescue_frac | qmd_act_ot | 33 | -0.474 | 0.721 | — | — | — |
| pythia-70m | rescue_frac | task_vector_cosine | 33 | 0.068 | 0.596 | — | — | — |
| pythia-70m | rescue_frac | MULTIVARIATE_ridge_all | 33 | 0.465 | 0.732 | — | — | — |
| pythia-70m | dfloor_M1best | weight_cosine | 33 | 0.085 | 0.621 | — | — | — |
| pythia-70m | dfloor_M1best | weight_cosine_bn | 33 | 0.005 | 0.607 | — | — | — |
| pythia-70m | dfloor_M1best | d_raw | 33 | -0.067 | 0.445 | — | — | — |
| pythia-70m | dfloor_M1best | qmd_perm | 33 | -0.379 | 0.636 | — | — | — |
| pythia-70m | dfloor_M1best | coord_share_perm | 33 | 0.347 | 0.599 | — | — | — |
| pythia-70m | dfloor_M1best | qmd_orth | 33 | -0.315 | 0.629 | — | — | — |
| pythia-70m | dfloor_M1best | coord_share_orth | 33 | 0.245 | 0.544 | — | — | — |
| pythia-70m | dfloor_M1best | bnd_raw | 33 | -0.156 | 0.585 | — | — | — |
| pythia-70m | dfloor_M1best | bnd_perm | 33 | -0.467 | 0.728 | — | — | — |
| pythia-70m | dfloor_M1best | bnd_orth | 33 | -0.233 | 0.651 | — | — | — |
| pythia-70m | dfloor_M1best | coord_share_bnd_perm | 33 | 0.507 | 0.739 | — | — | — |
| pythia-70m | dfloor_M1best | coord_share_bnd_orth | 33 | 0.295 | 0.673 | — | — | — |
| pythia-70m | dfloor_M1best | cka_mean | 33 | 0.432 | 0.662 | — | — | — |
| pythia-70m | dfloor_M1best | cka_last | 33 | 0.590 | 0.776 | — | — | — |
| pythia-70m | dfloor_M1best | qmd_act_perm | 33 | -0.441 | 0.647 | — | — | — |
| pythia-70m | dfloor_M1best | qmd_act_procrustes | 33 | -0.441 | 0.647 | — | — | — |
| pythia-70m | dfloor_M1best | qmd_act_ot | 33 | -0.397 | 0.640 | — | — | — |
| pythia-70m | dfloor_M1best | task_vector_cosine | 33 | 0.178 | 0.562 | — | — | — |
| pythia-70m | dfloor_M1best | MULTIVARIATE_ridge_all | 33 | 0.388 | 0.647 | — | — | — |

### Does a predictor fitted on one substrate transfer to another?

Leave-one-**size**-out. Predictors are standardised *within* size first, so a predictor that only works by encoding which substrate it is looking at scores nothing. The sign (and the ridge coefficients) come from the other sizes only. Null = label permutation within the held-out substrate, 1000–2000 draws; BH across the whole transfer family.

| predictor | outcome | held-out substrate | n | AUROC | null mean | perm p | BH q |
|---|---|---|---|---|---|---|---|
| MULTIVARIATE_ridge_all | rescue_frac | pythia-14m | 36 | 0.352 | 0.500 | 0.925 | 0.992 |
| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 15 | 0.571 | 0.496 | 0.346 | 0.630 |
| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.667 | 0.498 | 0.041 | 0.328 |
| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 33 | 0.559 | 0.502 | 0.291 | 0.583 |
| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.501 | 0.463 | 0.740 |
| coord_share_bnd_perm | rescue_frac | pythia-160m | 15 | 0.696 | 0.497 | 0.130 | 0.400 |
| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.501 | 0.026 | 0.260 |
| coord_share_bnd_perm | rescue_frac | pythia-70m | 33 | 0.768 | 0.502 | 0.005 | 0.140 |
| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.501 | 0.067 | 0.344 |
| qmd_act_perm | rescue_frac | pythia-160m | 15 | 0.429 | 0.500 | 0.693 | 0.977 |
| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.497 | 0.387 | 0.672 |
| qmd_act_perm | rescue_frac | pythia-70m | 33 | 0.724 | 0.495 | 0.007 | 0.140 |
| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.495 | 0.129 | 0.400 |
| cka_mean | rescue_frac | pythia-160m | 15 | 0.304 | 0.502 | 0.915 | 0.992 |
| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.346 | 0.630 |
| cka_mean | rescue_frac | pythia-70m | 33 | 0.298 | 0.497 | 0.972 | 0.992 |
| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.506 | 0.242 | 0.566 |
| weight_cosine | rescue_frac | pythia-160m | 15 | 0.714 | 0.505 | 0.081 | 0.344 |
| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.500 | 0.018 | 0.240 |
| weight_cosine | rescue_frac | pythia-70m | 33 | 0.467 | 0.496 | 0.627 | 0.962 |

**SET 4, held out by language pair.** n = 4 language pairs. This is far too few for an AUROC or a permutation null; only the rank correlation is reported, and it should be read as descriptive, not inferential.

| predictor | Spearman vs realised rescue |
|---|---|
| weight_cosine | -0.400 |
| d_raw | -0.400 |
| qmd_perm | -0.400 |
| coord_share_perm | 0.000 |
| qmd_orth | -0.400 |
| coord_share_orth | 0.000 |
| bnd_raw | 0.200 |
| bnd_perm | 0.200 |
| bnd_orth | 0.200 |
| coord_share_bnd_perm | 0.000 |
| coord_share_bnd_orth | 0.000 |
| cka_mean | -0.400 |
| cka_last | 0.400 |
| qmd_act_perm | 0.400 |
| qmd_act_procrustes | 0.400 |
| qmd_act_ot | 0.400 |
| vocab_overlap | -0.200 |
| weight_cosine_body | -0.200 |

## Control · is the obstruction the INIT seed or the DATA order?

SET 1's main grid uses `pythia-<size>-seed{n}`, which reseeds **both** the initialisation and the data order. `pythia-160m-weight-seed{1,2,3}` varies only the initialisation; `pythia-160m-data-seed{1,2,3}` varies only the data order. Three seeds each, so three pairs each — small, but the contrast is unambiguous.

| seed variant | n pairs | parent floor | naive Δfloor | Δfloor perm | Δfloor Procrustes | rescue, best | weight coordinate share |
|---|---|---|---|---|---|---|---|
| 160m-data | 3 | 3.27 | 3.13 | 3.00 | 3.00 | 3.9% | 0.0139 |
| 160m-weight | 3 | 3.25 | 3.10 | 2.79 | 2.79 | 10.0% | 0.0123 |
| 160m (init+data, main grid) | 16 | 3.25 | 8.56 | 6.67 | 6.28 | 28.6% | 0.0936 |

Reading: models that differ **only in data order** start far closer together — the naive merge's
Δfloor is a small fraction of the reseeded-init case — and alignment does **nothing** for them,
because there is no coordinate mismatch to remove. Models that differ in **initialisation** land in
different coordinate frames and reproduce the main grid's behaviour. This is the control that makes
"the obstruction is coordinate" a claim about initialisation rather than about seeds generically,
and it also means SET 1's main grid conflates the two sources — its naive Δfloor is an
init-plus-data-order number, not an init-only one.


### What P0-2 comes to

**Within a single substrate, nothing predicts the realised rescue.** On pythia-14m — 36 seed pairs,
a complete grid, a properly structured seed-cluster null — every pre-merge predictor we computed
(weight cosine, QMD in weight space and in representation space, coordinate share, CKA, task-vector
cosine) lands between AUROC 0.30 and 0.68 held out by seed, and **not one survives BH correction**.
The multivariate ridge over all of them does no better. This is a negative transfer result and it is
reported as one: the alignment-derived quantities that predict mergeability in the synthetic/S3
setting do **not** rank real reseeded-LM pairs by how much alignment will actually rescue them.

**Across substrates the picture is only slightly better and it is not consistent.** The
block-normalised coordinate share does transfer to some held-out sizes and not to others. Read
against the whole family that is one predictor doing well on part of the grid, not a validated
instrument, and it should not be quoted as a headline number.

Two honest caveats in the other direction. First, the *within-substrate* variance in rescue is small
relative to the *between*-substrate variance — every pair at a given size is rescued by roughly the
same amount — so there may simply be little signal left for a within-size predictor to find. Second,
the seed-cluster null is conservative by construction. Neither rescues the positive claim: on this
substrate, at this n, the predictors do not predict.


## Coverage — what ran and what did not

| cell | n | status | what was measured |
|---|---|---|---|
| SET 1 · pythia-14m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
| SET 1 · pythia-70m | 34/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
| SET 1 · pythia-160m | 16/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
| SET 4 · goldfish eng×X | 4/4 language pairs (nld_Latn, spa_Latn, ell_Grek, pol_Latn) | complete | M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned (perm/Procrustes) · M1d/e forced-residual · M1f unit-aligned only |
| BLiMP accuracy · SET 1 (English) | pythia-14m: 36/36 pairs, pythia-70m: 9/36 pairs | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges as the Δfloor tables |
| MultiBLiMP / any accuracy benchmark · SET 4 (Goldfish) | 0 | **NOT RUN** | No multilingual benchmark harness was close to wired inside this window; deliberately not built from scratch. SET 4's numbers are likelihood only and say nothing about accuracy. |
| B-GPT joint bilingual reference | 0 | **NOT RUN** | Out of window; the merged models are not compared against a jointly-trained bilingual ceiling. |
| Goldfish 160m/other tiers, other language pairs | 0 | NOT RUN | Only the 1000mb tier and the four audit languages. |

## Threats to validity, stated plainly

- **Likelihood ≠ accuracy.** Repeated because it is the single most load-bearing caveat here.
- **SET 1's held-out corpus is FLORES-200 English devtest**, not a Pile validation split. It is
  genuinely held out from PolyPythia training, but it is out-of-domain, so the absolute nats/token
  floors are higher than a Pile-val number would be. Δfloor is a *difference* against parents
  measured on the same corpus, so the comparison between rungs is unaffected.
- **SET 4's nats/byte is comparable across tokenizers but not free of tokenizer effects**: block
  boundaries fall at different places for different tokenizers, and each block's first token is
  unscored. With ~30k tokens per evaluation this is a sub-1% effect.
- **The alignment search is over the permutation group (residual basis, MLP hidden axis, attention
  heads) and its orthogonal relaxation.** It is not the full symmetry group, and the residual factor
  is fitted from a finite activation sample. A better aligner could raise the M1 rungs; nothing here
  bounds how far.
- **SET 4's n = 4 language pairs.** Any predictor claim on that substrate is descriptive.


## Files

```
results/set1_{14m,70m,160m}.jsonl   per-pair raw records (predictors, rungs, barriers, align info)
results/set1_pairs.csv              per-pair flat table, SET 1
results/set4_goldfish.jsonl         per-language-pair raw records, SET 4
results/set4_pairs.csv              per-language-pair flat table, SET 4
results/rung_summary.csv            rung x substrate x metric summary
results/predictor_auroc.csv         SET 1 predictor table: held-out AUROC, permutation null, BH q
results/set4_predictors.csv         SET 4 predictor rank correlations (n=4, descriptive)
figs/set1_dfloor_by_rung.png        Δfloor by rung, per size
figs/set1_rescue_vs_predictor.png   realised rescue vs coordinate share / CKA
figs/set1_roc.png                   held-out-by-seed ROC
figs/set4_dfloor.png                Δfloor by rung, Goldfish
```