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

Generated 2026-08-26 23:25 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,31m,70m,160m,410m}-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; BLiMP accuracy on the same merges	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); MultiBLiMP 1.0 accuracy on the same merges
What the metric is	Δfloor is a likelihood metric; BLiMP is an accuracy metric	Δfloor is a likelihood metric; MultiBLiMP is an accuracy metric

Δfloor is a likelihood metric, not benchmark accuracy — and here they come apart. The audit's sharpest point is that a likelihood rescue has not been shown to transfer to accuracy. We tested that transfer directly, on the same merges, with BLiMP (SET 1) and MultiBLiMP 1.0 (SET 4), and it does not hold in either direction: in SET 1 a ~70% Δfloor rescue buys ~0.03 BLiMP accuracy over the naive merge, and in SET 4 a merge whose Δfloor says it is destroyed still scores 0.68 on MultiBLiMP-English. Neither metric may be reported as a proxy for the other. Every table below states which one it is.

Headline findings

1. Naive averaging of two seed-only-different real LMs is catastrophic, at every size. Δfloor 14m: +32.4 · 31m: +20.4 · 70m: +20.2 · 160m: +9.0 · 410m: +6.5 nats/token against parent floors of 3–4.4 nats/token, i.e. above the uniform-over-vocabulary reference of 10.8 for all but the largest. n = 36 / 36 / 36 / 36 / 15 pairs.
2. Unit alignment removes a large fraction of that gap and still does not produce a usable model. The exactly function-preserving permutation rung removes 14m: 70% · 31m: 48% · 70m: 44% · 160m: 23% · 410m: 8% — leaving 9.6 · 9.6 · 11.0 · 6.8 · 6.0 nats/token above the better parent, i.e. an absolute 14.0 · 13.5 · 14.6 · 10.0 · 8.9 nats/token against parent floors of 3.0–4.4 and a uniform-over-vocabulary reference of 10.8. At 14m, 31m, 70m the aligned merge is still worse than predicting uniformly over the vocabulary; at the larger sizes it is below that line but still 2–3x the parent's loss. (A Procrustes rung is also reported, but it is not function-preserving on LayerNorm transformers — see Validation — so the coordinate claim rests on the permutation rung.)
3. The rescue shrinks monotonically with scale (14m: 70% → 410m: 8% on the exact rung) while the naive gap shrinks too — so the coordinate-removable share of the obstruction is falling in exactly the direction the field is scaling. (Per-size n is listed in (1); the largest sizes carry the fewest pairs, so read the trend from the sizes with complete 36-pair grids and treat the largest as directional.)
4. The likelihood rescue does not transfer to accuracy — and this is the sharpest result here. Same merges, scored on BLiMP. On pythia-14m (n=36) parents average 0.652, the naive merge 0.518 and the aligned merge 0.544, against chance 0.500 — a ~70% Δfloor rescue buys ~0.026 accuracy, and pair by pair the two rescues are uncorrelated. Across the ladder the merged model scores 14m 0.547 · 31m 0.550 · 70m 0.554 · 160m 0.553 · 410m 0.556 — it retains 29%→19% of the parents' above-chance margin — while the likelihood rescue over the same range falls from ~70% to ~8%. The accuracy the merge keeps is essentially independent of how much likelihood alignment recovered.
5. On the real bilingual-composition models the merge fails and alignment does not rescue it. Goldfish eng×{nld,spa,ell,pol}: naive Δfloor on English text +0.91 nats/byte against a 0.81 floor; the best M1 rung +0.90. The binding constraint is the vocabulary, not the coordinate frame — the English tokenizer UNK-s 45% of Greek and 11% of Polish, and no permutation or rotation can address that. Anchoring on the partner language instead (whose tokenizers handle English at <0.1% UNK) removes that wall and the merge still fails. 5b. Give alignment a shared vocabulary and it finally does something — still not enough. Merging two bilingual B-GPT models of the same language pair (~94% tokenizer overlap instead of 13–28%), vocabulary transport plus unit alignment moves MultiBLiMP from 0.618 to 0.655 and Δfloor from +1.04 to +0.87 nats/byte. The parents are at 0.96 and Δfloor 0. This is the clean decomposition: vocabulary is the wall in SET 4, and independent training is the wall behind it.
6. …and the accuracy dissociation runs the other way there. The same likelihood-destroyed Goldfish merges retain 0.68 on MultiBLiMP-English (parent 0.96, chance 0.50). Δfloor and benchmark accuracy dissociate in both directions; neither implies the other.
7. P0-2: the pre-merge predictors do not reliably predict the realised rescue. Held out by seed pair, with a seed-cluster permutation null and BH within the five-predictor family the audit brief itself names: 0 of 25 cells significant. The strongest predictor is the coordinate share — AUROC 0.81 at pythia-70m with a raw permutation p of 0.002 — and its held-out AUROC across the substrates is 14m: 0.48 · 31m: 0.71 · 70m: 0.81 · 160m: 0.61 · 410m: 0.45 — i.e. it does not replicate. Nothing survives BH across the wider exploratory family either. Reported as the negative transfer result it is.
8. The residual obstruction is not coordinate. A same-basin control (the 160M Pythia data-seed / weight-seed ablations, weight cosine 0.56 against 0.02 for two PolyPythia seeds) still pays ~3.1 nats/token to a naive average, and alignment removes only a few percent of it — correctly, since there is no coordinate mismatch left. Merging is not free even inside a basin, and what remains after alignment is not something the permutation group describes.
9. This is not an under-trying artifact. REPAIR-style statistics correction on top of the alignment — the strongest training-free merge here — improves the likelihood further and still leaves BLiMP near chance.

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 — 36 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	36	23.79	20.16	18.93	13.88	0/36	0.0%
M1_perm_avg	36	14.62	10.99	8.77	6.69	31/36	43.9%
M1_orth_avg	36	13.32	9.70	9.90	6.30	36/36	50.4%
M2_task_arith	36	95.14	91.52	90.58	45.14	0/36	-357.8%
M3_ties	36	151.39	147.77	147.75	112.97	0/36	-650.7%

Linear-mode-connectivity barrier (eval.merge_barrier): naive 20.17, permutation-aligned 10.98 nats/token.

pythia-160m — 36 seed pairs · mean parent floor 3.252 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	12.25	8.99	8.47	6.88	0/36	0.0%
M1_perm_avg	36	10.02	6.77	6.44	5.50	33/36	23.5%
M1_orth_avg	36	9.44	6.19	6.22	5.13	36/36	30.3%
M2_task_arith	36	30.85	27.60	27.55	17.88	0/36	-205.3%
M3_ties	36	61.55	58.29	57.97	49.30	0/36	-557.4%

Linear-mode-connectivity barrier (eval.merge_barrier): naive 8.99, permutation-aligned 6.76 nats/token.

pythia-410m — 15 seed pairs · mean parent floor 2.984 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	15	9.51	6.53	6.50	5.95	0/15	0.0%
M1_perm_avg	15	8.94	5.96	5.82	5.56	12/15	8.3%
M1_orth_avg	15	9.01	6.03	6.04	5.44	13/15	7.4%
M2_task_arith	15	14.15	11.17	10.69	5.28	1/15	-71.5%
M3_ties	15	13.04	10.06	10.17	9.32	0/15	-54.7%

Linear-mode-connectivity barrier (eval.merge_barrier): naive 6.54, permutation-aligned 5.93 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. At 14m/31m/70m the aligned merge is still worse than predicting uniformly over the vocabulary; at 160m/410m it drops below that line but still sits at 2–3× the better parent's loss. 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. There is no interpolation coefficient that helps. Across every linear-mode-connectivity curve computed here — 302 of them, naive and aligned, over all five sizes — not one has an interior minimum. The best point on the path is always an endpoint, i.e. one of the parents. Tuning the merge weight is not a way out.

Validation: is the alignment actually function-preserving? (One rung is not.)

Every M1 rung is only an alignment if g.θ_B computes exactly what θ_B computes. This was checked empirically rather than assumed: take a parent, apply the map, and re-evaluate.

substrate	map	change in the parent's nats/token	verdict
set1_pythia14m	permutation_residual+mlp	+3.026e-06	EXACT
set1_pythia14m	permutation_full(+heads)	+5.893e-06	EXACT
set1_pythia14m	orthogonal_residual+mlp	+27.262	NOT function-preserving
set4_goldfish_nld	perm_residual_only	+0.000e+00	EXACT
set4_goldfish_nld	mlp_only	+0.000e+00	EXACT
set4_goldfish_nld	heads_only	+0.000e+00	EXACT
set4_goldfish_nld	perm_full	+0.000e+00	EXACT
set4_goldfish_nld	orth_full	+0.069	negligible

The permutation family is exact — residual basis, free MLP hidden axis and attention heads, on both architectures, to float32 noise. Those rungs are genuine alignments.

The orthogonal/Procrustes residual map is not, and on GPTNeoX it is badly not: applying it to a PolyPythia parent costs that parent +27 nats/token on its own. The reason is structural rather than a bug — LayerNorm subtracts the mean over the residual axis and applies a learned elementwise gain, and neither commutes with a general rotation (an RMSNorm model would be much closer to safe). On the GPT-2 Goldfish models the same map costs only +0.07 nats/token, so the defect is architecture-specific in magnitude.

Internal consistency. The BLiMP, REPAIR and SLERP arms each re-derive the alignment and the merges from scratch, in separate processes, from the raw checkpoints. On the pairs they share with the main SET 1 grid they reproduce its M0 and M1 Δfloor values to machine precision (max absolute difference 0.0000 over 116 and 18 overlapping pairs respectively). The rungs compared across sections are the same objects, not merely the same recipe.

Consequence for the tables. The M1_orth / M1c / M1e rows are still real measurements of a merged model's loss — a merge is a merge, and the number is what it is — but they must not be read as "how much of the obstruction is coordinate". On SET 1 they merge parent A with a damaged copy of parent B, and any apparent rescue is partly the arithmetic of averaging toward one parent. The coordinate claim in this report rests on the permutation rung, which is exact. Where the two disagree, believe the permutation rung. This is flagged again at every table that contains an orthogonal row.

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	36	3.63	20.16	43.9%	50.4%	55.1%	0.671	0.428	0.0793
pythia-160m	36	3.25	8.99	23.5%	30.3%	32.0%	0.747	0.761	0.0867
pythia-410m	15	2.98	6.53	8.3%	7.4%	10.4%	0.463	0.412	0.0355

Read the permutation column: it is the one that is exactly function-preserving (see Validation above). The Procrustes column is shown for completeness but on GPTNeoX that map damages the model it is applied to, so its "rescue" is not a clean coordinate measurement.

The coordinator flagged this trend from the first two pairs and asked whether it survives the full grid. It does, monotonically, across every size we ran, on the exact rung alone. 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	UNK rate, partner tokenizer on ENGLISH text	bytes/token, English tok	bytes/token, own tok
eng_Latn	0.1%	0.1%	—	4.92	4.92
nld_Latn	0.3%	0.1%	0.1%	2.71	5.09
spa_Latn	5.3%	0.1%	0.0%	2.83	5.01
ell_Grek	46.5%	0.0%	0.1%	5.73	8.92
pol_Latn	11.4%	0.0%	0.1%	2.24	5.15

The wall is one-directional. Every partner tokenizer handles English at under 0.1% UNK; the English tokenizer cannot represent Greek or Polish. 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	M1g_emb_procrustes	M1h_emb_proc_units	M1f_perm_novocab
eng–nld_Latn	0.889	1.056	1.058	1.058	1.167	0.990	1.085	0.975	0.891
eng–spa_Latn	0.892	1.034	1.033	1.033	1.131	1.054	0.973	0.970	0.891
eng–ell_Grek	0.983	1.054	1.054	1.054	1.080	1.041	0.965	1.006	0.983
eng–pol_Latn	0.859	0.976	0.976	0.976	1.093	0.985	1.057	0.972	0.859
mean of the 4	0.906	1.030	1.030	1.030	1.118	1.018	1.020	0.981	0.906

On the clean English cell, every M1 rung is worse than the naive merge: naive 0.906, best M1 0.906 nats/byte averaged over the four pairs. Averaged over both languages the best M1 rung removes 1.4% of the naive Δfloor — within noise of zero. For contrast, on SET 1, where the two parents share data, architecture and tokenizer and differ only in seed, the same family of aligners removes ~70% at 14M. The Goldfish obstruction is not the kind of obstruction alignment addresses. The rest of this section establishes why: the binding constraint is the vocabulary, and it lives on an axis the alignment group does not act on.

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	M1g_emb_procrustes	M1h_emb_proc_units	M1f_perm_novocab
eng–nld_Latn	27.8%	0.811	0.792	1.689	1.763	1.766	1.766	2.004	1.601	1.732	1.559	1.691
eng–spa_Latn	23.1%	0.811	0.746	1.643	1.637	1.635	1.635	1.831	1.632	1.503	1.426	1.643
eng–ell_Grek	12.9%	0.811	0.428	0.844	0.942	0.943	0.943	1.491	1.353	1.078	1.202	0.844
eng–pol_Latn	15.5%	0.811	0.799	1.789	1.687	1.687	1.687	2.065	1.656	1.693	1.693	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	M1g_emb_procrustes	1.085	2.380	0.043
eng–nld_Latn	M1h_emb_proc_units	0.975	2.143	-0.130
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	M1g_emb_procrustes	0.973	2.032	-0.141
eng–spa_Latn	M1h_emb_proc_units	0.970	1.883	-0.217
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	M1g_emb_procrustes	0.965	1.191	0.234
eng–ell_Grek	M1h_emb_proc_units	1.006	1.397	0.358
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	M1g_emb_procrustes	1.057	2.329	-0.096
eng–pol_Latn	M1h_emb_proc_units	0.972	2.414	-0.096
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. Item budget is 200 minimal pairs per paradigm at 14M/31M/70M, 150 at 160M and 100 at 410M — 6,700–13,400 pairs per evaluation, which puts the binomial standard error on each cell below 0.006.

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-31m	36	0.691	0.698	0.526	0.536	0.537	25.2%
pythia-70m	36	0.717	0.722	0.516	0.541	0.542	24.4%
pythia-160m	36	0.772	0.776	0.532	0.537	0.539	19.3%
pythia-410m	15	0.789	0.802	0.535	0.543	0.543	18.5%

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 ~0.65. 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.

And the two quantities are flat against each other across the whole scale ladder. The share of the naive Δfloor that alignment removes falls from ~70% at 14M to ~11% at 410M — a sixfold change. The share of the parents' above-chance BLiMP margin the merged model retains barely moves over the same range: 28% → 25% → 24% → 19% → 19%. The merged model scores between 0.52 and 0.54 at every size, whether alignment recovered three quarters of the likelihood gap or a tenth of it. Whatever the likelihood rescue is buying, it is not this benchmark, and the amount of it makes almost no difference.

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-31m	36	-0.166	12.25	0.0211
pythia-70m	36	0.169	11.43	0.0361
pythia-160m	36	0.051	2.97	0.0179
pythia-410m	15	0.225	0.70	0.0165

Did we try hard enough? · REPAIR on top of the alignment

The obvious objection to a negative merging result is that averaging is a weak merge: it halves the variance of every pre-activation, and REPAIR (Jordan et al., ICLR 2023) shows that restoring those statistics recovers most of the remaining barrier on vision nets. This rung adds it, training-free: after the permutation-aligned average, walk the layers in order and affine-correct each Linear's per-unit pre-activation mean and std to the average of the two parents' own statistics on the same corpus. M5 applies the same correction to the naive merge, to separate what alignment contributes from what statistics-repair contributes.

substrate	n pairs	rung	mean Δfloor (nats/tok)	median Δfloor	BLiMP accuracy	% of the parents' above-chance margin retained
pythia-14m	36	M0_naive_avg	32.43	30.89	0.518	11.0%
pythia-14m	36	M1_perm_avg	9.61	9.01	0.533	19.9%
pythia-14m	36	M4_perm_repair	7.88	7.41	0.527	16.7%
pythia-14m	36	M5_naive_repair	32.50	31.10	0.512	7.2%
pythia-14m	36	parents	0.00	0.00	0.664	100.0%
pythia-31m	36	M0_naive_avg	20.35	20.09	0.526	13.0%
pythia-31m	36	M1_perm_avg	9.60	8.87	0.536	18.3%
pythia-31m	36	M4_perm_repair	8.48	7.47	0.532	16.2%
pythia-31m	36	M5_naive_repair	19.90	19.64	0.520	10.3%
pythia-31m	36	parents	0.00	0.00	0.698	100.0%
pythia-70m	36	M0_naive_avg	20.16	18.93	0.516	7.1%
pythia-70m	36	M1_perm_avg	10.99	8.77	0.541	18.5%
pythia-70m	36	M4_perm_repair	10.68	8.23	0.537	16.7%
pythia-70m	36	M5_naive_repair	19.52	18.99	0.516	7.2%
pythia-70m	36	parents	0.00	0.00	0.722	100.0%
pythia-160m	36	M0_naive_avg	8.99	8.47	0.532	11.5%
pythia-160m	36	M1_perm_avg	6.77	6.44	0.537	13.6%
pythia-160m	36	M4_perm_repair	6.89	6.39	0.534	12.1%
pythia-160m	36	M5_naive_repair	8.69	8.54	0.524	8.8%
pythia-160m	36	parents	0.00	0.00	0.776	100.0%

REPAIR does help the likelihood — it is the best training-free merge in this report, taking a further bite out of the aligned merge's Δfloor (on pythia-14m, 9.61 → 7.88 nats/token, a further 18%). And BLiMP does not follow it at all: 0.533 → 0.527, i.e. flat, and slightly down. That is the dissociation again, now inside a single rung comparison where the only thing that changed is a likelihood-improving correction. It does not change the conclusion. The repaired aligned merge is still many nats/token above the better parent, still above the uniform-over-vocabulary reference at the small sizes, and still close to chance on BLiMP. Applied to the naive merge it barely moves anything, which is the expected pattern: variance repair is only useful once the units correspond.

So the negative result is not an artifact of using a deliberately weak merge operator. Naive averaging, unit-aligned averaging, orthogonal alignment, task arithmetic, TIES and REPAIR-corrected alignment were all tried on the same pairs; the best of them recovers most of the likelihood gap at 14M, a quarter of it at 160M, and grammatical competence in none of them.

Robustness: is the Δfloor an artifact of the held-out corpus?

The main SET 1 tables score on FLORES-200 English devtest — genuinely held out from PolyPythia training, but out-of-domain for the Pile. The obvious objection is that the merge penalty is inflated by domain shift. The same pairs and the same merges, re-scored on a Pile sample (NeelNanda/pile-10k, in-distribution for Pythia) and on WikiText-103 validation:

substrate	n pairs	corpus	parent floor	naive Δfloor	Δfloor permutation-aligned	rescue
pythia-14m	36	flores_eng	4.38	32.43	9.61	69.9%
pythia-14m	36	pile_10k	4.19	32.95	10.23	68.4%
pythia-14m	36	wikitext103_val	4.98	32.95	10.48	67.7%
pythia-160m	36	flores_eng	3.25	8.99	6.77	23.5%
pythia-160m	36	pile_10k	3.14	9.35	7.51	18.4%
pythia-160m	36	wikitext103_val	3.24	9.59	8.11	14.4%

It is not a corpus artifact. Parent floors move with domain, as they should. The naive Δfloor barely moves at all — within 2% at 14M and within 7% at 160M — and the aligned Δfloor moves by under a nat. The rescue fraction is within 2 points across corpora at 14M; at 160M it drifts from 23% on FLORES to 14% on WikiText, which is worth stating rather than smoothing over, but it does not touch either conclusion: the merge penalty is enormous on the in-distribution Pile sample too, and the scale trend (large rescue at 14M, small at 160M) is present on all three corpora. The penalty is a property of the merge, not of the evaluation set.

The operator practitioners actually use · SLERP

Every rung above is a lab operator. A census of community merges on the Hub finds SLERP on about a quarter of them — more than TIES, DARE-TIES and task arithmetic combined — and unlike those it needs no shared base, which is exactly why it gets reached for when two models have no common ancestor. That is the PolyPythia seed case. Here it is, on the same pairs, before and after unit alignment, with both metrics.

substrate	n pairs	rung	mean Δfloor (nats/tok)	BLiMP accuracy
pythia-14m	36	M0_naive_avg	32.43	0.518
pythia-14m	36	M1_perm_avg	9.61	0.533
pythia-14m	36	M6_slerp	58.29	0.516
pythia-14m	36	M7_perm_slerp	11.77	0.524
pythia-14m	36	parents	0.00	0.664
pythia-31m	36	M0_naive_avg	20.35	0.526
pythia-31m	36	M1_perm_avg	9.60	0.536
pythia-31m	36	M6_slerp	41.38	0.521
pythia-31m	36	M7_perm_slerp	19.32	0.529
pythia-31m	36	parents	0.00	0.698
pythia-70m	36	M0_naive_avg	20.16	0.516
pythia-70m	36	M1_perm_avg	10.99	0.541
pythia-70m	36	M6_slerp	35.05	0.513
pythia-70m	36	M7_perm_slerp	14.24	0.541
pythia-70m	36	parents	0.00	0.722
pythia-160m	36	M0_naive_avg	8.99	0.532
pythia-160m	36	M1_perm_avg	6.77	0.537
pythia-160m	36	M6_slerp	13.76	0.529
pythia-160m	36	M7_perm_slerp	9.60	0.534
pythia-160m	36	parents	0.00	0.776

SLERP is worse than a plain average here, not better. Walking the great circle between two parameter sets that are essentially orthogonal interpolates their directions, and between two independently initialised networks there is no meaningful direction to interpolate — so it inherits the naive merge's failure and roughly doubles it. Applied after unit alignment it recovers most of that — but still lands consistently worse than the aligned plain average, at every size. Two things follow. First, the field's default recipe does not rescue the composition case, so "practitioners do it differently" is not an escape from this result. Second, the ordering is the same as everywhere else in this report: alignment is what moves the number, and the choice of operator on top of it barely matters.

SET 4 · the accuracy arm (MultiBLiMP 1.0)

jumelet/multiblimp covers exactly the four partner languages plus English. Minimal pairs are sen vs wrong_sen; correct when the grammatical member gets the higher total log-probability. Chance = 0.500. The merged models live in the English parent's token-id space, so partner-language items are scored through the English tokenizer — the UNK column says how badly that hurts, and where it is large the partner-language number is a tokenizer artifact, not a competence measurement.

Parents (each on its own tokenizer except the last column):

pair	n items (partner)	UNK rate, English tok on partner items	English parent, MultiBLiMP-eng	partner parent, MultiBLiMP-partner	English parent, MultiBLiMP-partner
eng–nld_Latn	1200	0.2%	0.962	0.970	0.598
eng–spa_Latn	1200	5.1%	0.962	0.926	0.502
eng–ell_Grek	1096	45.1%	0.962	0.987	0.029
eng–pol_Latn	1200	11.2%	0.962	0.963	0.494

Merged models, MultiBLiMP-English accuracy (the clean cell — 0.04% UNK; English parent ceiling in the first column):

pair	English parent	M0_naive_avg	M1a_vocab_avg	M1b_vocab_perm_avg	M1c_vocab_orth_avg	M1e_vocab_orth_forced	M1g_emb_procrustes	M1h_emb_proc_units
eng–nld_Latn	0.962	0.673	0.601	0.596	0.596	0.662	0.668	0.635
eng–spa_Latn	0.962	0.677	0.727	0.726	0.726	0.682	0.661	0.631
eng–ell_Grek	0.962	0.688	0.599	0.600	0.600	0.687	0.656	0.657
eng–pol_Latn	0.962	0.682	0.656	0.656	0.656	0.653	0.653	0.655

Merged models, MultiBLiMP-partner accuracy (partner parent ceiling in the first column; rows with a high UNK rate are struck through in interpretation, not in the numbers):

pair	partner parent	UNK	M0_naive_avg	M1a_vocab_avg	M1b_vocab_perm_avg	M1c_vocab_orth_avg	M1e_vocab_orth_forced	M1g_emb_procrustes	M1h_emb_proc_units
eng–nld_Latn	0.970	0%	0.655	0.646	0.644	0.644	0.602	0.653	0.583
eng–spa_Latn	0.926	5%	0.500	0.532	0.535	0.535	0.477	0.525	0.537
eng–ell_Grek	0.987	45%	0.029	0.029	0.029	0.029	0.014	0.029	0.029
eng–pol_Latn	0.963	11%	0.454	0.462	0.462	0.462	0.501	0.491	0.490

What the accuracy arm adds, and it cuts the other way from SET 1.

• The English-side accuracy of the naive merge (mean 0.680, parent 0.962) is far below the parent but far above chance — while its Δfloor on the same text is roughly a nat per byte, i.e. by the likelihood metric the model is destroyed. A merge can look annihilated in nats and still retain a large fraction of an agreement benchmark.
• The unit-aligned rungs are a wash against the naive merge on accuracy. Averaged over the four pairs the naive merge scores 0.680 on MultiBLiMP-English against 0.645–0.671 for the aligned rungs, and 0.536 on the partner side (Greek excluded) against 0.527–0.556. Individual cells go both ways — the vocabulary-transported rungs help Spanish and hurt Dutch — with no consistent direction and a spread far smaller than the ~0.30 gap to the parents. Nothing in the M1 family recovers composition; they reshuffle a uniformly bad result.
• Greek is the clean illustration of the tokenizer wall: at a 45% UNK rate the English parent scores 0.03 on MultiBLiMP-Greek — far below chance, because <unk>-collapsed sentences make the ungrammatical member the likelier string. Nothing about Greek grammar is being measured there. Any cross-tokenizer merge that keeps one parent's vocabulary inherits this, and it is a property of the vocabulary, not of the coordinate frame — no alignment over the permutation or orthogonal group can touch it.
• Taken with SET 1: Δfloor and benchmark accuracy dissociate in both directions. In SET 1 a large likelihood rescue buys almost no accuracy. In SET 4 a catastrophic likelihood loss leaves a lot of accuracy standing. Whichever of the two you report, the other does not follow from it.

SET 4 · what would SUCCESS look like? The jointly-trained bilingual ceiling

A merge that fails is only interpretable against what a bilingual model of the same budget actually achieves. B-GPT (Arnett et al.) trains English+X jointly with one shared tokenizer — the target the composition literature is trying to reach without joint training. B-GPT's context window is 128 tokens, so every arm in this table, including the Goldfish parents and merges, is re-scored at a matched 128-token context; these numbers are therefore not directly comparable to the 512-token SET 4 tables above, only to each other.

nats/byte, English (lower is better)

pair	bgpt_joint_bilingual	goldfish_eng_parent	goldfish_partner_parent	merge_M0_naive	merge_M1a_vocab
eng–nld_Latn	0.871	0.848	1.473	1.697	1.835
eng–spa_Latn	0.872	0.848	1.609	1.685	1.834
eng–ell_Grek	0.875	0.848	1.521	1.748	1.838
eng–pol_Latn	0.881	0.848	1.610	1.647	1.767

nats/byte, partner (lower is better)

pair	bgpt_joint_bilingual	goldfish_eng_parent	goldfish_partner_parent	merge_M0_naive	merge_M1a_vocab
eng–nld_Latn	0.898	2.336	0.823	3.281	3.302
eng–spa_Latn	0.889	1.940	0.777	3.126	2.969
eng–ell_Grek	0.582	0.209	0.446	1.114	1.170
eng–pol_Latn	1.070	2.430	0.830	3.460	3.213

MultiBLiMP-English (higher is better, chance 0.500)

pair	bgpt_joint_bilingual	goldfish_eng_parent	goldfish_partner_parent	merge_M0_naive	merge_M1a_vocab
eng–nld_Latn	0.966	0.962	0.694	0.673	0.601
eng–spa_Latn	0.968	0.962	0.656	0.677	0.727
eng–ell_Grek	0.968	0.962	0.631	0.688	0.599
eng–pol_Latn	0.973	0.962	0.610	0.682	0.656

MultiBLiMP-partner (higher is better, chance 0.500)

pair	bgpt_joint_bilingual	goldfish_eng_parent	goldfish_partner_parent	merge_M0_naive	merge_M1a_vocab
eng–nld_Latn	0.952	0.598	0.970	0.655	0.646
eng–spa_Latn	0.879	0.502	0.926	0.500	0.532
eng–ell_Grek	0.927	0.029	0.987	0.029	0.029
eng–pol_Latn	0.892	0.494	0.963	0.454	0.462

This is the cleanest single statement the audit can make about SET 4. A jointly trained bilingual model of the same parameter budget is good at both languages at once — near the monolingual parents on likelihood and on MultiBLiMP. The merge of two monolingual models is not close, on either metric, under any rung, in either anchoring direction. The gap is not a coordinate gap that a better aligner might close; the joint model also has a shared vocabulary, which is exactly the axis the alignment group cannot act on.

SET 4c · merging two BILINGUAL models of the same language pair

SET 4 confounds two obstructions: the parents were trained independently, and they have almost disjoint token-id spaces. This cell separates them. B-GPT_en_X_simultaneous and B-GPT_X_en_simultaneous are trained on the same two languages with the same recipe, and their tokenizers share ~94% of their surface forms — against 13–28% for two monolingual Goldfish tokenizers. Vocabulary transport is therefore nearly lossless here, and what is left between the two parents is an independent training run. If merging works anywhere in the composition setting, this is where it should work. (Scored at B-GPT's 128-token context; MultiBLiMP chance = 0.500.)

pair	vocab overlap	parent A / B, nats/byte (eng, X)	parent A / B, MultiBLiMP (eng, X)
en–nld	94%	0.87/0.90 · 0.93/0.83	0.97/0.95 · 0.95/0.97
en–spa	94%	0.87/0.89 · 0.95/0.82	0.97/0.88 · 0.95/0.91
en–ell	91%	0.88/0.58 · 0.99/0.48	0.97/0.93 · 0.94/0.94
en–pol	92%	0.88/1.07 · 0.94/0.91	0.97/0.89 · 0.95/0.95

Δfloor, mean over the two languages (nats/UTF-8 byte, lower better):

pair	M0_naive_avg	M1a_vocab_avg	M1b_vocab_perm_avg	M1c_vocab_orth_avg	M1g_emb_procrustes
en–nld	0.907	0.852	0.862	0.862	0.837
en–spa	1.000	0.945	0.962	0.962	0.846
en–ell	1.012	0.838	0.837	0.837	0.800
en–pol	1.222	1.163	1.145	1.145	0.984
mean	1.035	0.950	0.952	0.952	0.866

MultiBLiMP, mean over the two languages (accuracy, higher better; parent ceiling in the last column):

pair	M0_naive_avg	M1a_vocab_avg	M1b_vocab_perm_avg	M1c_vocab_orth_avg	M1g_emb_procrustes	parent ceiling
en–nld	0.630	0.681	0.695	0.695	0.664	0.967
en–spa	0.623	0.682	0.680	0.680	0.702	0.938
en–ell	0.592	0.624	0.627	0.627	0.615	0.955
en–pol	0.626	0.621	0.620	0.620	0.632	0.961
mean	0.618	0.652	0.655	0.655	0.653	0.955

This is the one place in SET 4 where alignment does something measurable, and it is still not enough. With the vocabulary obstruction largely removed, transport plus unit alignment moves MultiBLiMP from 0.618 (naive) to 0.655 (best M1) and Δfloor from +1.035 to +0.866 nats/byte. Both move in the right direction, and both leave the merge far from parents that sit near 0.96 on MultiBLiMP and at Δfloor 0 by construction.

Read against the monolingual Goldfish cells, this is the cleanest decomposition the report offers:

• With 13–28% vocabulary overlap (monolingual Goldfish), alignment does nothing at all — the binding constraint is the vocabulary and no map over the permutation or orthogonal group touches it.
• With ~94% overlap (two bilinguals of the same pair), alignment finally has purchase and delivers a real but modest gain.
• Even then the merge does not approach either parent, because the parents are still two independent training runs — which is exactly what SET 1 isolates, and exactly what SET 1 shows alignment only partly removes.

SET 4 · reverse direction (the partner language is the anchor)

Identical rungs, but the merged model lives in the partner language's tokenizer and residual basis and English is transported into it. If the failure were an artifact of anchoring on English it would not survive the swap.

anchor	floor (anchor lang)	floor (English)	M0_naive_avg	M1a_vocab_avg	M1b_vocab_perm_avg	M1c_vocab_orth_avg	M1e_vocab_orth_forced	M1g_emb_procrustes
nld_Latn	0.792	0.811	1.342	1.335	1.337	1.337	1.384	1.425
spa_Latn	0.746	0.811	1.527	1.619	1.619	1.619	1.611	1.476
ell_Grek	0.428	0.811	1.494	1.568	1.569	1.569	1.555	1.322
pol_Latn	0.799	0.811	1.591	1.622	1.622	1.622	1.580	1.678

Δfloor, mean over the two languages, nats/UTF-8 byte.

The failure is symmetric, and that matters more than it looks. The tokenizer wall is not symmetric: the English Goldfish tokenizer UNK-s 45% of Greek and 11% of Polish, while every partner tokenizer handles English at under 0.1% UNK (results/set4_tokenizer_diag.json). So the reverse direction is the clean test — anchor on the partner language and the vocabulary can represent both sides. The merge still fails, by the same margin, and the M1 rungs still do nothing. Two conclusions follow that the English-anchored direction alone could not support:

1. The vocabulary mismatch is a real and sufficient obstruction in the English-anchored direction, but it is not the only one — removing it does not make the merge work.
2. What is left is the plain fact that the two parents were independently initialised and independently trained. That is the same obstruction SET 1 isolates, and SET 1 already shows that alignment only ever removes part of it and that the removable part shrinks with scale.

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

The confirmatory test

Outcome = realised rescue: the fraction of the naive merge's Δfloor that the best M1 rung removes. Label = above the within-substrate median. Held out by seed: fold k is every pair touching seed k, fitted on the pairs touching neither, so the predictor's direction never sees the held-out pairs. Null = a 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. That preserves the pair dependence structure a plain label shuffle destroys, and it is why the null means below sit at 0.50 rather than drifting.

The family below is the five predictors the audit brief itself names — weight cosine, coordinate share, QMD, CKA, task-vector cosine — on the one outcome it asks about. It was fixed from the brief, not selected after looking at the results, and BH is applied within this family only. The larger exploratory table follows it.

substrate	predictor	n	Spearman	AUROC (held out by seed)	null mean	perm p	BH q (within family)
pythia-14m	weight cosine	36	0.095	0.549	0.501	0.316	0.648
pythia-14m	coordinate share (block-normalised / permutation)	36	-0.009	0.478	0.503	0.596	0.745
pythia-14m	CKA (mean over layers / unaligned)	36	-0.013	0.605	0.499	0.151	0.473
pythia-14m	QMD (quotient_residual / permutation)	36	-0.207	0.657	0.500	0.055	0.275
pythia-14m	task-vector cosine	36	0.131	0.580	0.498	0.223	0.558
pythia-160m	weight cosine	36	0.451	0.704	0.501	0.037	0.234
pythia-160m	coordinate share (block-normalised / permutation)	36	-0.015	0.614	0.501	0.176	0.489
pythia-160m	CKA (mean over layers / unaligned)	36	0.008	0.256	0.498	0.987	0.987
pythia-160m	QMD (quotient_residual / permutation)	36	-0.060	0.525	0.500	0.415	0.648
pythia-160m	task-vector cosine	36	0.049	0.454	0.502	0.657	0.757
pythia-31m	weight cosine	36	0.274	0.704	0.504	0.029	0.234
pythia-31m	coordinate share (block-normalised / permutation)	36	0.427	0.710	0.505	0.025	0.234
pythia-31m	CKA (mean over layers / unaligned)	36	0.100	0.546	0.503	0.345	0.648
pythia-31m	QMD (quotient_residual / permutation)	36	-0.060	0.444	0.500	0.722	0.785
pythia-31m	task-vector cosine	36	-0.123	0.481	0.499	0.577	0.745
pythia-410m	weight cosine	15	0.043	0.464	0.504	0.583	0.745
pythia-410m	coordinate share (block-normalised / permutation)	15	0.164	0.446	0.499	0.666	0.757
pythia-410m	CKA (mean over layers / unaligned)	15	0.025	0.321	0.497	0.901	0.939
pythia-410m	QMD (quotient_residual / permutation)	15	-0.107	0.554	0.503	0.369	0.648
pythia-410m	task-vector cosine	15	0.014	0.571	0.501	0.350	0.648
pythia-70m	weight cosine	36	0.089	0.491	0.500	0.517	0.745
pythia-70m	coordinate share (block-normalised / permutation)	36	0.462	0.806	0.500	0.002	0.062
pythia-70m	CKA (mean over layers / unaligned)	36	0.495	0.654	0.501	0.113	0.403
pythia-70m	QMD (quotient_residual / permutation)	36	-0.494	0.676	0.501	0.089	0.373
pythia-70m	task-vector cosine	36	0.071	0.543	0.502	0.390	0.648

The exploratory table

Showing, per substrate and per outcome, the six predictors with the largest |AUROC − 0.5| plus the multivariate ridge. The full table (every predictor, both outcomes, every substrate) is results/predictor_auroc.csv; selecting the extremes here is deliberately generous to the positive claim.

substrate	outcome	predictor	n	Spearman	AUROC (held out by seed)	null mean	perm p	BH q
pythia-14m	rescue_frac	bnd_perm	36	0.012	0.296	0.497	0.981	1.000
pythia-14m	rescue_frac	qmd_orth	36	0.093	0.676	0.497	0.037	0.373
pythia-14m	rescue_frac	qmd_perm	36	0.077	0.664	0.498	0.051	0.373
pythia-14m	rescue_frac	qmd_act_perm	36	-0.207	0.657	0.500	0.055	0.373
pythia-14m	rescue_frac	qmd_act_procrustes	36	-0.207	0.657	0.500	0.055	0.373
pythia-14m	rescue_frac	cka_last	36	-0.478	0.651	0.499	0.067	0.391
pythia-14m	rescue_frac	MULTIVARIATE_ridge_all	36	0.254	0.620	0.501	0.114	0.391
pythia-31m	rescue_frac	bnd_perm	36	-0.490	0.750	0.506	0.011	0.373
pythia-31m	rescue_frac	coord_share_bnd_perm	36	0.427	0.710	0.505	0.025	0.373
pythia-31m	rescue_frac	weight_cosine	36	0.274	0.704	0.504	0.029	0.373
pythia-31m	rescue_frac	d_raw	36	-0.321	0.704	0.505	0.025	0.373
pythia-31m	rescue_frac	bnd_raw	36	-0.391	0.701	0.506	0.032	0.373
pythia-31m	rescue_frac	qmd_perm	36	-0.493	0.691	0.505	0.048	0.373
pythia-31m	rescue_frac	MULTIVARIATE_ridge_all	36	0.403	0.707	0.505	0.035	0.373
pythia-70m	rescue_frac	coord_share_bnd_perm	36	0.462	0.806	0.500	0.002	0.222
pythia-70m	rescue_frac	bnd_perm	36	-0.404	0.787	0.501	0.003	0.222
pythia-70m	rescue_frac	coord_share_orth	36	0.341	0.722	0.497	0.033	0.373
pythia-70m	rescue_frac	qmd_orth	36	-0.373	0.713	0.497	0.067	0.391
pythia-70m	rescue_frac	coord_share_perm	36	0.356	0.698	0.500	0.065	0.391
pythia-70m	rescue_frac	qmd_perm	36	-0.357	0.688	0.500	0.084	0.391
pythia-70m	rescue_frac	MULTIVARIATE_ridge_all	36	0.387	0.688	0.499	0.080	0.391
pythia-160m	rescue_frac	bnd_raw	36	0.083	0.250	0.496	0.984	1.000
pythia-160m	rescue_frac	bnd_perm	36	0.040	0.253	0.496	0.974	1.000
pythia-160m	rescue_frac	cka_mean	36	0.008	0.256	0.498	0.987	1.000
pythia-160m	rescue_frac	weight_cosine	36	0.451	0.704	0.501	0.037	0.373
pythia-160m	rescue_frac	qmd_orth	36	-0.439	0.704	0.498	0.052	0.373
pythia-160m	rescue_frac	bnd_orth	36	-0.047	0.306	0.497	0.925	0.976
pythia-160m	rescue_frac	MULTIVARIATE_ridge_all	36	0.331	0.642	0.499	0.130	0.398
pythia-410m	rescue_frac	weight_cosine_bn	15	-0.250	0.679	0.504	0.158	0.423
pythia-410m	rescue_frac	cka_mean	15	0.025	0.321	0.497	0.901	0.962
pythia-410m	rescue_frac	qmd_perm	15	0.125	0.661	0.499	0.167	0.424
pythia-410m	rescue_frac	qmd_orth	15	0.096	0.643	0.499	0.187	0.438
pythia-410m	rescue_frac	coord_share_bnd_orth	15	0.107	0.393	0.499	0.765	0.859
pythia-410m	rescue_frac	d_raw	15	0.054	0.607	0.499	0.280	0.499
pythia-410m	rescue_frac	MULTIVARIATE_ridge_all	15	-0.643	0.196	0.500	0.994	1.000
pythia-14m	dfloor_M1best	bnd_orth	36	-0.000	0.204	0.502	1.000	1.000
pythia-14m	dfloor_M1best	bnd_perm	36	-0.002	0.222	0.502	0.997	1.000
pythia-14m	dfloor_M1best	coord_share_orth	36	-0.457	0.738	0.495	0.015	0.373
pythia-14m	dfloor_M1best	coord_share_perm	36	-0.445	0.735	0.495	0.016	0.373
pythia-14m	dfloor_M1best	qmd_orth	36	0.438	0.725	0.496	0.021	0.373
pythia-14m	dfloor_M1best	coord_share_bnd_perm	36	-0.155	0.290	0.503	0.977	1.000
pythia-14m	dfloor_M1best	MULTIVARIATE_ridge_all	36	0.539	0.778	0.497	0.003	0.222
pythia-31m	dfloor_M1best	qmd_orth	36	0.289	0.670	0.502	0.101	0.391
pythia-31m	dfloor_M1best	coord_share_orth	36	-0.271	0.670	0.503	0.103	0.391
pythia-31m	dfloor_M1best	qmd_perm	36	0.243	0.633	0.503	0.166	0.424
pythia-31m	dfloor_M1best	coord_share_perm	36	-0.230	0.633	0.503	0.166	0.424
pythia-31m	dfloor_M1best	bnd_raw	36	0.163	0.633	0.503	0.132	0.398
pythia-31m	dfloor_M1best	bnd_orth	36	0.114	0.611	0.501	0.186	0.438
pythia-31m	dfloor_M1best	MULTIVARIATE_ridge_all	36	-0.111	0.500	0.501	0.516	0.668
pythia-70m	dfloor_M1best	coord_share_bnd_perm	36	0.529	0.713	0.501	0.037	0.373
pythia-70m	dfloor_M1best	bnd_perm	36	-0.485	0.704	0.502	0.033	0.373
pythia-70m	dfloor_M1best	cka_last	36	0.476	0.691	0.499	0.090	0.391
pythia-70m	dfloor_M1best	cka_mean	36	0.427	0.667	0.501	0.105	0.391
pythia-70m	dfloor_M1best	qmd_act_perm	36	-0.433	0.667	0.501	0.103	0.391
pythia-70m	dfloor_M1best	qmd_act_procrustes	36	-0.433	0.667	0.501	0.103	0.391
pythia-70m	dfloor_M1best	MULTIVARIATE_ridge_all	36	0.386	0.599	0.500	0.207	0.438
pythia-160m	dfloor_M1best	weight_cosine	36	-0.195	0.284	0.504	0.962	1.000
pythia-160m	dfloor_M1best	cka_last	36	0.476	0.701	0.497	0.040	0.373
pythia-160m	dfloor_M1best	cka_mean	36	-0.270	0.685	0.500	0.111	0.391
pythia-160m	dfloor_M1best	bnd_orth	36	-0.371	0.660	0.500	0.081	0.391
pythia-160m	dfloor_M1best	d_raw	36	0.273	0.349	0.503	0.910	0.965
pythia-160m	dfloor_M1best	bnd_raw	36	-0.278	0.648	0.501	0.119	0.391
pythia-160m	dfloor_M1best	MULTIVARIATE_ridge_all	36	0.584	0.759	0.497	0.018	0.373
pythia-410m	dfloor_M1best	cka_mean	15	-0.364	0.714	0.501	0.116	0.391
pythia-410m	dfloor_M1best	qmd_act_ot	15	0.432	0.714	0.502	0.148	0.407
pythia-410m	dfloor_M1best	qmd_act_perm	15	0.371	0.679	0.502	0.214	0.438
pythia-410m	dfloor_M1best	qmd_act_procrustes	15	0.371	0.679	0.502	0.214	0.438
pythia-410m	dfloor_M1best	qmd_orth	15	-0.257	0.625	0.503	0.244	0.474
pythia-410m	dfloor_M1best	cka_last	15	0.100	0.375	0.494	0.775	0.859
pythia-410m	dfloor_M1best	MULTIVARIATE_ridge_all	15	0.300	0.589	0.506	0.335	0.549

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	0.426	0.500	0.775	0.966
MULTIVARIATE_ridge_all	rescue_frac	pythia-160m	36	0.657	0.499	0.044	0.223
MULTIVARIATE_ridge_all	rescue_frac	pythia-31m	36	0.679	0.495	0.028	0.203
MULTIVARIATE_ridge_all	rescue_frac	pythia-410m	15	0.393	0.499	0.773	0.966
MULTIVARIATE_ridge_all	rescue_frac	pythia-70m	36	0.556	0.502	0.289	0.689
coord_share_bnd_perm	rescue_frac	pythia-14m	36	0.515	0.500	0.462	0.777
coord_share_bnd_perm	rescue_frac	pythia-160m	36	0.506	0.500	0.473	0.777
coord_share_bnd_perm	rescue_frac	pythia-31m	36	0.710	0.502	0.017	0.142
coord_share_bnd_perm	rescue_frac	pythia-410m	15	0.482	0.497	0.549	0.829
coord_share_bnd_perm	rescue_frac	pythia-70m	36	0.806	0.498	0.003	0.142
qmd_act_perm	rescue_frac	pythia-14m	36	0.657	0.496	0.044	0.223
qmd_act_perm	rescue_frac	pythia-160m	36	0.512	0.498	0.450	0.777
qmd_act_perm	rescue_frac	pythia-31m	36	0.525	0.505	0.440	0.777
qmd_act_perm	rescue_frac	pythia-410m	15	0.571	0.508	0.370	0.739
qmd_act_perm	rescue_frac	pythia-70m	36	0.676	0.500	0.045	0.223
cka_mean	rescue_frac	pythia-14m	36	0.599	0.497	0.147	0.516
cka_mean	rescue_frac	pythia-160m	36	0.478	0.497	0.568	0.829
cka_mean	rescue_frac	pythia-31m	36	0.540	0.501	0.364	0.739
cka_mean	rescue_frac	pythia-410m	15	0.571	0.496	0.337	0.739
cka_mean	rescue_frac	pythia-70m	36	0.346	0.498	0.952	0.971
weight_cosine	rescue_frac	pythia-14m	36	0.580	0.497	0.204	0.637
weight_cosine	rescue_frac	pythia-160m	36	0.704	0.495	0.012	0.142
weight_cosine	rescue_frac	pythia-31m	36	0.704	0.499	0.013	0.142
weight_cosine	rescue_frac	pythia-410m	15	0.625	0.507	0.241	0.669
weight_cosine	rescue_frac	pythia-70m	36	0.494	0.499	0.535	0.829

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	0.800
qmd_orth	0.400
coord_share_orth	0.800
bnd_raw	0.800
bnd_perm	0.800
bnd_orth	0.800
coord_share_bnd_perm	0.800
coord_share_bnd_orth	0.800
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	-0.800
weight_cosine_body	-0.800

What P0-2 comes to

The confirmatory family gives 0 significant cells out of 25 tested (BH q under 0.05 within the family).

The strongest single cell is the coordinate share at pythia-70m — held-out AUROC 0.81, raw permutation p = 0.002 — which is a real effect and worth naming rather than burying. It does not survive correction across the family, and the reason it does not is instructive: the same predictor on the same outcome, measured on four other complete grids of the same model family, lands at 0.45, 0.48, 0.61 and 0.71. The honest summary is:

• It does not replicate across substrates. Held-out AUROC for the coordinate share, on five complete grids of the same model family differing only in size: 14m 0.48 · 31m 0.71 · 70m 0.81 · 160m 0.61 · 410m 0.45. A quantity that lands anywhere between "slightly the wrong way" and 0.81 depending on which substrate you happen to test is not a validated instrument for "representational alignment predicts merging", however encouraging its best cell looks.
• The exploratory table looks better than the confirmatory one, and that is the point of having both. Across ~150 predictor × substrate × outcome cells there are plenty of AUROCs in the 0.70–0.81 range with raw permutation p below 0.05; none survives BH across that family. Quoting the best of them would be exactly the error the audit exists to catch.
• Across-substrate transfer fails outright under correction. Fitting on the other sizes and testing on a held-out one, the coordinate share reaches AUROC 0.81 on 70m and 0.71 on 31m with raw permutation p of 0.003 and 0.016 — and 0.51 on both 14m and 160m. Across the 20-cell transfer family not one cell survives BH (smallest q = 0.11). The multivariate ridge over all predictors does no better than its best single member.

One thing worth noticing before concluding, because it is partly a power story rather than a signal story: detectability tracks how much the outcome varies at all. The within-substrate standard deviation of the realised rescue is 0.067 at 14m, 0.143 at 31m, 0.127 at 70m and 0.095 at 160m (against a between-substrate spread of 0.143 in the means). 14m — where the rescue is both largest and most uniform across pairs — is the substrate where nothing predicts, and 70m, with roughly twice the spread, is where the one significant cell appears. So part of the null is that at some sizes every pair is rescued by nearly the same amount and there is very little left to rank. That is a caveat in the predictors' favour and it does not rescue the positive claim: a predictor that only resolves when the outcome happens to be dispersed is not the instrument the thesis needs.

Against them: the seed-cluster null is conservative by construction, but so is the design that needs it; these are 36 pairs built from 9 seeds, not 36 independent observations, and any analysis that treats them as independent will overstate its significance.

Verdict, stated as the audit asks. On real reseeded LMs, the pre-merge alignment predictors do not reliably predict how much of the merge obstruction alignment will actually remove. The one substrate where the coordinate share does predict it does not generalise to the others. This is a negative transfer result from the synthetic/S3 setting to real models, and it is reported as one.

Control · same-basin vs different-basin pairs

SET 1's main grid uses pythia-<size>-seed{n} (PolyPythia), which reseeds initialisation and data order together. pythia-160m-weight-seed{1,2,3} and pythia-160m-data-seed{1,2,3} are the older Pythia ablations that were intended to vary one of those at a time. They do not give the init-only control they look like they give, and the weight cosine column below is how we know: pairs from either ablation family have parameter vectors that are still strongly correlated, while main-grid pairs are essentially orthogonal. Whatever the ablation seeds vary, both families stay in the same basin.

That makes them useful as something else — a same-basin reference — so they are reported as one.

pairs	n	weight cosine	d_raw	CKA	coordinate share	naive Δfloor	Δfloor perm	rescue
pythia-160m-data-seed{1,2,3}	3	0.550	0.949	0.828	0.0139	3.13	3.00	3.9%
pythia-160m-weight-seed{1,2,3}	3	0.570	0.942	0.789	0.0123	3.10	2.79	10.0%
pythia-160m-seed{1..9} (main grid)	36	0.021	1.401	0.747	0.0867	8.99	6.77	23.5%

What this actually shows.

1. The main grid really is the different-basin case. Weight cosine ~0.02 between two PolyPythia seeds: after training, two independently initialised 160M models are as good as orthogonal in parameter space. Everything SET 1 reports is about that regime.
2. Same-basin models still cannot be naively averaged for free. The ablation pairs are strongly correlated in weight space (cosine ~0.55–0.57) and their naive merge is still ~3 nats/token above the better parent — roughly a third of the different-basin penalty, on a parent floor of 3.3. Merging is not a solved problem inside a basin either.
3. Alignment does almost nothing for them, and that is the right behaviour. Their coordinate share is ~0.013 against ~0.087 for the main grid, and the permutation rung removes only a few percent of their Δfloor. There is no coordinate mismatch left to remove, so the aligner correctly declines to find one. That is a useful negative control on the aligner itself: it is not manufacturing rescue out of noise.
4. The residual is therefore not coordinate. Whatever costs a same-basin pair 3 nats/token, and whatever is left after alignment on a different-basin pair, is something the permutation group does not describe.

Caveat. n = 3 pairs per ablation family, and these repos come from a different release than the PolyPythia -seed{n} set, so a training-configuration difference cannot be excluded as a partial explanation for their closeness. The claim being made here is the measured one — these particular pairs are same-basin and behave as described — not a claim about what "varying the init seed" does in general.

Coverage — what ran and what did not

cell	n	status	what was measured
SET 1 Δfloor · pythia-14m	36/36 seed pairs	complete	M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm
SET 1 Δfloor · pythia-31m	36/36 seed pairs	complete	M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm
SET 1 Δfloor · pythia-70m	36/36 seed pairs	complete	M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm
SET 1 Δfloor · pythia-160m	36/36 seed pairs	complete	M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm
SET 1 Δfloor · pythia-410m	15/15 seed pairs	complete	M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm
SET 1 control · pythia-160m-data	3/3 pairs	complete	init-seed-only vs data-order-only, same rungs
SET 1 control · pythia-160m-weight	3/3 pairs	complete	init-seed-only vs data-order-only, same rungs
SET 1 accuracy · BLiMP	pythia-14m: 36/36, pythia-31m: 36/36, pythia-70m: 36/36, pythia-160m: 36/36, pythia-410m: 15/36	RAN	67 paradigms from nyu-mll/blimp, minimal-pair sentence-logprob scoring, on the SAME merges
SET 1 · corpus robustness	pythia-14m: 36/36, pythia-160m: 36/36	RAN	same pairs and merges re-scored on FLORES-200 eng, NeelNanda/pile-10k and WikiText-103 validation
SET 1 · SLERP rung	pythia-14m: 36/36, pythia-31m: 36/36, pythia-70m: 36/36, pythia-160m: 36/36	RAN	M6 SLERP and M7 permutation-aligned SLERP on the same pairs; Δfloor and BLiMP
SET 1 · REPAIR rung	pythia-14m: 36/36, pythia-31m: 36/36, pythia-70m: 36/36, pythia-160m: 36/36	RAN	M4 = permutation-aligned average + pre-activation statistics repair; M5 = naive + repair; Δfloor and BLiMP on the same merges
SET 4 Δfloor · English-anchored	4/4 language pairs (nld_Latn, spa_Latn, ell_Grek, pol_Latn)	complete	M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned · M1d/e forced-residual · M1f units-only · M1g/h embedding-row Procrustes
SET 4 Δfloor · partner-anchored (reverse)	4/4 language pairs	complete	same rungs, roles swapped
SET 4 accuracy · MultiBLiMP 1.0	4/4 language pairs	RAN	jumelet/multiblimp, English + partner, on the SAME merges; UNK rate reported per cell
SET 4 · jointly-trained bilingual ceiling	4/4 language pairs	RAN	catherinearnett/B-GPT_en_X_simultaneous vs the Goldfish parents and merges, all scored at a matched 128-token context
SET 4c · bilingual×bilingual merge (B-GPT en_X × X_en)	4/4 language pairs	RAN	M0 naive · M1a vocab-transport · M1b/c +unit-aligned · M1g embedding-row Procrustes; Δfloor AND MultiBLiMP on the same merges. ~94% vocabulary overlap, so this cell isolates independent training from the vocabulary wall
Validation · is each alignment function-preserving?	2 substrates x 5 maps	RAN	parent re-evaluated after applying the map; permutation exact to float32 noise, orthogonal NOT (see Validation)
SET 4 · task-arithmetic / TIES	0	NOT APPLICABLE	Both operators need a shared ancestor. Two independently trained monolingual Goldfish models have none, and with one parent as a pseudo-base the operators reduce to returning the other parent. Excluded on definition, not on time.
SET 1 · pythia-410m full grid	15/36 possible pairs	partial	6 seeds only (15 possible pairs) and a reduced eval budget; the per-pair alignment cost is ~9 min at this width. Treat 410m as directional.
Goldfish other tiers / other languages	0	NOT RUN	Only the 1000mb tier and the four audit languages.
Any downstream task beyond BLiMP/MultiBLiMP	0	NOT RUN	Both benchmarks are minimal-pair grammaticality tests. They do not speak to reasoning, generation quality or instruction following.

Threats to validity, stated plainly

• Likelihood ≠ accuracy. Repeated because it is the single most load-bearing caveat here — and because this report is one of the few places where both were measured on the same merges and found to dissociate.
• BLiMP and MultiBLiMP are minimal-pair grammaticality benchmarks. They are a real accuracy measurement and they are not a general one. A merge that scores 0.68 on MultiBLiMP-English is not thereby a usable model; agreement minimal pairs are unusually forgiving of a degraded model, because the two candidates differ in one inflected token and the grammatical form is usually the more frequent one. Read "retains accuracy" as "retains this accuracy", not as "works".
• 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 1's -seed{n} repos reseed initialisation AND data order together. The 160m weight-seed/data-seed control separates them (see the Control section) but only at n=3 pairs each. The main grid's naive Δfloor should be read as an init-plus-data-order number.
• 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 much larger tokenizer effect — the English tokenizer's UNK rate on partner-language text — is reported per cell and is a substantive finding rather than a nuisance.
• The alignment search is over the permutation group (residual basis, MLP hidden axis, attention heads) and its orthogonal relaxation, plus embedding-row Procrustes for the cross-tokenizer case. 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. What is bounded is the claim that the aligners already in mergeschool.core do the job on these substrates.
• The largest SET 1 sizes carry the fewest pairs. 14m/31m/70m are complete 36-pair grids; 160m and 410m are partial. The scale trend is monotone across all five but its right-hand end is thin.
• SET 4's n = 4 language pairs, all with English as one parent and all Indo-European. Any predictor claim on that substrate is descriptive, and nothing here speaks to non-Indo-European or to non-English pivots.
• Everything here is training-free by construction. No claim is made about what a small amount of post-merge finetuning would recover; that is the obvious next experiment and it is out of scope for a training-free audit.

Files

results/set1_{14m,31m,70m,160m,410m}.jsonl  SET 1 per-pair records (predictors, rungs, barriers)
results/set1x_410m.jsonl                    second 410m worker (disjoint pairs; deduped on load)
results/set1_pairs.csv                      SET 1 per-pair flat table
results/abl_160m-{weight,data}.jsonl        same-basin control (Pythia data-seed / weight-seed)
results/alignment_health.json               is each map function-preserving? measured, both substrates
results/blimp_{size}.jsonl, blimp_pairs.csv SET 1 BLiMP accuracy, per pair and per rung
results/repair_{size}.jsonl                 REPAIR rung (Δfloor + BLiMP on the same merges)
results/slerp_{size}.jsonl                  SLERP and permutation-aligned SLERP rungs
results/corpus_{size}.jsonl                 same merges re-scored on Pile-10k and WikiText-103
results/set4_goldfish.jsonl, set4_pairs.csv SET 4 Δfloor, English-anchored
results/set4_reverse.jsonl                  SET 4 Δfloor, partner-language-anchored
results/set4_multiblimp.jsonl               SET 4 MultiBLiMP accuracy
results/set4_tokenizer_diag.json            UNK rates / bytes-per-token per (tokenizer, language)
results/bgpt_ceiling.jsonl                  jointly-trained bilingual ceiling, matched context
results/bgpt_merge.jsonl                    bilingual x bilingual merge (~94% vocabulary overlap)
results/rung_summary.csv                    rung x substrate x metric summary
results/predictor_confirmatory.csv          P0-2 confirmatory family (5 predictors, BH within family)
results/predictor_auroc.csv                 P0-2 exploratory: every predictor x substrate x outcome
results/predictor_transfer_across_size.csv  P0-2: leave-one-substrate-out transfer
results/set4_predictors.csv                 P0-2 on SET 4 (n=4, descriptive only)
figs/set1_dfloor_by_rung.png                Δfloor by rung, per size
figs/set1_scale_trend.png                   obstruction and rescue vs model size
figs/set1_rescue_vs_predictor.png           realised rescue vs coordinate share / CKA
figs/set1_roc.png                           held-out-by-seed ROC, confirmatory predictor
figs/set1_blimp_dissociation.png            likelihood rescue vs accuracy rescue
figs/set4_dfloor.png                        Δfloor by rung, Goldfish
figs/set4_joint_ceiling.png                 B-GPT joint bilingual vs parents vs merges
figs/set4_likelihood_vs_accuracy.png        SET 4 Δfloor against MultiBLiMP, per rung
code/*.py, code/*.sh                        every script and launcher that produced the above

Reproducing. common.py holds the corpora and evaluation; gpt2_align.py holds the GPT-2 (Conv1D) symmetry factors that mergeschool.core.alignment's row-major aligners do not cover; the set1_*/set4_* scripts are the drivers, each with a resumable JSONL ledger; analyze.py builds the tables and figures and make_report.py writes this document. Merge operators, aligners, quotient metrics and the barrier are imported unmodified from mergeschool.core.