compose-audit refresh 2026-08-26 22:07 UTC

README.md

@@ -11,7 +11,7 @@ tags:
 
 # Compose-audit: putting the alignment map and the merging payoff on the SAME real models
 
-_Generated 2026-08-26 21:04 UTC · training-free · code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from `mergeschool.core` (`/root/mergeability`, treated as read-only)._
+_Generated 2026-08-26 22:07 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
 
@@ -34,14 +34,16 @@ _Generated 2026-08-26 21:04 UTC · training-free · code: `/root/compose-audit`
 
 ## 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: +8.8 · 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 / 30 / 3 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: 11% — leaving 9.6 · 9.6 · 11.0 · 6.7 · 5.7 nats/token above the better parent, i.e. an absolute 14.0 · 13.5 · 14.6 · 10.0 · 8.7 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: 11% 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.)
+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 / 14 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: 7% — 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 · 9.0 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: 7% 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.** On pythia-14m (n=36), parents average 0.652 on BLiMP; the naive merge 0.518 and the aligned merge 0.544, against chance 0.500. A ~70% Δfloor rescue buys ~0.026 accuracy. Pairwise, the two rescues are uncorrelated.
-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.
+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: **1 of 15 cells significant** (pythia-70m, coordinate share (block-normalised / permutation), AUROC 0.81, q=0.037). It does not replicate across substrates — the same predictor sits below 0.5 at the largest size — and nothing survives BH across the wider exploratory family. Reported as the negative transfer result it is.
-8. **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.
+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: **1 of 20 cells significant** (pythia-70m, coordinate share (block-normalised / permutation), AUROC 0.81, q=0.050). The carrying predictor is the coordinate share, whose held-out AUROC across the substrates is 14m: 0.48 · 31m: 0.71 · 70m: 0.81 · 160m: 0.61 · 410m: 0.61 — 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)
@@ -88,30 +90,30 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.30**, permut
 Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.17**, permutation-aligned **10.98** nats/token.
 
 
-### pythia-160m — 30 seed pairs · mean parent floor **3.254** nats/token · uniform-over-vocabulary reference **10.826** 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 | 30 | 12.10 | 8.84 | 8.38 | 6.88 | 0/30 | 0.0% |
-| M1_perm_avg | 30 | 9.96 | 6.70 | 6.38 | 5.50 | 27/30 | 22.8% |
-| M1_orth_avg | 30 | 9.42 | 6.16 | 6.14 | 5.13 | 30/30 | 29.4% |
-| M2_task_arith | 30 | 30.31 | 27.05 | 26.97 | 17.88 | 0/30 | -205.1% |
-| M3_ties | 30 | 60.28 | 57.03 | 57.47 | 49.30 | 0/30 | -555.5% |
+| 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 **8.83**, permutation-aligned **6.70** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.99**, permutation-aligned **6.76** nats/token.
 
 
-### pythia-410m — 3 seed pairs · mean parent floor **2.971** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+### pythia-410m — 14 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 | 3 | 9.46 | 6.49 | 6.50 | 6.19 | 0/3 | 0.0% |
-| M1_perm_avg | 3 | 8.72 | 5.75 | 5.64 | 5.56 | 3/3 | 11.2% |
-| M1_orth_avg | 3 | 8.85 | 5.88 | 5.81 | 5.68 | 3/3 | 9.2% |
-| M2_task_arith | 3 | 13.29 | 10.32 | 10.37 | 7.52 | 0/3 | -60.7% |
-| M3_ties | 3 | 13.03 | 10.06 | 10.17 | 9.43 | 0/3 | -55.2% |
+| M0_naive_avg | 14 | 9.43 | 6.45 | 6.46 | 5.95 | 0/14 | 0.0% |
+| M1_perm_avg | 14 | 8.96 | 5.98 | 5.87 | 5.56 | 11/14 | 7.1% |
+| M1_orth_avg | 14 | 9.01 | 6.02 | 6.00 | 5.44 | 12/14 | 6.5% |
+| M2_task_arith | 14 | 14.19 | 11.20 | 11.88 | 5.28 | 1/14 | -73.8% |
+| M3_ties | 14 | 13.07 | 10.09 | 10.23 | 9.32 | 0/14 | -56.7% |
 
-Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permutation-aligned **5.90** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.47**, permutation-aligned **5.96** nats/token.
 
 
 **What this says.**
@@ -131,8 +133,10 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permuta
    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.
+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.)
@@ -162,6 +166,12 @@ gain, and neither commutes with a general rotation (an RMSNorm model would be mu
 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*
@@ -178,8 +188,8 @@ orthogonal row.
 | 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 | 30 | 3.25 | 8.84 | 22.8% | 29.4% | 31.2% | 0.739 | 0.746 | 0.0871 |
-| pythia-410m | 3 | 2.97 | 6.49 | 11.2% | 9.2% | 11.2% | 0.410 | 0.372 | 0.0333 |
+| pythia-160m | 36 | 3.25 | 8.99 | 23.5% | 30.3% | 32.0% | 0.747 | 0.761 | 0.0867 |
+| pythia-410m | 14 | 2.98 | 6.45 | 7.1% | 6.5% | 9.2% | 0.476 | 0.427 | 0.0371 |
 
 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
@@ -206,15 +216,15 @@ exactly the direction the field is scaling.
 
 **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 |
+| 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 |
 
-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.
+**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.
 
@@ -229,7 +239,13 @@ Uniform-over-vocabulary reference (a model that has learned nothing), mean over
 | 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** |
 
-Averaged over the four pairs the best M1 rung removes **1.4%** of the naive merge's Δfloor. 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.
+**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):
@@ -300,24 +316,31 @@ PolyPythia parents are English LMs, so BLiMP applies directly to SET 1's merges.
 | 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 | 30 | 0.690 | 0.697 | 0.523 | 0.532 | 0.534 | 24.3% |
+| 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 | 1 | 0.774 | 0.780 | 0.562 | 0.545 | 0.556 | 22.1% |
+| pythia-160m | 36 | 0.772 | 0.776 | 0.532 | 0.537 | 0.539 | 19.3% |
 
 **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
+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 that the merged model retains does not track it
+at all: it sits at roughly a fifth at 14M, 31M and 70M and drops at 160M. 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 | 30 | -0.141 | 12.58 | 0.0213 |
+| 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 |
 
 ## Did we try hard enough? · REPAIR on top of the alignment
 
@@ -330,11 +353,21 @@ The obvious objection to a negative merging result is that averaging is a weak m
 | 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-70m | 10 | M0_naive_avg | 18.33 | 17.75 | 0.523 | 10.3% |
-| pythia-70m | 10 | M1_perm_avg | 16.91 | 16.26 | 0.541 | 17.9% |
-| pythia-70m | 10 | M4_perm_repair | 16.88 | 17.01 | 0.535 | 15.6% |
-| pythia-70m | 10 | M5_naive_repair | 18.29 | 18.49 | 0.516 | 7.1% |
-| pythia-70m | 10 | **parents** | 0.00 | 0.00 | 0.727 | 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 | 33 | M0_naive_avg | 8.97 | 8.45 | 0.532 | 11.5% |
+| pythia-160m | 33 | M1_perm_avg | 6.78 | 6.47 | 0.539 | 14.0% |
+| pythia-160m | 33 | M4_perm_repair | 6.85 | 6.34 | 0.534 | 12.3% |
+| pythia-160m | 33 | M5_naive_repair | 8.65 | 8.51 | 0.525 | 9.2% |
+| pythia-160m | 33 | **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
@@ -352,6 +385,54 @@ alignment were all tried on the same pairs; the best of them recovers most of th
 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 | 28 | flores_eng | 3.25 | 8.84 | 6.72 | 22.6% |
+| pythia-160m | 28 | pile_10k | 3.15 | 9.22 | 7.45 | 17.7% |
+| pythia-160m | 28 | wikitext103_val | 3.25 | 9.41 | 8.05 | 13.3% |
+
+**It is not a corpus artifact.** The parent floors move with domain, as they should, but the naive Δfloor, the aligned Δfloor and the rescue fraction are stable across all three corpora — including the in-distribution Pile sample. The merge 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 | 1 | M0_naive_avg | 16.51 | 0.568 |
+| pythia-70m | 1 | M1_perm_avg | 16.04 | 0.538 |
+| pythia-70m | 1 | M6_slerp | 39.21 | 0.538 |
+| pythia-70m | 1 | M7_perm_slerp | 29.95 | 0.526 |
+| pythia-70m | 1 | **parents** | 0.00 | 0.731 |
+
+**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 adds to it. Applied *after* unit alignment it comes back to roughly
+where the aligned average already was. 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.
@@ -455,6 +536,60 @@ aligner might close; the joint model also has a *shared vocabulary*, which is ex
 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.
@@ -503,26 +638,31 @@ 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 | 0.517 |
-| pythia-14m | coordinate share (block-normalised / permutation) | 36 | -0.009 | 0.478 | 0.503 | 0.596 | 0.639 |
-| pythia-14m | CKA (mean over layers / unaligned) | 36 | -0.013 | 0.605 | 0.499 | 0.151 | 0.324 |
-| pythia-14m | QMD (quotient_residual / permutation) | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.206 |
-| pythia-14m | task-vector cosine | 36 | 0.131 | 0.580 | 0.498 | 0.223 | 0.419 |
-| pythia-160m | weight cosine | 27 | 0.516 | 0.665 | — | — | — |
-| pythia-160m | coordinate share (block-normalised / permutation) | 27 | -0.029 | 0.379 | — | — | — |
-| pythia-160m | CKA (mean over layers / unaligned) | 27 | -0.194 | 0.478 | — | — | — |
-| pythia-160m | QMD (quotient_residual / permutation) | 27 | 0.140 | 0.533 | — | — | — |
-| pythia-160m | task-vector cosine | 27 | -0.044 | 0.330 | — | — | — |
-| pythia-31m | weight cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.145 |
-| pythia-31m | coordinate share (block-normalised / permutation) | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.145 |
-| pythia-31m | CKA (mean over layers / unaligned) | 36 | 0.100 | 0.546 | 0.503 | 0.345 | 0.517 |
-| pythia-31m | QMD (quotient_residual / permutation) | 36 | -0.060 | 0.444 | 0.500 | 0.722 | 0.722 |
-| pythia-31m | task-vector cosine | 36 | -0.123 | 0.481 | 0.499 | 0.577 | 0.639 |
-| pythia-70m | weight cosine | 36 | 0.089 | 0.491 | 0.500 | 0.517 | 0.639 |
-| pythia-70m | coordinate share (block-normalised / permutation) | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.037 |
-| pythia-70m | CKA (mean over layers / unaligned) | 36 | 0.495 | 0.654 | 0.501 | 0.113 | 0.282 |
-| pythia-70m | QMD (quotient_residual / permutation) | 36 | -0.494 | 0.676 | 0.501 | 0.089 | 0.268 |
-| pythia-70m | task-vector cosine | 36 | 0.071 | 0.543 | 0.502 | 0.390 | 0.532 |
+| pythia-14m | weight cosine | 36 | 0.095 | 0.549 | 0.501 | 0.316 | 0.575 |
+| pythia-14m | coordinate share (block-normalised / permutation) | 36 | -0.009 | 0.478 | 0.503 | 0.596 | 0.701 |
+| pythia-14m | CKA (mean over layers / unaligned) | 36 | -0.013 | 0.605 | 0.499 | 0.151 | 0.379 |
+| pythia-14m | QMD (quotient_residual / permutation) | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.220 |
+| pythia-14m | task-vector cosine | 36 | 0.131 | 0.580 | 0.498 | 0.223 | 0.447 |
+| pythia-160m | weight cosine | 36 | 0.451 | 0.704 | 0.501 | 0.037 | 0.187 |
+| pythia-160m | coordinate share (block-normalised / permutation) | 36 | -0.015 | 0.614 | 0.501 | 0.176 | 0.391 |
+| 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 | 0.593 |
+| pythia-160m | task-vector cosine | 36 | 0.049 | 0.454 | 0.502 | 0.657 | 0.730 |
+| pythia-31m | weight cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.187 |
+| pythia-31m | coordinate share (block-normalised / permutation) | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.187 |
+| pythia-31m | CKA (mean over layers / unaligned) | 36 | 0.100 | 0.546 | 0.503 | 0.345 | 0.575 |
+| pythia-31m | QMD (quotient_residual / permutation) | 36 | -0.060 | 0.444 | 0.500 | 0.722 | 0.760 |
+| pythia-31m | task-vector cosine | 36 | -0.123 | 0.481 | 0.499 | 0.577 | 0.701 |
+| pythia-410m | weight cosine | 14 | -0.125 | 0.510 | — | — | — |
+| pythia-410m | coordinate share (block-normalised / permutation) | 14 | 0.244 | 0.612 | — | — | — |
+| pythia-410m | CKA (mean over layers / unaligned) | 14 | 0.235 | 0.612 | — | — | — |
+| pythia-410m | QMD (quotient_residual / permutation) | 14 | -0.134 | 0.551 | — | — | — |
+| pythia-410m | task-vector cosine | 14 | -0.103 | 0.531 | — | — | — |
+| pythia-70m | weight cosine | 36 | 0.089 | 0.491 | 0.500 | 0.517 | 0.689 |
+| pythia-70m | coordinate share (block-normalised / permutation) | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.050 |
+| pythia-70m | CKA (mean over layers / unaligned) | 36 | 0.495 | 0.654 | 0.501 | 0.113 | 0.323 |
+| pythia-70m | QMD (quotient_residual / permutation) | 36 | -0.494 | 0.676 | 0.501 | 0.089 | 0.298 |
+| pythia-70m | task-vector cosine | 36 | 0.071 | 0.543 | 0.502 | 0.390 | 0.593 |
 
 ### The exploratory table
 
@@ -530,62 +670,76 @@ Showing, per substrate and per outcome, the **six predictors with the largest |A
 
 | 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 | 0.998 |
-| pythia-14m | rescue_frac | qmd_orth | 36 | 0.093 | 0.676 | 0.497 | 0.037 | 0.251 |
-| pythia-14m | rescue_frac | qmd_perm | 36 | 0.077 | 0.664 | 0.498 | 0.051 | 0.261 |
-| pythia-14m | rescue_frac | qmd_act_perm | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.261 |
-| pythia-14m | rescue_frac | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.261 |
-| pythia-14m | rescue_frac | cka_last | 36 | -0.478 | 0.651 | 0.499 | 0.067 | 0.268 |
-| pythia-14m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | 0.501 | 0.114 | 0.278 |
-| pythia-31m | rescue_frac | bnd_perm | 36 | -0.490 | 0.750 | 0.506 | 0.011 | 0.251 |
-| pythia-31m | rescue_frac | coord_share_bnd_perm | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.251 |
-| pythia-31m | rescue_frac | weight_cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.251 |
-| pythia-31m | rescue_frac | d_raw | 36 | -0.321 | 0.704 | 0.505 | 0.025 | 0.251 |
-| pythia-31m | rescue_frac | bnd_raw | 36 | -0.391 | 0.701 | 0.506 | 0.032 | 0.251 |
-| pythia-31m | rescue_frac | qmd_perm | 36 | -0.493 | 0.691 | 0.505 | 0.048 | 0.261 |
-| pythia-31m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.403 | 0.707 | 0.505 | 0.035 | 0.251 |
-| pythia-70m | rescue_frac | coord_share_bnd_perm | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.133 |
-| pythia-70m | rescue_frac | bnd_perm | 36 | -0.404 | 0.787 | 0.501 | 0.003 | 0.133 |
-| pythia-70m | rescue_frac | coord_share_orth | 36 | 0.341 | 0.722 | 0.497 | 0.033 | 0.251 |
-| pythia-70m | rescue_frac | qmd_orth | 36 | -0.373 | 0.713 | 0.497 | 0.067 | 0.268 |
-| pythia-70m | rescue_frac | coord_share_perm | 36 | 0.356 | 0.698 | 0.500 | 0.065 | 0.268 |
-| pythia-70m | rescue_frac | qmd_perm | 36 | -0.357 | 0.688 | 0.500 | 0.084 | 0.268 |
-| pythia-70m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.387 | 0.688 | 0.499 | 0.080 | 0.268 |
-| pythia-160m | rescue_frac | qmd_orth | 27 | -0.629 | 0.802 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_orth | 27 | 0.443 | 0.786 | — | — | — |
-| pythia-160m | rescue_frac | qmd_perm | 27 | -0.482 | 0.731 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_perm | 27 | 0.294 | 0.714 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_bnd_orth | 27 | 0.152 | 0.676 | — | — | — |
-| pythia-160m | rescue_frac | task_vector_cosine | 27 | -0.044 | 0.330 | — | — | — |
-| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 27 | 0.426 | 0.643 | — | — | — |
+| 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 | 0.298 |
+| pythia-14m | rescue_frac | qmd_perm | 36 | 0.077 | 0.664 | 0.498 | 0.051 | 0.298 |
+| pythia-14m | rescue_frac | qmd_act_perm | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.298 |
+| pythia-14m | rescue_frac | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.298 |
+| pythia-14m | rescue_frac | cka_last | 36 | -0.478 | 0.651 | 0.499 | 0.067 | 0.316 |
+| pythia-14m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | 0.501 | 0.114 | 0.318 |
+| pythia-31m | rescue_frac | bnd_perm | 36 | -0.490 | 0.750 | 0.506 | 0.011 | 0.298 |
+| pythia-31m | rescue_frac | coord_share_bnd_perm | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.298 |
+| pythia-31m | rescue_frac | weight_cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.298 |
+| pythia-31m | rescue_frac | d_raw | 36 | -0.321 | 0.704 | 0.505 | 0.025 | 0.298 |
+| pythia-31m | rescue_frac | bnd_raw | 36 | -0.391 | 0.701 | 0.506 | 0.032 | 0.298 |
+| pythia-31m | rescue_frac | qmd_perm | 36 | -0.493 | 0.691 | 0.505 | 0.048 | 0.298 |
+| pythia-31m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.403 | 0.707 | 0.505 | 0.035 | 0.298 |
+| pythia-70m | rescue_frac | coord_share_bnd_perm | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.177 |
+| pythia-70m | rescue_frac | bnd_perm | 36 | -0.404 | 0.787 | 0.501 | 0.003 | 0.177 |
+| pythia-70m | rescue_frac | coord_share_orth | 36 | 0.341 | 0.722 | 0.497 | 0.033 | 0.298 |
+| pythia-70m | rescue_frac | qmd_orth | 36 | -0.373 | 0.713 | 0.497 | 0.067 | 0.316 |
+| pythia-70m | rescue_frac | coord_share_perm | 36 | 0.356 | 0.698 | 0.500 | 0.065 | 0.316 |
+| pythia-70m | rescue_frac | qmd_perm | 36 | -0.357 | 0.688 | 0.500 | 0.084 | 0.316 |
+| pythia-70m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.387 | 0.688 | 0.499 | 0.080 | 0.316 |
+| 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 | 0.298 |
+| pythia-160m | rescue_frac | qmd_orth | 36 | -0.439 | 0.704 | 0.498 | 0.052 | 0.298 |
+| pythia-160m | rescue_frac | bnd_orth | 36 | -0.047 | 0.306 | 0.497 | 0.925 | 0.983 |
+| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.331 | 0.642 | 0.499 | 0.130 | 0.323 |
+| pythia-410m | rescue_frac | d_raw | 14 | 0.059 | 0.286 | — | — | — |
+| pythia-410m | rescue_frac | weight_cosine_bn | 14 | -0.420 | 0.633 | — | — | — |
+| pythia-410m | rescue_frac | bnd_perm | 14 | -0.156 | 0.633 | — | — | — |
+| pythia-410m | rescue_frac | cka_last | 14 | 0.077 | 0.367 | — | — | — |
+| pythia-410m | rescue_frac | bnd_raw | 14 | -0.152 | 0.612 | — | — | — |
+| pythia-410m | rescue_frac | bnd_orth | 14 | -0.152 | 0.612 | — | — | — |
+| pythia-410m | rescue_frac | MULTIVARIATE_ridge_all | 14 | -0.525 | 0.245 | — | — | — |
 | 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 | 0.251 |
-| pythia-14m | dfloor_M1best | coord_share_perm | 36 | -0.445 | 0.735 | 0.495 | 0.016 | 0.251 |
-| pythia-14m | dfloor_M1best | qmd_orth | 36 | 0.438 | 0.725 | 0.496 | 0.021 | 0.251 |
-| pythia-14m | dfloor_M1best | coord_share_bnd_perm | 36 | -0.155 | 0.290 | 0.503 | 0.977 | 0.998 |
-| pythia-14m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.539 | 0.778 | 0.497 | 0.003 | 0.133 |
-| pythia-31m | dfloor_M1best | qmd_orth | 36 | 0.289 | 0.670 | 0.502 | 0.101 | 0.268 |
-| pythia-31m | dfloor_M1best | coord_share_orth | 36 | -0.271 | 0.670 | 0.503 | 0.103 | 0.268 |
-| pythia-31m | dfloor_M1best | qmd_perm | 36 | 0.243 | 0.633 | 0.503 | 0.166 | 0.322 |
-| pythia-31m | dfloor_M1best | coord_share_perm | 36 | -0.230 | 0.633 | 0.503 | 0.166 | 0.322 |
-| pythia-31m | dfloor_M1best | bnd_raw | 36 | 0.163 | 0.633 | 0.503 | 0.132 | 0.299 |
-| pythia-31m | dfloor_M1best | bnd_orth | 36 | 0.114 | 0.611 | 0.501 | 0.186 | 0.343 |
-| pythia-31m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | -0.111 | 0.500 | 0.501 | 0.516 | 0.647 |
-| pythia-70m | dfloor_M1best | coord_share_bnd_perm | 36 | 0.529 | 0.713 | 0.501 | 0.037 | 0.251 |
-| pythia-70m | dfloor_M1best | bnd_perm | 36 | -0.485 | 0.704 | 0.502 | 0.033 | 0.251 |
-| pythia-70m | dfloor_M1best | cka_last | 36 | 0.476 | 0.691 | 0.499 | 0.090 | 0.268 |
-| pythia-70m | dfloor_M1best | cka_mean | 36 | 0.427 | 0.667 | 0.501 | 0.105 | 0.268 |
-| pythia-70m | dfloor_M1best | qmd_act_perm | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.268 |
-| pythia-70m | dfloor_M1best | qmd_act_procrustes | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.268 |
-| pythia-70m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.386 | 0.599 | 0.500 | 0.207 | 0.347 |
-| pythia-160m | dfloor_M1best | cka_mean | 27 | -0.398 | 0.742 | — | — | — |
-| pythia-160m | dfloor_M1best | bnd_perm | 27 | -0.426 | 0.736 | — | — | — |
-| pythia-160m | dfloor_M1best | bnd_orth | 27 | -0.421 | 0.714 | — | — | — |
-| pythia-160m | dfloor_M1best | coord_share_bnd_perm | 27 | 0.322 | 0.703 | — | — | — |
-| pythia-160m | dfloor_M1best | task_vector_cosine | 27 | 0.272 | 0.692 | — | — | — |
-| pythia-160m | dfloor_M1best | d_raw | 27 | 0.122 | 0.313 | — | — | — |
-| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 27 | 0.454 | 0.676 | — | — | — |
+| pythia-14m | dfloor_M1best | coord_share_orth | 36 | -0.457 | 0.738 | 0.495 | 0.015 | 0.298 |
+| pythia-14m | dfloor_M1best | coord_share_perm | 36 | -0.445 | 0.735 | 0.495 | 0.016 | 0.298 |
+| pythia-14m | dfloor_M1best | qmd_orth | 36 | 0.438 | 0.725 | 0.496 | 0.021 | 0.298 |
+| 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 | 0.177 |
+| pythia-31m | dfloor_M1best | qmd_orth | 36 | 0.289 | 0.670 | 0.502 | 0.101 | 0.316 |
+| pythia-31m | dfloor_M1best | coord_share_orth | 36 | -0.271 | 0.670 | 0.503 | 0.103 | 0.316 |
+| pythia-31m | dfloor_M1best | qmd_perm | 36 | 0.243 | 0.633 | 0.503 | 0.166 | 0.356 |
+| pythia-31m | dfloor_M1best | coord_share_perm | 36 | -0.230 | 0.633 | 0.503 | 0.166 | 0.356 |
+| pythia-31m | dfloor_M1best | bnd_raw | 36 | 0.163 | 0.633 | 0.503 | 0.132 | 0.323 |
+| pythia-31m | dfloor_M1best | bnd_orth | 36 | 0.114 | 0.611 | 0.501 | 0.186 | 0.373 |
+| pythia-31m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | -0.111 | 0.500 | 0.501 | 0.516 | 0.671 |
+| pythia-70m | dfloor_M1best | coord_share_bnd_perm | 36 | 0.529 | 0.713 | 0.501 | 0.037 | 0.298 |
+| pythia-70m | dfloor_M1best | bnd_perm | 36 | -0.485 | 0.704 | 0.502 | 0.033 | 0.298 |
+| pythia-70m | dfloor_M1best | cka_last | 36 | 0.476 | 0.691 | 0.499 | 0.090 | 0.316 |
+| pythia-70m | dfloor_M1best | cka_mean | 36 | 0.427 | 0.667 | 0.501 | 0.105 | 0.316 |
+| pythia-70m | dfloor_M1best | qmd_act_perm | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.316 |
+| pythia-70m | dfloor_M1best | qmd_act_procrustes | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.316 |
+| pythia-70m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.386 | 0.599 | 0.500 | 0.207 | 0.376 |
+| 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 | 0.298 |
+| pythia-160m | dfloor_M1best | cka_mean | 36 | -0.270 | 0.685 | 0.500 | 0.111 | 0.318 |
+| pythia-160m | dfloor_M1best | bnd_orth | 36 | -0.371 | 0.660 | 0.500 | 0.081 | 0.316 |
+| pythia-160m | dfloor_M1best | d_raw | 36 | 0.273 | 0.349 | 0.503 | 0.910 | 0.974 |
+| pythia-160m | dfloor_M1best | bnd_raw | 36 | -0.278 | 0.648 | 0.501 | 0.119 | 0.318 |
+| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.584 | 0.759 | 0.497 | 0.018 | 0.298 |
+| pythia-410m | dfloor_M1best | qmd_act_ot | 14 | 0.420 | 0.837 | — | — | — |
+| pythia-410m | dfloor_M1best | cka_mean | 14 | -0.323 | 0.816 | — | — | — |
+| pythia-410m | dfloor_M1best | qmd_act_perm | 14 | 0.380 | 0.796 | — | — | — |
+| pythia-410m | dfloor_M1best | qmd_act_procrustes | 14 | 0.380 | 0.796 | — | — | — |
+| pythia-410m | dfloor_M1best | task_vector_cosine | 14 | -0.125 | 0.245 | — | — | — |
+| pythia-410m | dfloor_M1best | d_raw | 14 | -0.270 | 0.306 | — | — | — |
+| pythia-410m | dfloor_M1best | MULTIVARIATE_ridge_all | 14 | 0.429 | 0.755 | — | — | — |
 
 ### Does a predictor fitted on one substrate transfer to another?
 
@@ -593,26 +747,31 @@ Leave-one-**size**-out. Predictors are standardised *within* size first, so a pr
 
 | predictor | outcome | held-out substrate | n | AUROC | null mean | perm p | BH q |
 |---|---|---|---|---|---|---|---|
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-14m | 36 | 0.355 | 0.500 | 0.928 | 0.958 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 27 | 0.670 | 0.499 | 0.070 | 0.246 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.691 | 0.496 | 0.025 | 0.200 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 36 | 0.531 | 0.503 | 0.400 | 0.705 |
-| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.505 | 0.469 | 0.750 |
-| coord_share_bnd_perm | rescue_frac | pythia-160m | 27 | 0.555 | 0.499 | 0.336 | 0.693 |
-| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.506 | 0.014 | 0.186 |
-| coord_share_bnd_perm | rescue_frac | pythia-70m | 36 | 0.806 | 0.499 | 0.002 | 0.080 |
-| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.496 | 0.046 | 0.213 |
-| qmd_act_perm | rescue_frac | pythia-160m | 27 | 0.467 | 0.502 | 0.626 | 0.889 |
-| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.499 | 0.406 | 0.705 |
-| qmd_act_perm | rescue_frac | pythia-70m | 36 | 0.676 | 0.499 | 0.031 | 0.206 |
-| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.500 | 0.149 | 0.397 |
-| cka_mean | rescue_frac | pythia-160m | 27 | 0.451 | 0.497 | 0.668 | 0.891 |
-| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.347 | 0.693 |
-| cka_mean | rescue_frac | pythia-70m | 36 | 0.346 | 0.498 | 0.934 | 0.958 |
-| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.506 | 0.235 | 0.552 |
-| weight_cosine | rescue_frac | pythia-160m | 27 | 0.665 | 0.506 | 0.088 | 0.251 |
-| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.499 | 0.020 | 0.200 |
-| weight_cosine | rescue_frac | pythia-70m | 36 | 0.494 | 0.499 | 0.526 | 0.780 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-14m | 36 | 0.414 | 0.500 | 0.814 | 0.966 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 36 | 0.654 | 0.499 | 0.048 | 0.220 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.685 | 0.495 | 0.024 | 0.175 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-410m | 14 | 0.531 | 0.498 | 0.446 | 0.737 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 36 | 0.556 | 0.502 | 0.292 | 0.664 |
+| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.500 | 0.459 | 0.737 |
+| coord_share_bnd_perm | rescue_frac | pythia-160m | 36 | 0.506 | 0.500 | 0.473 | 0.737 |
+| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.502 | 0.016 | 0.133 |
+| coord_share_bnd_perm | rescue_frac | pythia-410m | 14 | 0.612 | 0.492 | 0.252 | 0.664 |
+| coord_share_bnd_perm | rescue_frac | pythia-70m | 36 | 0.806 | 0.497 | 0.002 | 0.100 |
+| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.497 | 0.047 | 0.220 |
+| qmd_act_perm | rescue_frac | pythia-160m | 36 | 0.512 | 0.497 | 0.444 | 0.737 |
+| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.506 | 0.446 | 0.737 |
+| qmd_act_perm | rescue_frac | pythia-410m | 14 | 0.571 | 0.501 | 0.347 | 0.713 |
+| qmd_act_perm | rescue_frac | pythia-70m | 36 | 0.676 | 0.501 | 0.045 | 0.220 |
+| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.497 | 0.150 | 0.526 |
+| cka_mean | rescue_frac | pythia-160m | 36 | 0.478 | 0.498 | 0.570 | 0.792 |
+| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.357 | 0.713 |
+| cka_mean | rescue_frac | pythia-410m | 14 | 0.612 | 0.501 | 0.287 | 0.664 |
+| cka_mean | rescue_frac | pythia-70m | 36 | 0.346 | 0.498 | 0.950 | 0.980 |
+| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.498 | 0.217 | 0.664 |
+| weight_cosine | rescue_frac | pythia-160m | 36 | 0.704 | 0.496 | 0.013 | 0.130 |
+| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.497 | 0.011 | 0.130 |
+| weight_cosine | rescue_frac | pythia-410m | 14 | 0.510 | 0.493 | 0.484 | 0.737 |
+| weight_cosine | rescue_frac | pythia-70m | 36 | 0.494 | 0.501 | 0.547 | 0.782 |
 
 **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.
 
@@ -640,24 +799,28 @@ Leave-one-**size**-out. Predictors are standardised *within* size first, so a pr
 ### What P0-2 comes to
 
 **The confirmatory family gives 1 significant cell out of
-15 tested** (BH q < 0.05 within the family):
+20 tested** (BH q < 0.05 within the family):
 
-- pythia-70m · coordinate share (block-normalised / permutation) · AUROC 0.806 · q = 0.037
+- pythia-70m · coordinate share (block-normalised / permutation) · AUROC 0.806 · q = 0.050
 
 That is a real effect and it should not be rounded down to zero. It should also not be rounded up.
 The predictor that carries it is the **coordinate share** — exactly the quantity the manuscript's
 thesis is about — and the honest summary is:
 
-- **It does not replicate across substrates.** The same predictor's held-out AUROC across the sizes
-  we ran is not stable, and at the largest size it sits *below* 0.5, i.e. pointing the wrong way. A
-  quantity that predicts the rescue on one substrate and anti-predicts it on another is not a
-  validated instrument for "representational alignment predicts merging".
+- **It does not replicate across substrates.** The same predictor's held-out AUROC ranges from ~0.48
+  (chance, and slightly the wrong way) to 0.81 across four complete 36-pair grids of the *same*
+  model family differing only in size. A quantity that lands anywhere in that range 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 is likewise partial.** Fitting on the other sizes and testing on a
-  held-out one, the coordinate share transfers to some substrates and not to others (table above).
+- **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
@@ -680,23 +843,47 @@ substrate where the coordinate share does predict it does not generalise to the
 negative transfer result from the synthetic/S3 setting to real models, and it is reported as one.
 
 
-## Control · is the obstruction the INIT seed or the DATA order?
+## Control · same-basin vs different-basin pairs
 
-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.
+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.
 
-| 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) | 30 | 3.25 | 8.84 | 6.70 | 6.16 | 31.2% | 0.0871 |
+That makes them useful as something else — a **same-basin reference** — so they are reported as one.
 
-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.
+| 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
@@ -706,18 +893,22 @@ init-plus-data-order number, not an init-only one.
 | 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 | 30/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
-| SET 1 Δfloor · pythia-410m | 3/15 seed pairs | partial | 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 | 14/15 seed pairs | partial | 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: 30/36, pythia-70m: 36/36, pythia-160m: 1/36 | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges |
-| SET 1 · REPAIR rung | pythia-14m: 36/36, pythia-70m: 10/36 | RAN | M4 = permutation-aligned average + pre-activation statistics repair; M5 = naive + repair; Δfloor and BLiMP on the same merges |
+| SET 1 accuracy · BLiMP | pythia-14m: 36/36, pythia-31m: 36/36, pythia-70m: 36/36, pythia-160m: 36/36 | 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: 28/36 | 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: 1/36 | 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: 33/36 | 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 | 3/36 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. |
+| SET 1 · pythia-410m full grid | 14/36 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. |
 
@@ -761,26 +952,35 @@ init-plus-data-order number, not an init-only one.
 ## Files
 
 ```
-results/set1_{14m,31m,70m,160m,410m}.jsonl  SET 1 per-pair raw records (predictors, rungs, barriers)
+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        init-seed-only vs data-order-only control
+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_auroc.csv                 P0-2: held-out-by-seed AUROC, seed-cluster null, BH q
+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
+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
-code/*.py                                   every script that produced the above
+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

RESULTS_COMPOSE_AUDIT.md

@@ -1,6 +1,6 @@
 # Compose-audit: putting the alignment map and the merging payoff on the SAME real models
 
-_Generated 2026-08-26 21:04 UTC · training-free · code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from `mergeschool.core` (`/root/mergeability`, treated as read-only)._
+_Generated 2026-08-26 22:07 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
 
@@ -23,14 +23,16 @@ _Generated 2026-08-26 21:04 UTC · training-free · code: `/root/compose-audit`
 
 ## 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: +8.8 · 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 / 30 / 3 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: 11% — leaving 9.6 · 9.6 · 11.0 · 6.7 · 5.7 nats/token above the better parent, i.e. an absolute 14.0 · 13.5 · 14.6 · 10.0 · 8.7 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: 11% 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.)
+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 / 14 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: 7% — 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 · 9.0 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: 7% 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.** On pythia-14m (n=36), parents average 0.652 on BLiMP; the naive merge 0.518 and the aligned merge 0.544, against chance 0.500. A ~70% Δfloor rescue buys ~0.026 accuracy. Pairwise, the two rescues are uncorrelated.
-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.
+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: **1 of 15 cells significant** (pythia-70m, coordinate share (block-normalised / permutation), AUROC 0.81, q=0.037). It does not replicate across substrates — the same predictor sits below 0.5 at the largest size — and nothing survives BH across the wider exploratory family. Reported as the negative transfer result it is.
-8. **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.
+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: **1 of 20 cells significant** (pythia-70m, coordinate share (block-normalised / permutation), AUROC 0.81, q=0.050). The carrying predictor is the coordinate share, whose held-out AUROC across the substrates is 14m: 0.48 · 31m: 0.71 · 70m: 0.81 · 160m: 0.61 · 410m: 0.61 — 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)
@@ -77,30 +79,30 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.30**, permut
 Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **20.17**, permutation-aligned **10.98** nats/token.
 
 
-### pythia-160m — 30 seed pairs · mean parent floor **3.254** nats/token · uniform-over-vocabulary reference **10.826** 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 | 30 | 12.10 | 8.84 | 8.38 | 6.88 | 0/30 | 0.0% |
-| M1_perm_avg | 30 | 9.96 | 6.70 | 6.38 | 5.50 | 27/30 | 22.8% |
-| M1_orth_avg | 30 | 9.42 | 6.16 | 6.14 | 5.13 | 30/30 | 29.4% |
-| M2_task_arith | 30 | 30.31 | 27.05 | 26.97 | 17.88 | 0/30 | -205.1% |
-| M3_ties | 30 | 60.28 | 57.03 | 57.47 | 49.30 | 0/30 | -555.5% |
+| 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 **8.83**, permutation-aligned **6.70** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.99**, permutation-aligned **6.76** nats/token.
 
 
-### pythia-410m — 3 seed pairs · mean parent floor **2.971** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+### pythia-410m — 14 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 | 3 | 9.46 | 6.49 | 6.50 | 6.19 | 0/3 | 0.0% |
-| M1_perm_avg | 3 | 8.72 | 5.75 | 5.64 | 5.56 | 3/3 | 11.2% |
-| M1_orth_avg | 3 | 8.85 | 5.88 | 5.81 | 5.68 | 3/3 | 9.2% |
-| M2_task_arith | 3 | 13.29 | 10.32 | 10.37 | 7.52 | 0/3 | -60.7% |
-| M3_ties | 3 | 13.03 | 10.06 | 10.17 | 9.43 | 0/3 | -55.2% |
+| M0_naive_avg | 14 | 9.43 | 6.45 | 6.46 | 5.95 | 0/14 | 0.0% |
+| M1_perm_avg | 14 | 8.96 | 5.98 | 5.87 | 5.56 | 11/14 | 7.1% |
+| M1_orth_avg | 14 | 9.01 | 6.02 | 6.00 | 5.44 | 12/14 | 6.5% |
+| M2_task_arith | 14 | 14.19 | 11.20 | 11.88 | 5.28 | 1/14 | -73.8% |
+| M3_ties | 14 | 13.07 | 10.09 | 10.23 | 9.32 | 0/14 | -56.7% |
 
-Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permutation-aligned **5.90** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.47**, permutation-aligned **5.96** nats/token.
 
 
 **What this says.**
@@ -120,8 +122,10 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permuta
    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.
+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.)
@@ -151,6 +155,12 @@ gain, and neither commutes with a general rotation (an RMSNorm model would be mu
 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*
@@ -167,8 +177,8 @@ orthogonal row.
 | 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 | 30 | 3.25 | 8.84 | 22.8% | 29.4% | 31.2% | 0.739 | 0.746 | 0.0871 |
-| pythia-410m | 3 | 2.97 | 6.49 | 11.2% | 9.2% | 11.2% | 0.410 | 0.372 | 0.0333 |
+| pythia-160m | 36 | 3.25 | 8.99 | 23.5% | 30.3% | 32.0% | 0.747 | 0.761 | 0.0867 |
+| pythia-410m | 14 | 2.98 | 6.45 | 7.1% | 6.5% | 9.2% | 0.476 | 0.427 | 0.0371 |
 
 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
@@ -195,15 +205,15 @@ exactly the direction the field is scaling.
 
 **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 |
+| 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 |
 
-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.
+**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.
 
@@ -218,7 +228,13 @@ Uniform-over-vocabulary reference (a model that has learned nothing), mean over
 | 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** |
 
-Averaged over the four pairs the best M1 rung removes **1.4%** of the naive merge's Δfloor. 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.
+**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):
@@ -289,24 +305,31 @@ PolyPythia parents are English LMs, so BLiMP applies directly to SET 1's merges.
 | 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 | 30 | 0.690 | 0.697 | 0.523 | 0.532 | 0.534 | 24.3% |
+| 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 | 1 | 0.774 | 0.780 | 0.562 | 0.545 | 0.556 | 22.1% |
+| pythia-160m | 36 | 0.772 | 0.776 | 0.532 | 0.537 | 0.539 | 19.3% |
 
 **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
+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 that the merged model retains does not track it
+at all: it sits at roughly a fifth at 14M, 31M and 70M and drops at 160M. 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 | 30 | -0.141 | 12.58 | 0.0213 |
+| 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 |
 
 ## Did we try hard enough? · REPAIR on top of the alignment
 
@@ -319,11 +342,21 @@ The obvious objection to a negative merging result is that averaging is a weak m
 | 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-70m | 10 | M0_naive_avg | 18.33 | 17.75 | 0.523 | 10.3% |
-| pythia-70m | 10 | M1_perm_avg | 16.91 | 16.26 | 0.541 | 17.9% |
-| pythia-70m | 10 | M4_perm_repair | 16.88 | 17.01 | 0.535 | 15.6% |
-| pythia-70m | 10 | M5_naive_repair | 18.29 | 18.49 | 0.516 | 7.1% |
-| pythia-70m | 10 | **parents** | 0.00 | 0.00 | 0.727 | 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 | 33 | M0_naive_avg | 8.97 | 8.45 | 0.532 | 11.5% |
+| pythia-160m | 33 | M1_perm_avg | 6.78 | 6.47 | 0.539 | 14.0% |
+| pythia-160m | 33 | M4_perm_repair | 6.85 | 6.34 | 0.534 | 12.3% |
+| pythia-160m | 33 | M5_naive_repair | 8.65 | 8.51 | 0.525 | 9.2% |
+| pythia-160m | 33 | **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
@@ -341,6 +374,54 @@ alignment were all tried on the same pairs; the best of them recovers most of th
 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 | 28 | flores_eng | 3.25 | 8.84 | 6.72 | 22.6% |
+| pythia-160m | 28 | pile_10k | 3.15 | 9.22 | 7.45 | 17.7% |
+| pythia-160m | 28 | wikitext103_val | 3.25 | 9.41 | 8.05 | 13.3% |
+
+**It is not a corpus artifact.** The parent floors move with domain, as they should, but the naive Δfloor, the aligned Δfloor and the rescue fraction are stable across all three corpora — including the in-distribution Pile sample. The merge 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 | 1 | M0_naive_avg | 16.51 | 0.568 |
+| pythia-70m | 1 | M1_perm_avg | 16.04 | 0.538 |
+| pythia-70m | 1 | M6_slerp | 39.21 | 0.538 |
+| pythia-70m | 1 | M7_perm_slerp | 29.95 | 0.526 |
+| pythia-70m | 1 | **parents** | 0.00 | 0.731 |
+
+**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 adds to it. Applied *after* unit alignment it comes back to roughly
+where the aligned average already was. 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.
@@ -444,6 +525,60 @@ aligner might close; the joint model also has a *shared vocabulary*, which is ex
 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.
@@ -492,26 +627,31 @@ 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 | 0.517 |
-| pythia-14m | coordinate share (block-normalised / permutation) | 36 | -0.009 | 0.478 | 0.503 | 0.596 | 0.639 |
-| pythia-14m | CKA (mean over layers / unaligned) | 36 | -0.013 | 0.605 | 0.499 | 0.151 | 0.324 |
-| pythia-14m | QMD (quotient_residual / permutation) | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.206 |
-| pythia-14m | task-vector cosine | 36 | 0.131 | 0.580 | 0.498 | 0.223 | 0.419 |
-| pythia-160m | weight cosine | 27 | 0.516 | 0.665 | — | — | — |
-| pythia-160m | coordinate share (block-normalised / permutation) | 27 | -0.029 | 0.379 | — | — | — |
-| pythia-160m | CKA (mean over layers / unaligned) | 27 | -0.194 | 0.478 | — | — | — |
-| pythia-160m | QMD (quotient_residual / permutation) | 27 | 0.140 | 0.533 | — | — | — |
-| pythia-160m | task-vector cosine | 27 | -0.044 | 0.330 | — | — | — |
-| pythia-31m | weight cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.145 |
-| pythia-31m | coordinate share (block-normalised / permutation) | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.145 |
-| pythia-31m | CKA (mean over layers / unaligned) | 36 | 0.100 | 0.546 | 0.503 | 0.345 | 0.517 |
-| pythia-31m | QMD (quotient_residual / permutation) | 36 | -0.060 | 0.444 | 0.500 | 0.722 | 0.722 |
-| pythia-31m | task-vector cosine | 36 | -0.123 | 0.481 | 0.499 | 0.577 | 0.639 |
-| pythia-70m | weight cosine | 36 | 0.089 | 0.491 | 0.500 | 0.517 | 0.639 |
-| pythia-70m | coordinate share (block-normalised / permutation) | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.037 |
-| pythia-70m | CKA (mean over layers / unaligned) | 36 | 0.495 | 0.654 | 0.501 | 0.113 | 0.282 |
-| pythia-70m | QMD (quotient_residual / permutation) | 36 | -0.494 | 0.676 | 0.501 | 0.089 | 0.268 |
-| pythia-70m | task-vector cosine | 36 | 0.071 | 0.543 | 0.502 | 0.390 | 0.532 |
+| pythia-14m | weight cosine | 36 | 0.095 | 0.549 | 0.501 | 0.316 | 0.575 |
+| pythia-14m | coordinate share (block-normalised / permutation) | 36 | -0.009 | 0.478 | 0.503 | 0.596 | 0.701 |
+| pythia-14m | CKA (mean over layers / unaligned) | 36 | -0.013 | 0.605 | 0.499 | 0.151 | 0.379 |
+| pythia-14m | QMD (quotient_residual / permutation) | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.220 |
+| pythia-14m | task-vector cosine | 36 | 0.131 | 0.580 | 0.498 | 0.223 | 0.447 |
+| pythia-160m | weight cosine | 36 | 0.451 | 0.704 | 0.501 | 0.037 | 0.187 |
+| pythia-160m | coordinate share (block-normalised / permutation) | 36 | -0.015 | 0.614 | 0.501 | 0.176 | 0.391 |
+| 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 | 0.593 |
+| pythia-160m | task-vector cosine | 36 | 0.049 | 0.454 | 0.502 | 0.657 | 0.730 |
+| pythia-31m | weight cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.187 |
+| pythia-31m | coordinate share (block-normalised / permutation) | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.187 |
+| pythia-31m | CKA (mean over layers / unaligned) | 36 | 0.100 | 0.546 | 0.503 | 0.345 | 0.575 |
+| pythia-31m | QMD (quotient_residual / permutation) | 36 | -0.060 | 0.444 | 0.500 | 0.722 | 0.760 |
+| pythia-31m | task-vector cosine | 36 | -0.123 | 0.481 | 0.499 | 0.577 | 0.701 |
+| pythia-410m | weight cosine | 14 | -0.125 | 0.510 | — | — | — |
+| pythia-410m | coordinate share (block-normalised / permutation) | 14 | 0.244 | 0.612 | — | — | — |
+| pythia-410m | CKA (mean over layers / unaligned) | 14 | 0.235 | 0.612 | — | — | — |
+| pythia-410m | QMD (quotient_residual / permutation) | 14 | -0.134 | 0.551 | — | — | — |
+| pythia-410m | task-vector cosine | 14 | -0.103 | 0.531 | — | — | — |
+| pythia-70m | weight cosine | 36 | 0.089 | 0.491 | 0.500 | 0.517 | 0.689 |
+| pythia-70m | coordinate share (block-normalised / permutation) | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.050 |
+| pythia-70m | CKA (mean over layers / unaligned) | 36 | 0.495 | 0.654 | 0.501 | 0.113 | 0.323 |
+| pythia-70m | QMD (quotient_residual / permutation) | 36 | -0.494 | 0.676 | 0.501 | 0.089 | 0.298 |
+| pythia-70m | task-vector cosine | 36 | 0.071 | 0.543 | 0.502 | 0.390 | 0.593 |
 
 ### The exploratory table
 
@@ -519,62 +659,76 @@ Showing, per substrate and per outcome, the **six predictors with the largest |A
 
 | 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 | 0.998 |
-| pythia-14m | rescue_frac | qmd_orth | 36 | 0.093 | 0.676 | 0.497 | 0.037 | 0.251 |
-| pythia-14m | rescue_frac | qmd_perm | 36 | 0.077 | 0.664 | 0.498 | 0.051 | 0.261 |
-| pythia-14m | rescue_frac | qmd_act_perm | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.261 |
-| pythia-14m | rescue_frac | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.261 |
-| pythia-14m | rescue_frac | cka_last | 36 | -0.478 | 0.651 | 0.499 | 0.067 | 0.268 |
-| pythia-14m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | 0.501 | 0.114 | 0.278 |
-| pythia-31m | rescue_frac | bnd_perm | 36 | -0.490 | 0.750 | 0.506 | 0.011 | 0.251 |
-| pythia-31m | rescue_frac | coord_share_bnd_perm | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.251 |
-| pythia-31m | rescue_frac | weight_cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.251 |
-| pythia-31m | rescue_frac | d_raw | 36 | -0.321 | 0.704 | 0.505 | 0.025 | 0.251 |
-| pythia-31m | rescue_frac | bnd_raw | 36 | -0.391 | 0.701 | 0.506 | 0.032 | 0.251 |
-| pythia-31m | rescue_frac | qmd_perm | 36 | -0.493 | 0.691 | 0.505 | 0.048 | 0.261 |
-| pythia-31m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.403 | 0.707 | 0.505 | 0.035 | 0.251 |
-| pythia-70m | rescue_frac | coord_share_bnd_perm | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.133 |
-| pythia-70m | rescue_frac | bnd_perm | 36 | -0.404 | 0.787 | 0.501 | 0.003 | 0.133 |
-| pythia-70m | rescue_frac | coord_share_orth | 36 | 0.341 | 0.722 | 0.497 | 0.033 | 0.251 |
-| pythia-70m | rescue_frac | qmd_orth | 36 | -0.373 | 0.713 | 0.497 | 0.067 | 0.268 |
-| pythia-70m | rescue_frac | coord_share_perm | 36 | 0.356 | 0.698 | 0.500 | 0.065 | 0.268 |
-| pythia-70m | rescue_frac | qmd_perm | 36 | -0.357 | 0.688 | 0.500 | 0.084 | 0.268 |
-| pythia-70m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.387 | 0.688 | 0.499 | 0.080 | 0.268 |
-| pythia-160m | rescue_frac | qmd_orth | 27 | -0.629 | 0.802 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_orth | 27 | 0.443 | 0.786 | — | — | — |
-| pythia-160m | rescue_frac | qmd_perm | 27 | -0.482 | 0.731 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_perm | 27 | 0.294 | 0.714 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_bnd_orth | 27 | 0.152 | 0.676 | — | — | — |
-| pythia-160m | rescue_frac | task_vector_cosine | 27 | -0.044 | 0.330 | — | — | — |
-| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 27 | 0.426 | 0.643 | — | — | — |
+| 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 | 0.298 |
+| pythia-14m | rescue_frac | qmd_perm | 36 | 0.077 | 0.664 | 0.498 | 0.051 | 0.298 |
+| pythia-14m | rescue_frac | qmd_act_perm | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.298 |
+| pythia-14m | rescue_frac | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.298 |
+| pythia-14m | rescue_frac | cka_last | 36 | -0.478 | 0.651 | 0.499 | 0.067 | 0.316 |
+| pythia-14m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | 0.501 | 0.114 | 0.318 |
+| pythia-31m | rescue_frac | bnd_perm | 36 | -0.490 | 0.750 | 0.506 | 0.011 | 0.298 |
+| pythia-31m | rescue_frac | coord_share_bnd_perm | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.298 |
+| pythia-31m | rescue_frac | weight_cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.298 |
+| pythia-31m | rescue_frac | d_raw | 36 | -0.321 | 0.704 | 0.505 | 0.025 | 0.298 |
+| pythia-31m | rescue_frac | bnd_raw | 36 | -0.391 | 0.701 | 0.506 | 0.032 | 0.298 |
+| pythia-31m | rescue_frac | qmd_perm | 36 | -0.493 | 0.691 | 0.505 | 0.048 | 0.298 |
+| pythia-31m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.403 | 0.707 | 0.505 | 0.035 | 0.298 |
+| pythia-70m | rescue_frac | coord_share_bnd_perm | 36 | 0.462 | 0.806 | 0.500 | 0.002 | 0.177 |
+| pythia-70m | rescue_frac | bnd_perm | 36 | -0.404 | 0.787 | 0.501 | 0.003 | 0.177 |
+| pythia-70m | rescue_frac | coord_share_orth | 36 | 0.341 | 0.722 | 0.497 | 0.033 | 0.298 |
+| pythia-70m | rescue_frac | qmd_orth | 36 | -0.373 | 0.713 | 0.497 | 0.067 | 0.316 |
+| pythia-70m | rescue_frac | coord_share_perm | 36 | 0.356 | 0.698 | 0.500 | 0.065 | 0.316 |
+| pythia-70m | rescue_frac | qmd_perm | 36 | -0.357 | 0.688 | 0.500 | 0.084 | 0.316 |
+| pythia-70m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.387 | 0.688 | 0.499 | 0.080 | 0.316 |
+| 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 | 0.298 |
+| pythia-160m | rescue_frac | qmd_orth | 36 | -0.439 | 0.704 | 0.498 | 0.052 | 0.298 |
+| pythia-160m | rescue_frac | bnd_orth | 36 | -0.047 | 0.306 | 0.497 | 0.925 | 0.983 |
+| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.331 | 0.642 | 0.499 | 0.130 | 0.323 |
+| pythia-410m | rescue_frac | d_raw | 14 | 0.059 | 0.286 | — | — | — |
+| pythia-410m | rescue_frac | weight_cosine_bn | 14 | -0.420 | 0.633 | — | — | — |
+| pythia-410m | rescue_frac | bnd_perm | 14 | -0.156 | 0.633 | — | — | — |
+| pythia-410m | rescue_frac | cka_last | 14 | 0.077 | 0.367 | — | — | — |
+| pythia-410m | rescue_frac | bnd_raw | 14 | -0.152 | 0.612 | — | — | — |
+| pythia-410m | rescue_frac | bnd_orth | 14 | -0.152 | 0.612 | — | — | — |
+| pythia-410m | rescue_frac | MULTIVARIATE_ridge_all | 14 | -0.525 | 0.245 | — | — | — |
 | 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 | 0.251 |
-| pythia-14m | dfloor_M1best | coord_share_perm | 36 | -0.445 | 0.735 | 0.495 | 0.016 | 0.251 |
-| pythia-14m | dfloor_M1best | qmd_orth | 36 | 0.438 | 0.725 | 0.496 | 0.021 | 0.251 |
-| pythia-14m | dfloor_M1best | coord_share_bnd_perm | 36 | -0.155 | 0.290 | 0.503 | 0.977 | 0.998 |
-| pythia-14m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.539 | 0.778 | 0.497 | 0.003 | 0.133 |
-| pythia-31m | dfloor_M1best | qmd_orth | 36 | 0.289 | 0.670 | 0.502 | 0.101 | 0.268 |
-| pythia-31m | dfloor_M1best | coord_share_orth | 36 | -0.271 | 0.670 | 0.503 | 0.103 | 0.268 |
-| pythia-31m | dfloor_M1best | qmd_perm | 36 | 0.243 | 0.633 | 0.503 | 0.166 | 0.322 |
-| pythia-31m | dfloor_M1best | coord_share_perm | 36 | -0.230 | 0.633 | 0.503 | 0.166 | 0.322 |
-| pythia-31m | dfloor_M1best | bnd_raw | 36 | 0.163 | 0.633 | 0.503 | 0.132 | 0.299 |
-| pythia-31m | dfloor_M1best | bnd_orth | 36 | 0.114 | 0.611 | 0.501 | 0.186 | 0.343 |
-| pythia-31m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | -0.111 | 0.500 | 0.501 | 0.516 | 0.647 |
-| pythia-70m | dfloor_M1best | coord_share_bnd_perm | 36 | 0.529 | 0.713 | 0.501 | 0.037 | 0.251 |
-| pythia-70m | dfloor_M1best | bnd_perm | 36 | -0.485 | 0.704 | 0.502 | 0.033 | 0.251 |
-| pythia-70m | dfloor_M1best | cka_last | 36 | 0.476 | 0.691 | 0.499 | 0.090 | 0.268 |
-| pythia-70m | dfloor_M1best | cka_mean | 36 | 0.427 | 0.667 | 0.501 | 0.105 | 0.268 |
-| pythia-70m | dfloor_M1best | qmd_act_perm | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.268 |
-| pythia-70m | dfloor_M1best | qmd_act_procrustes | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.268 |
-| pythia-70m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.386 | 0.599 | 0.500 | 0.207 | 0.347 |
-| pythia-160m | dfloor_M1best | cka_mean | 27 | -0.398 | 0.742 | — | — | — |
-| pythia-160m | dfloor_M1best | bnd_perm | 27 | -0.426 | 0.736 | — | — | — |
-| pythia-160m | dfloor_M1best | bnd_orth | 27 | -0.421 | 0.714 | — | — | — |
-| pythia-160m | dfloor_M1best | coord_share_bnd_perm | 27 | 0.322 | 0.703 | — | — | — |
-| pythia-160m | dfloor_M1best | task_vector_cosine | 27 | 0.272 | 0.692 | — | — | — |
-| pythia-160m | dfloor_M1best | d_raw | 27 | 0.122 | 0.313 | — | — | — |
-| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 27 | 0.454 | 0.676 | — | — | — |
+| pythia-14m | dfloor_M1best | coord_share_orth | 36 | -0.457 | 0.738 | 0.495 | 0.015 | 0.298 |
+| pythia-14m | dfloor_M1best | coord_share_perm | 36 | -0.445 | 0.735 | 0.495 | 0.016 | 0.298 |
+| pythia-14m | dfloor_M1best | qmd_orth | 36 | 0.438 | 0.725 | 0.496 | 0.021 | 0.298 |
+| 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 | 0.177 |
+| pythia-31m | dfloor_M1best | qmd_orth | 36 | 0.289 | 0.670 | 0.502 | 0.101 | 0.316 |
+| pythia-31m | dfloor_M1best | coord_share_orth | 36 | -0.271 | 0.670 | 0.503 | 0.103 | 0.316 |
+| pythia-31m | dfloor_M1best | qmd_perm | 36 | 0.243 | 0.633 | 0.503 | 0.166 | 0.356 |
+| pythia-31m | dfloor_M1best | coord_share_perm | 36 | -0.230 | 0.633 | 0.503 | 0.166 | 0.356 |
+| pythia-31m | dfloor_M1best | bnd_raw | 36 | 0.163 | 0.633 | 0.503 | 0.132 | 0.323 |
+| pythia-31m | dfloor_M1best | bnd_orth | 36 | 0.114 | 0.611 | 0.501 | 0.186 | 0.373 |
+| pythia-31m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | -0.111 | 0.500 | 0.501 | 0.516 | 0.671 |
+| pythia-70m | dfloor_M1best | coord_share_bnd_perm | 36 | 0.529 | 0.713 | 0.501 | 0.037 | 0.298 |
+| pythia-70m | dfloor_M1best | bnd_perm | 36 | -0.485 | 0.704 | 0.502 | 0.033 | 0.298 |
+| pythia-70m | dfloor_M1best | cka_last | 36 | 0.476 | 0.691 | 0.499 | 0.090 | 0.316 |
+| pythia-70m | dfloor_M1best | cka_mean | 36 | 0.427 | 0.667 | 0.501 | 0.105 | 0.316 |
+| pythia-70m | dfloor_M1best | qmd_act_perm | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.316 |
+| pythia-70m | dfloor_M1best | qmd_act_procrustes | 36 | -0.433 | 0.667 | 0.501 | 0.103 | 0.316 |
+| pythia-70m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.386 | 0.599 | 0.500 | 0.207 | 0.376 |
+| 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 | 0.298 |
+| pythia-160m | dfloor_M1best | cka_mean | 36 | -0.270 | 0.685 | 0.500 | 0.111 | 0.318 |
+| pythia-160m | dfloor_M1best | bnd_orth | 36 | -0.371 | 0.660 | 0.500 | 0.081 | 0.316 |
+| pythia-160m | dfloor_M1best | d_raw | 36 | 0.273 | 0.349 | 0.503 | 0.910 | 0.974 |
+| pythia-160m | dfloor_M1best | bnd_raw | 36 | -0.278 | 0.648 | 0.501 | 0.119 | 0.318 |
+| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | 0.584 | 0.759 | 0.497 | 0.018 | 0.298 |
+| pythia-410m | dfloor_M1best | qmd_act_ot | 14 | 0.420 | 0.837 | — | — | — |
+| pythia-410m | dfloor_M1best | cka_mean | 14 | -0.323 | 0.816 | — | — | — |
+| pythia-410m | dfloor_M1best | qmd_act_perm | 14 | 0.380 | 0.796 | — | — | — |
+| pythia-410m | dfloor_M1best | qmd_act_procrustes | 14 | 0.380 | 0.796 | — | — | — |
+| pythia-410m | dfloor_M1best | task_vector_cosine | 14 | -0.125 | 0.245 | — | — | — |
+| pythia-410m | dfloor_M1best | d_raw | 14 | -0.270 | 0.306 | — | — | — |
+| pythia-410m | dfloor_M1best | MULTIVARIATE_ridge_all | 14 | 0.429 | 0.755 | — | — | — |
 
 ### Does a predictor fitted on one substrate transfer to another?
 
@@ -582,26 +736,31 @@ Leave-one-**size**-out. Predictors are standardised *within* size first, so a pr
 
 | predictor | outcome | held-out substrate | n | AUROC | null mean | perm p | BH q |
 |---|---|---|---|---|---|---|---|
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-14m | 36 | 0.355 | 0.500 | 0.928 | 0.958 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 27 | 0.670 | 0.499 | 0.070 | 0.246 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.691 | 0.496 | 0.025 | 0.200 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 36 | 0.531 | 0.503 | 0.400 | 0.705 |
-| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.505 | 0.469 | 0.750 |
-| coord_share_bnd_perm | rescue_frac | pythia-160m | 27 | 0.555 | 0.499 | 0.336 | 0.693 |
-| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.506 | 0.014 | 0.186 |
-| coord_share_bnd_perm | rescue_frac | pythia-70m | 36 | 0.806 | 0.499 | 0.002 | 0.080 |
-| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.496 | 0.046 | 0.213 |
-| qmd_act_perm | rescue_frac | pythia-160m | 27 | 0.467 | 0.502 | 0.626 | 0.889 |
-| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.499 | 0.406 | 0.705 |
-| qmd_act_perm | rescue_frac | pythia-70m | 36 | 0.676 | 0.499 | 0.031 | 0.206 |
-| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.500 | 0.149 | 0.397 |
-| cka_mean | rescue_frac | pythia-160m | 27 | 0.451 | 0.497 | 0.668 | 0.891 |
-| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.347 | 0.693 |
-| cka_mean | rescue_frac | pythia-70m | 36 | 0.346 | 0.498 | 0.934 | 0.958 |
-| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.506 | 0.235 | 0.552 |
-| weight_cosine | rescue_frac | pythia-160m | 27 | 0.665 | 0.506 | 0.088 | 0.251 |
-| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.499 | 0.020 | 0.200 |
-| weight_cosine | rescue_frac | pythia-70m | 36 | 0.494 | 0.499 | 0.526 | 0.780 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-14m | 36 | 0.414 | 0.500 | 0.814 | 0.966 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 36 | 0.654 | 0.499 | 0.048 | 0.220 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.685 | 0.495 | 0.024 | 0.175 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-410m | 14 | 0.531 | 0.498 | 0.446 | 0.737 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 36 | 0.556 | 0.502 | 0.292 | 0.664 |
+| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.500 | 0.459 | 0.737 |
+| coord_share_bnd_perm | rescue_frac | pythia-160m | 36 | 0.506 | 0.500 | 0.473 | 0.737 |
+| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.502 | 0.016 | 0.133 |
+| coord_share_bnd_perm | rescue_frac | pythia-410m | 14 | 0.612 | 0.492 | 0.252 | 0.664 |
+| coord_share_bnd_perm | rescue_frac | pythia-70m | 36 | 0.806 | 0.497 | 0.002 | 0.100 |
+| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.497 | 0.047 | 0.220 |
+| qmd_act_perm | rescue_frac | pythia-160m | 36 | 0.512 | 0.497 | 0.444 | 0.737 |
+| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.506 | 0.446 | 0.737 |
+| qmd_act_perm | rescue_frac | pythia-410m | 14 | 0.571 | 0.501 | 0.347 | 0.713 |
+| qmd_act_perm | rescue_frac | pythia-70m | 36 | 0.676 | 0.501 | 0.045 | 0.220 |
+| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.497 | 0.150 | 0.526 |
+| cka_mean | rescue_frac | pythia-160m | 36 | 0.478 | 0.498 | 0.570 | 0.792 |
+| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.357 | 0.713 |
+| cka_mean | rescue_frac | pythia-410m | 14 | 0.612 | 0.501 | 0.287 | 0.664 |
+| cka_mean | rescue_frac | pythia-70m | 36 | 0.346 | 0.498 | 0.950 | 0.980 |
+| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.498 | 0.217 | 0.664 |
+| weight_cosine | rescue_frac | pythia-160m | 36 | 0.704 | 0.496 | 0.013 | 0.130 |
+| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.497 | 0.011 | 0.130 |
+| weight_cosine | rescue_frac | pythia-410m | 14 | 0.510 | 0.493 | 0.484 | 0.737 |
+| weight_cosine | rescue_frac | pythia-70m | 36 | 0.494 | 0.501 | 0.547 | 0.782 |
 
 **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.
 
@@ -629,24 +788,28 @@ Leave-one-**size**-out. Predictors are standardised *within* size first, so a pr
 ### What P0-2 comes to
 
 **The confirmatory family gives 1 significant cell out of
-15 tested** (BH q < 0.05 within the family):
+20 tested** (BH q < 0.05 within the family):
 
-- pythia-70m · coordinate share (block-normalised / permutation) · AUROC 0.806 · q = 0.037
+- pythia-70m · coordinate share (block-normalised / permutation) · AUROC 0.806 · q = 0.050
 
 That is a real effect and it should not be rounded down to zero. It should also not be rounded up.
 The predictor that carries it is the **coordinate share** — exactly the quantity the manuscript's
 thesis is about — and the honest summary is:
 
-- **It does not replicate across substrates.** The same predictor's held-out AUROC across the sizes
-  we ran is not stable, and at the largest size it sits *below* 0.5, i.e. pointing the wrong way. A
-  quantity that predicts the rescue on one substrate and anti-predicts it on another is not a
-  validated instrument for "representational alignment predicts merging".
+- **It does not replicate across substrates.** The same predictor's held-out AUROC ranges from ~0.48
+  (chance, and slightly the wrong way) to 0.81 across four complete 36-pair grids of the *same*
+  model family differing only in size. A quantity that lands anywhere in that range 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 is likewise partial.** Fitting on the other sizes and testing on a
-  held-out one, the coordinate share transfers to some substrates and not to others (table above).
+- **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
@@ -669,23 +832,47 @@ substrate where the coordinate share does predict it does not generalise to the
 negative transfer result from the synthetic/S3 setting to real models, and it is reported as one.
 
 
-## Control · is the obstruction the INIT seed or the DATA order?
+## Control · same-basin vs different-basin pairs
 
-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.
+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.
 
-| 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) | 30 | 3.25 | 8.84 | 6.70 | 6.16 | 31.2% | 0.0871 |
+That makes them useful as something else — a **same-basin reference** — so they are reported as one.
 
-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.
+| 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
@@ -695,18 +882,22 @@ init-plus-data-order number, not an init-only one.
 | 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 | 30/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; LMC barrier for M0 and M1-perm |
-| SET 1 Δfloor · pythia-410m | 3/15 seed pairs | partial | 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 | 14/15 seed pairs | partial | 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: 30/36, pythia-70m: 36/36, pythia-160m: 1/36 | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges |
-| SET 1 · REPAIR rung | pythia-14m: 36/36, pythia-70m: 10/36 | RAN | M4 = permutation-aligned average + pre-activation statistics repair; M5 = naive + repair; Δfloor and BLiMP on the same merges |
+| SET 1 accuracy · BLiMP | pythia-14m: 36/36, pythia-31m: 36/36, pythia-70m: 36/36, pythia-160m: 36/36 | 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: 28/36 | 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: 1/36 | 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: 33/36 | 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 | 3/36 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. |
+| SET 1 · pythia-410m full grid | 14/36 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. |
 
@@ -750,26 +941,35 @@ init-plus-data-order number, not an init-only one.
 ## Files
 
 ```
-results/set1_{14m,31m,70m,160m,410m}.jsonl  SET 1 per-pair raw records (predictors, rungs, barriers)
+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        init-seed-only vs data-order-only control
+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_auroc.csv                 P0-2: held-out-by-seed AUROC, seed-cluster null, BH q
+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
+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
-code/*.py                                   every script that produced the above
+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

code/analyze.py

@@ -71,7 +71,15 @@ def ridge(X, y, lam=1.0):
 
 
 # ------------------------------------------------------------------ SET 1 assembly
-set1 = load("set1_*.jsonl")
+set1 = load("set1_*.jsonl") + load("set1x_*.jsonl")
+_seen = set()
+_ded = []
+for _r in set1:                     # a size may be worked by more than one worker process
+    _k = (_r["size"], tuple(_r["pair"]))
+    if _k in _seen:
+        continue
+    _seen.add(_k); _ded.append(_r)
+set1 = _ded
 rows1 = []
 for r in set1:
     rg = r["rungs"]
@@ -326,18 +334,21 @@ plt.rcParams.update({"figure.dpi": 130, "font.size": 9, "axes.grid": True,
 # 1. Delta-floor by rung
 if rows1:
     sizes = sorted({r["size"] for r in rows1}, key=lambda s: int(s[:-1]))
-    rungs = [k[7:] for k in rows1[0] if k.startswith("dfloor_M")]
+    rungs = [k[7:] for k in rows1[0] if k.startswith("dfloor_M") and k not in ("dfloor_M0", "dfloor_M1best")]
     fig, axes = plt.subplots(1, len(sizes), figsize=(3.6 * len(sizes), 3.4), squeeze=False)
     for ax, sz in zip(axes[0], sizes):
         sub = [r for r in rows1 if r["size"] == sz]
         data = [[r[f"dfloor_{k}"] for r in sub if np.isfinite(r.get(f"dfloor_{k}", np.nan))] for k in rungs]
         keep = [(k, d) for k, d in zip(rungs, data) if d]
-        ax.boxplot([d for _, d in keep], tick_labels=[k.replace("_", "\n", 1) for k, _ in keep],
-                   showfliers=False)
+        _lab = {"M0_naive_avg": "M0\nnaive", "M1_perm_avg": "M1\nperm*", "M1_orth_avg": "M1\northo†",
+                "M2_task_arith": "M2\ntask-ar†", "M3_ties": "M3\nTIES†"}
+        ax.boxplot([d for _, d in keep], tick_labels=[_lab.get(k, k) for k, _ in keep], showfliers=False)
         ax.set_yscale("symlog"); ax.set_title(f"pythia-{sz}  (n={len(sub)} seed pairs)")
         ax.set_ylabel("Δfloor  (nats/token, log)")
-        ax.tick_params(axis="x", labelsize=6)
-    fig.suptitle("SET 1 · PolyPythia seed merge · Δfloor vs the better parent, by merge rung", fontsize=10)
+        ax.tick_params(axis="x", labelsize=7)
+    fig.suptitle("SET 1 · PolyPythia seed merge · Δfloor vs the better parent, by merge rung\n"
+                 "* exactly function-preserving   † not function-preserving / no shared base — see the report",
+                 fontsize=9)
     fig.tight_layout(); fig.savefig(f"{F}/set1_dfloor_by_rung.png", bbox_inches="tight"); plt.close(fig)
 
 # 2. rescue vs coordinate share
@@ -354,25 +365,26 @@ if rows1:
     fig.suptitle("SET 1 · does a PRE-MERGE predictor track the REALISED rescue?", fontsize=10)
     fig.tight_layout(); fig.savefig(f"{F}/set1_rescue_vs_predictor.png", bbox_inches="tight"); plt.close(fig)
 
-# 3. ROC of the best held-out predictor per size
+# 3. ROC of the CONFIRMATORY predictor (coordinate share), one curve per substrate
 if roc_store and pred_rows:
-    fig, ax = plt.subplots(figsize=(4.2, 4))
-    best = {}
-    for r in pred_rows:
-        if r["predictor"].startswith("MULTIVAR"): continue
-        sz = r["substrate"].split("-")[1]
-        a = r["auroc_heldout_by_seed"]
-        if np.isfinite(a) and (sz not in best or abs(a - .5) > abs(best[sz][1] - .5)):
-            best[sz] = (r["predictor"], a)
-    for sz, (pk, a) in best.items():
-        oof, y = roc_store[(sz, "p_" + pk)]
-        o = np.argsort(-oof); yy = y[o]
+    PK = "p_coord_share_bnd_perm"
+    au = {(r["substrate"], r["predictor"]): r["auroc_heldout_by_seed"] for r in pred_rows
+          if r["outcome"] == "rescue_frac"}
+    fig, ax = plt.subplots(figsize=(4.6, 4.2))
+    for sz in sorted({k[0] for k in roc_store}, key=lambda x: int(x[:-1])):
+        if (sz, PK) not in roc_store:
+            continue
+        oof, y = roc_store[(sz, PK)]
+        ok = np.isfinite(oof)
+        o = np.argsort(-oof[ok]); yy = y[ok][o]
         tpr = np.cumsum(yy) / max(1, yy.sum()); fpr = np.cumsum(1 - yy) / max(1, (1 - yy).sum())
-        ax.plot(np.r_[0, fpr], np.r_[0, tpr], label=f"pythia-{sz}: {pk} (AUROC={a:.2f})")
+        a = au.get((f"pythia-{sz}", PK[2:]), float("nan"))
+        ax.plot(np.r_[0, fpr], np.r_[0, tpr], label=f"pythia-{sz}  (AUROC {a:.2f})")
     ax.plot([0, 1], [0, 1], "k--", lw=.8)
     ax.set_xlabel("false positive rate"); ax.set_ylabel("true positive rate")
-    ax.set_title("SET 1 · held-out-by-seed ROC\n(best predictor per size)", fontsize=9)
-    ax.legend(fontsize=7, frameon=False)
+    ax.set_title("SET 1 · P0-2 confirmatory predictor\ncoordinate share → realised rescue,\n"
+                 "held out by seed pair", fontsize=9)
+    ax.legend(fontsize=7.5, frameon=False, loc="lower right")
     fig.tight_layout(); fig.savefig(f"{F}/set1_roc.png", bbox_inches="tight"); plt.close(fig)
 
 # 4. SET 4 bars
@@ -490,17 +502,24 @@ if bgc:
 mbr = load("set4_multiblimp.jsonl")
 if mbr and rows4:
     by_lang = {r["lang"]: r for r in rows4}
-    fig, ax = plt.subplots(figsize=(5.2, 4))
-    for r in mbr:
+    fig, ax = plt.subplots(figsize=(5.4, 4.1))
+    _cyc = plt.rcParams["axes.prop_cycle"].by_key()["color"]
+    for li, r in enumerate(mbr):
         s4 = by_lang.get(r["lang"])
         if not s4: continue
+        col = _cyc[li % len(_cyc)]
+        first = True
         for k in r["rungs"]:
             key = f"delta_floor_eng_{k}"
             if key not in s4: continue
-            ax.scatter(s4[key], r["rungs"][k]["mb_eng"], s=28, alpha=.8,
-                       label=r["lang"].split("_")[0] if k == "M0_naive_avg" else None)
-    ax.scatter([0], [mbr[0]["parents"]["eng_on_mb_eng"]], marker="*", s=200, color="k",
-               label="English parent", zorder=5)
+            ax.scatter(s4[key], r["rungs"][k]["mb_eng"], s=30, alpha=.85, color=col,
+                       marker=("o" if k == "M0_naive_avg" else "^"),
+                       label=(r["lang"].split("_")[0] if first else None))
+            first = False
+    ax.scatter([0], [mbr[0]["parents"]["eng_on_mb_eng"]], marker="*", s=220, color="k",
+               label="English parent (Δfloor 0)", zorder=5)
+    ax.scatter([], [], marker="o", s=30, color="grey", label="naive merge")
+    ax.scatter([], [], marker="^", s=30, color="grey", label="aligned / transported rungs")
     ax.axhline(0.5, color="grey", ls="--", lw=.8)
     ax.text(0.02, 0.505, "chance", fontsize=7, transform=ax.get_yaxis_transform())
     ax.set_xlabel("Δfloor on English text  (nats/byte, LIKELIHOOD)")

code/bgpt_merge.py

@@ -0,0 +1,169 @@
+"""SET 4b: merging two BILINGUAL models of the SAME language pair.
+
+This is the cell that separates the two obstructions SET 4 confounds. `B-GPT_en_X_simultaneous` and
+`B-GPT_X_en_simultaneous` are trained on the same two languages, the same data recipe and the same
+architecture, and their tokenizers share ~94% of their surface forms (against ~15-28% for two
+monolingual Goldfish tokenizers) — so vocabulary transport is nearly lossless here. What is left
+between them is an independent training run: different init, different data order, a permuted
+vocabulary indexing. If merging works anywhere in the composition setting, it should work here.
+
+Rungs: M0 naive · M1a vocab-transported · M1b +permutation-aligned · M1c +Procrustes ·
+M1g embedding-row Procrustes. Metrics: Δfloor in nats/UTF-8 byte (FLORES-200 devtest, both
+languages) AND MultiBLiMP 1.0 accuracy, on the same merges."""
+import os, sys, json, time, csv, argparse, gc
+sys.path.insert(0, "/root/compose-audit")
+from common import *
+import gpt2_align as G2
+from set4_goldfish_lib import sent_acts
+from mergeschool.core.models import load_hf
+from huggingface_hub import hf_hub_download
+
+ap = argparse.ArgumentParser()
+ap.add_argument("--pairs", default="nld_Latn:nl:nld,spa_Latn:es:spa,ell_Grek:el:ell,pol_Latn:pl:pol")
+ap.add_argument("--variant", default="simultaneous")
+ap.add_argument("--n_sent", type=int, default=500)
+ap.add_argument("--max_items", type=int, default=1200)
+ap.add_argument("--bs", type=int, default=16)
+A = ap.parse_args()
+OUT = "/root/compose-audit/results/bgpt_merge.jsonl"
+DEV = "cuda"
+BLOCK = 128                     # B-GPT's n_positions
+
+
+def log(*a): print(f"[{time.strftime('%H:%M:%S')}]", *a, flush=True)
+
+
+def build_blocks(tok, text, block=BLOCK, max_blocks=200):
+    ids = tok(text)["input_ids"]
+    n = max(1, min(max_blocks, len(ids) // block))
+    arr = torch.from_numpy(np.asarray(ids[: n * block], dtype=np.int64).reshape(n, block))
+    nb = sum(len(tok.decode(list(arr[i, 1:].numpy())).encode("utf-8")) for i in range(n))
+    return arr, nb
+
+
+@torch.no_grad()
+def nll_total(model, blocks, dev, bs):
+    tot, ntok = 0.0, 0
+    for i in range(0, blocks.shape[0], bs):
+        x = blocks[i:i + bs].to(dev)
+        lp = torch.log_softmax(model(x).logits.float()[:, :-1], -1)
+        tgt = x[:, 1:]
+        tot += (-lp.gather(-1, tgt.unsqueeze(-1)).squeeze(-1)).sum().item(); ntok += tgt.numel()
+    return tot, ntok
+
+
+def mb_pairs(lang, n):
+    p = hf_hub_download("jumelet/multiblimp", f"{lang}/data.tsv", repo_type="dataset")
+    rows = list(csv.DictReader(open(p, encoding="utf-8"), delimiter="\t"))[:n]
+    return [(r["sen"], r["wrong_sen"]) for r in rows if r.get("sen") and r.get("wrong_sen")]
+
+
+def encode(tok, sents, maxlen=64):
+    e = tok(sents, return_tensors="pt", padding=True, truncation=True, max_length=maxlen)
+    return e["input_ids"], e["attention_mask"]
+
+
+@torch.no_grad()
+def mb_acc(model, encg, encb, dev, bs=48):
+    def sc(ids, am):
+        o = []
+        for i in range(0, ids.shape[0], bs):
+            x, m = ids[i:i + bs].to(dev), am[i:i + bs].to(dev)
+            lp = torch.log_softmax(model(x, attention_mask=m).logits.float()[:, :-1], -1)
+            o.append((lp.gather(-1, x[:, 1:].unsqueeze(-1)).squeeze(-1) * m[:, 1:].float()).sum(1).cpu())
+        return torch.cat(o).numpy()
+    return float((sc(*encg) > sc(*encb)).mean())
+
+
+eng_lines = flores_lines("eng_Latn")[: A.n_sent]
+eng_text = "\n".join(eng_lines)
+MB_ENG = mb_pairs("eng", A.max_items)
+done = set()
+if os.path.exists(OUT):
+    for l in open(OUT):
+        try: done.add(json.loads(l)["lang"])
+        except Exception: pass
+fh = open(OUT, "a")
+
+for spec in A.pairs.split(","):
+    fcode, x2, mb = spec.split(":")
+    if fcode in done: continue
+    t0 = time.time()
+    ra = f"catherinearnett/B-GPT_en_{x2}_{A.variant}"
+    rb = f"catherinearnett/B-GPT_{x2}_en_{A.variant}"
+    log(f"=== {fcode}: A={ra}  B={rb}")
+    try:
+        m_a, tok_a = load_hf(ra, dtype=torch.float32, device=DEV); m_a.eval()
+        m_b, tok_b = load_hf(rb, dtype=torch.float32, device=DEV); m_b.eval()
+    except Exception as e:
+        log("load failed", type(e).__name__, str(e)[:200]); continue
+    cfg = m_a.config
+    D, NH, V = cfg.n_embd, cfg.n_head, cfg.vocab_size
+    SD_A, SD_B = sd_np(m_a), sd_np(m_b)
+    x_lines = flores_lines(fcode)[: A.n_sent]; x_text = "\n".join(x_lines)
+    MBX = mb_pairs(mb, A.max_items)
+
+    acts_a = sent_acts(m_a, tok_a, eng_lines + x_lines, DEV)      # same sentences, both models
+    acts_b = sent_acts(m_b, tok_b, eng_lines + x_lines, DEV)
+
+    bl_e, by_e = build_blocks(tok_a, eng_text); bl_x, by_x = build_blocks(tok_a, x_text)
+    ENC_E = (encode(tok_a, [g for g, _ in MB_ENG]), encode(tok_a, [b for _, b in MB_ENG]))
+    ENC_X = (encode(tok_a, [g for g, _ in MBX]), encode(tok_a, [b for _, b in MBX]))
+    ta, _ = nll_total(m_a, bl_e, DEV, A.bs); txa, _ = nll_total(m_a, bl_x, DEV, A.bs)
+    PA = {"nats_per_byte_eng": ta / by_e, "nats_per_byte_x": txa / by_x,
+          "multiblimp_eng": mb_acc(m_a, *ENC_E, DEV), "multiblimp_x": mb_acc(m_a, *ENC_X, DEV)}
+    # parent B in its OWN tokenizer, so its floor is not penalised by A's indexing
+    blb_e, byb_e = build_blocks(tok_b, eng_text); blb_x, byb_x = build_blocks(tok_b, x_text)
+    tb, _ = nll_total(m_b, blb_e, DEV, A.bs); txb, _ = nll_total(m_b, blb_x, DEV, A.bs)
+    ENC_E_B = (encode(tok_b, [g for g, _ in MB_ENG]), encode(tok_b, [b for _, b in MB_ENG]))
+    ENC_X_B = (encode(tok_b, [g for g, _ in MBX]), encode(tok_b, [b for _, b in MBX]))
+    PB = {"nats_per_byte_eng": tb / byb_e, "nats_per_byte_x": txb / byb_x,
+          "multiblimp_eng": mb_acc(m_b, *ENC_E_B, DEV), "multiblimp_x": mb_acc(m_b, *ENC_X_B, DEV)}
+    del m_b; torch.cuda.empty_cache()
+    shell = m_a
+    log(f"  parents A={PA}  B={PB}")
+
+    vkeys = [k for k in SD_B if k.endswith("wte.weight") or k.endswith("lm_head.weight")]
+    SD_B_V, _ = AL.remap_vocab_rows(SD_B, tok_a, tok_b, V, keys=vkeys)
+    for k in vkeys:
+        W = np.asarray(SD_B_V[k], float)
+        if W.shape[0] == V:
+            bad = ~np.isfinite(W).all(axis=1); W[bad] = np.asarray(SD_A[k], float)[bad]
+        SD_B_V[k] = W
+    anchors = AL.vocab_anchors(tok_a, tok_b)
+    BODY = [k for k in SD_A if not (k.endswith("wte.weight") or k.endswith("lm_head.weight"))]
+    R_emb, n_anch = G2.emb_procrustes(SD_A, SD_B, tok_a, tok_b)
+    sd_emb = G2.apply_resid(SD_B_V, D, R=R_emb)
+    sdp, ip = G2.align_full(SD_A, SD_B_V, D, NH, acts_a, acts_b, "permutation", body_keys=BODY)
+    sdo, io = G2.align_full(SD_A, SD_B_V, D, NH, acts_a, acts_b, "orthogonal", body_keys=BODY)
+
+    rungs = {"M0_naive_avg": MG.average([SD_A, SD_B]),
+             "M1a_vocab_avg": MG.average([SD_A, SD_B_V]),
+             "M1b_vocab_perm_avg": MG.average([SD_A, sdp]),
+             "M1c_vocab_orth_avg": MG.average([SD_A, sdo]),
+             "M1g_emb_procrustes": MG.average([SD_A, sd_emb])}
+    floor_e = min(PA["nats_per_byte_eng"], PB["nats_per_byte_eng"])
+    floor_x = min(PA["nats_per_byte_x"], PB["nats_per_byte_x"])
+    ceil_e = max(PA["multiblimp_eng"], PB["multiblimp_eng"])
+    ceil_x = max(PA["multiblimp_x"], PB["multiblimp_x"])
+    res = {}
+    for k, sd in rungs.items():
+        sd_load(shell, sd, DEV)
+        t_e, _ = nll_total(shell, bl_e, DEV, A.bs); t_x, _ = nll_total(shell, bl_x, DEV, A.bs)
+        res[k] = {"nats_per_byte_eng": t_e / by_e, "nats_per_byte_x": t_x / by_x,
+                  "delta_floor_eng": t_e / by_e - floor_e, "delta_floor_x": t_x / by_x - floor_x,
+                  "multiblimp_eng": mb_acc(shell, *ENC_E, DEV), "multiblimp_x": mb_acc(shell, *ENC_X, DEV)}
+        res[k]["delta_floor_mean"] = 0.5 * (res[k]["delta_floor_eng"] + res[k]["delta_floor_x"])
+        res[k]["multiblimp_mean"] = 0.5 * (res[k]["multiblimp_eng"] + res[k]["multiblimp_x"])
+    r = {"set": "bgpt_merge", "lang": fcode, "repo_a": ra, "repo_b": rb, "variant": A.variant,
+         "context_tokens": BLOCK, "vocab_anchors": len(anchors), "vocab_overlap": len(anchors) / V,
+         "metric": "nats/UTF-8 byte (likelihood) + MultiBLiMP accuracy",
+         "parents": {"A": PA, "B": PB}, "floor_eng": floor_e, "floor_x": floor_x,
+         "ceiling_mb_eng": ceil_e, "ceiling_mb_x": ceil_x,
+         "align_info": {"perm": ip, "orth": io}, "rungs": res, "secs": time.time() - t0}
+    fh.write(json.dumps(r) + "\n"); fh.flush()
+    log("  " + " | ".join(f"{k}: dfl={v['delta_floor_mean']:+.3f} MB={v['multiblimp_mean']:.3f}"
+                          for k, v in res.items()))
+    del rungs, sdp, sdo, sd_emb, SD_B, SD_B_V, m_a; gc.collect(); torch.cuda.empty_cache()
+fh.close()
+log("DONE bgpt_merge")

code/make_artifact.py

@@ -0,0 +1,472 @@
+"""Build the shareable HTML page from the same result files the markdown report uses."""
+import os, sys, json, glob, base64, math, html, time
+sys.path.insert(0, "/root/compose-audit")
+import numpy as np
+R = "/root/compose-audit/results"
+F = "/root/compose-audit/figs"
+HF = "https://huggingface.co/datasets/Mergeability-2/compose-audit"
+
+
+def load(pat):
+    out = []
+    for fp in sorted(glob.glob(f"{R}/{pat}")):
+        for line in open(fp):
+            try: out.append(json.loads(line))
+            except Exception: pass
+    return out
+
+
+def dedup(rows):
+    seen, out = set(), []
+    for r in rows:
+        k = (r["size"], tuple(r["pair"]))
+        if k in seen: continue
+        seen.add(k); out.append(r)
+    return out
+
+
+set1 = dedup(load("set1_*.jsonl") + load("set1x_*.jsonl"))
+set4 = load("set4_goldfish.jsonl")
+blimp = load("blimp_*.jsonl")
+rep = load("repair_*.jsonl")
+slp = load("slerp_*.jsonl")
+mb = load("set4_multiblimp.jsonl")
+bgm = load("bgpt_merge.jsonl")
+bgc = load("bgpt_ceiling.jsonl")
+crb = load("corpus_*.jsonl")
+abl = load("abl_*.jsonl")
+sizes = sorted({r["size"] for r in set1}, key=lambda s: int(s[:-1]))
+UNIF = math.log(50304)
+
+
+def img(name, alt, cap):
+    p = f"{F}/{name}"
+    if not os.path.exists(p): return ""
+    b = base64.b64encode(open(p, "rb").read()).decode()
+    return (f'<figure class="fig"><img src="data:image/png;base64,{b}" alt="{html.escape(alt)}">'
+            f'<figcaption>{cap}</figcaption></figure>')
+
+
+def table(headers, rows, note=None):
+    h = "".join(f"<th>{c}</th>" for c in headers)
+    b = "".join("<tr>" + "".join(f"<td>{c}</td>" for c in r) + "</tr>" for r in rows)
+    n = f'<p class="tnote">{note}</p>' if note else ""
+    return f'<div class="tw"><table><thead><tr>{h}</tr></thead><tbody>{b}</tbody></table></div>{n}'
+
+
+# ---------------------------------------------------------------- numbers
+S1 = {}
+for sz in sizes:
+    sub = [r for r in set1 if r["size"] == sz]
+    d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in sub])
+    dp = np.array([r["rungs"]["M1_perm_avg"]["delta_floor"] for r in sub])
+    do = np.array([r["rungs"]["M1_orth_avg"]["delta_floor"] for r in sub])
+    fl = np.mean([r["floor"] for r in sub])
+    S1[sz] = dict(n=len(sub), floor=fl, d0=d0.mean(), dp=dp.mean(), do=do.mean(),
+                  resc=float(np.mean(1 - dp / d0) * 100), abs_p=fl + dp.mean(), abs_0=fl + d0.mean())
+
+BL = {}
+for sz in sorted({b["size"] for b in blimp}, key=lambda s: int(s[:-1])):
+    sub = [b for b in blimp if b["size"] == sz]
+    ce = np.mean([b["ceiling"] for b in sub])
+    BL[sz] = dict(n=len(sub), ceil=ce,
+                  par=float(np.mean([np.mean(list(b["parent_acc"].values())) for b in sub])),
+                  m0=float(np.mean([b["rungs"]["M0_naive_avg"]["blimp_acc"] for b in sub])),
+                  m1=float(np.mean([b["rungs"]["M1_perm_avg"]["blimp_acc"] for b in sub])),
+                  keep=float(np.mean([b["rungs"]["M1_perm_avg"]["blimp_acc"] for b in sub]) - 0.5) / (ce - 0.5) * 100)
+
+conf = []
+if os.path.exists(f"{R}/predictor_confirmatory.csv"):
+    rows = [l.rstrip("\n").split(",") for l in open(f"{R}/predictor_confirmatory.csv")]
+    ix = {h: i for i, h in enumerate(rows[0])}
+    for d in rows[1:]:
+        try:
+            conf.append(dict(sub=d[ix["substrate"]], pred=d[ix["predictor"]],
+                             auroc=float(d[ix["auroc_heldout_by_seed"]]),
+                             p=float(d[ix["perm_p"]] or "nan"),
+                             q=float(d[ix["bh_q_within_confirmatory_family"]] or "nan")))
+        except Exception: pass
+sig = [c for c in conf if c["q"] == c["q"] and c["q"] < 0.05]
+tested = [c for c in conf if c["q"] == c["q"]]
+cs_by = {c["sub"]: c["auroc"] for c in conf if "coordinate share" in c["pred"]}
+
+s4e0 = np.mean([r["rungs"]["M0_naive_avg"]["delta_floor_eng"] for r in set4]) if set4 else float("nan")
+s4eb = min(np.mean([r["rungs"][k]["delta_floor_eng"] for r in set4])
+           for k in set4[0]["rungs"] if k.startswith("M1")) if set4 else float("nan")
+mb_e0 = float(np.mean([r["rungs"]["M0_naive_avg"]["mb_eng"] for r in mb])) if mb else float("nan")
+mb_par = mb[0]["parents"]["eng_on_mb_eng"] if mb else float("nan")
+bg_m0 = float(np.mean([r["rungs"]["M0_naive_avg"]["multiblimp_mean"] for r in bgm])) if bgm else float("nan")
+bg_m1 = max(float(np.mean([r["rungs"][k]["multiblimp_mean"] for r in bgm]))
+            for k in bgm[0]["rungs"] if k.startswith("M1")) if bgm else float("nan")
+bg_ce = float(np.mean([0.5 * (r["ceiling_mb_eng"] + r["ceiling_mb_x"]) for r in bgm])) if bgm else float("nan")
+
+# ---------------------------------------------------------------- findings
+_d0s = " · ".join("<b>%s</b> +%.1f" % (sz, S1[sz]["d0"]) for sz in sizes)
+_rescs = " · ".join("<b>%s</b> %.0f%%" % (sz, S1[sz]["resc"]) for sz in sizes)
+_abss = " · ".join("%.1f" % S1[sz]["abs_p"] for sz in sizes)
+_flmin = min(S1[s_]["floor"] for s_ in sizes)
+_flmax = max(S1[s_]["floor"] for s_ in sizes)
+_cs_str = " · ".join("%s %.2f" % (k.split("-")[1], v)
+                     for k, v in sorted(cs_by.items(), key=lambda kv: int(kv[0].split("-")[1][:-1])))
+_sig_str = (" (%s, coordinate share, AUROC %.2f, q=%.3f)" % (sig[0]["sub"], sig[0]["auroc"], sig[0]["q"])) if sig else ""
+FIND = []
+FIND.append(("Naive averaging destroys the model — at every size",
+  f"Two PolyPythia checkpoints differ only in the seed: same data, same architecture, same tokenizer. "
+  f"Averaging their weights costs {_d0s} nats/token against parent floors of "
+  f"{_flmin:.1f}–{_flmax:.1f}. "
+  f"At the three smallest sizes the merged model is worse than predicting uniformly over the "
+  f"vocabulary ({UNIF:.1f} nats/token). This is the pure-coordinate case — there is no data, "
+  f"architecture or tokenizer difference left to blame."))
+FIND.append(("Unit alignment removes most of the gap and still leaves an unusable model",
+  f"The exactly function-preserving permutation rung (residual basis + free MLP axis + attention "
+  f"heads) removes {_rescs} of that penalty. "
+  f"What is left is {_abss} nats/token absolute. "
+  f"Alignment <em>predicts and reduces</em> the obstruction without <em>enabling</em> the merge."))
+FIND.append(("The rescue shrinks monotonically with scale",
+  f"From {S1[sizes[0]]['resc']:.0f}% at {sizes[0]} to {S1[sizes[-1]]['resc']:.0f}% at {sizes[-1]}. "
+  f"The naive penalty shrinks with scale too — but the coordinate-removable <em>share</em> of it "
+  f"shrinks faster. Alignment has the most purchase exactly where the obstruction matters least, "
+  f"and loses it in the direction the field is scaling."))
+if BL:
+    k0 = list(BL)[0]
+    FIND.append(("The likelihood rescue buys almost no accuracy",
+      f"Same merges, scored on BLiMP. On pythia-{k0} (n={BL[k0]['n']}) the parents average "
+      f"{BL[k0]['par']:.3f}; the naive merge {BL[k0]['m0']:.3f} and the aligned merge "
+      f"{BL[k0]['m1']:.3f}, against chance 0.500. A ~70% Δfloor rescue is worth about "
+      f"{BL[k0]['m1'] - BL[k0]['m0']:+.3f} accuracy. Across the whole scale ladder the share of the "
+      f"parents' above-chance margin the merge retains stays near a fifth, while the likelihood "
+      f"rescue varies sixfold. Pair by pair, the two rescues are uncorrelated."))
+FIND.append(("On the real bilingual models, the wall is the vocabulary",
+  f"Goldfish eng×{{nld,spa,ell,pol}}: the naive merge is +{s4e0:.2f} nats/byte over the English "
+  f"parent's 0.81 floor, and the best aligned rung is +{s4eb:.2f} — no better. The English "
+  f"tokenizer cannot represent 45% of Greek or 11% of Polish, and no permutation or rotation acts "
+  f"on the vocabulary axis. Anchoring on the partner language instead (their tokenizers handle "
+  f"English at &lt;0.1% unknown) removes that wall — and the merge still fails."))
+if bgm:
+    FIND.append(("Give alignment a shared vocabulary and it finally does something. It is still not enough.",
+      f"Merging two <em>bilingual</em> B-GPT models of the same language pair — ~94% tokenizer "
+      f"overlap instead of 13–28% — vocabulary transport plus unit alignment lifts MultiBLiMP from "
+      f"{bg_m0:.3f} to {bg_m1:.3f}. The parents sit at {bg_ce:.2f}. Vocabulary is the wall in the "
+      f"composition setting; independent training is the wall behind it."))
+if mb:
+    FIND.append(("Likelihood and accuracy dissociate in <em>both</em> directions",
+      f"In the seed setting a large likelihood rescue buys no accuracy. In the bilingual setting the "
+      f"reverse: a merge whose Δfloor says it is destroyed still scores {mb_e0:.2f} on "
+      f"MultiBLiMP-English against a parent at {mb_par:.2f} and chance at 0.50. Neither metric may "
+      f"be reported as a proxy for the other."))
+FIND.append(("The predictors do not predict the rescue",
+  f"Held out by seed pair, with a seed-cluster permutation null and Benjamini–Hochberg within the "
+  f"five predictors the brief itself names: <b>{len(sig)} of {len(tested)} cells significant</b>"
+  f"{_sig_str}. That predictor's held-out AUROC across four complete 36-pair grids is {_cs_str}"
+  " — it does not replicate. Nothing survives correction in the wider exploratory family either."))
+if abl:
+    wc_a = float(np.mean([r["predictors"]["weight_cosine"] for r in abl]))
+    m160 = [r for r in set1 if r["size"] == "160m"]
+    wc_m = float(np.mean([r["predictors"]["weight_cosine"] for r in m160])) if m160 else float("nan")
+    d_a = float(np.mean([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in abl]))
+    FIND.append(("What remains after alignment is not coordinate",
+      f"A same-basin control — the 160M Pythia data-seed / weight-seed ablations, weight cosine "
+      f"{wc_a:.2f} against {wc_m:.2f} for two PolyPythia seeds — still pays ~{d_a:.1f} nats/token to "
+      f"a naive average, and alignment removes only a few percent of it. Correctly: there is no "
+      f"coordinate mismatch left to remove. Merging is not free inside a basin either."))
+if rep or slp:
+    FIND.append(("Not an under-trying artifact",
+      "Naive averaging, permutation alignment, Procrustes, task arithmetic, TIES, SLERP — the "
+      "operator practitioners actually use — and REPAIR-style pre-activation statistics correction "
+      "were all run on the same pairs. REPAIR is the best training-free merge here and takes a "
+      "further bite out of the likelihood gap; BLiMP does not follow it at all. SLERP is worse than "
+      "a plain average. Alignment is what moves the number; the operator on top of it barely matters."))
+
+find_html = "".join(
+    f'<li class="find"><div class="fnum">{i + 1:02d}</div><div class="fbody">'
+    f'<h3>{t}</h3><p>{b}</p></div></li>' for i, (t, b) in enumerate(FIND))
+
+# ---------------------------------------------------------------- tables
+t_scale = table(
+    ["substrate", "pairs", "parent floor", "naive Δfloor", "aligned Δfloor", "rescue", "absolute, aligned"],
+    [[f"pythia-{sz}", S1[sz]["n"], f"{S1[sz]['floor']:.2f}", f"+{S1[sz]['d0']:.1f}",
+      f"+{S1[sz]['dp']:.1f}", f"{S1[sz]['resc']:.0f}%",
+      f"{S1[sz]['abs_p']:.1f}" + (" ⚠" if S1[sz]["abs_p"] > UNIF else "")] for sz in sizes],
+    note=f"nats/token on FLORES-200 English devtest. ⚠ marks a merged model worse than predicting "
+         f"uniformly over the 50,304-token vocabulary ({UNIF:.2f} nats/token). The aligned rung is the "
+         f"permutation family, verified function-preserving to float32 noise.")
+
+t_blimp = table(["substrate", "pairs", "parents", "naive merge", "aligned merge", "margin retained"],
+                [[f"pythia-{sz}", BL[sz]["n"], f"{BL[sz]['par']:.3f}", f"{BL[sz]['m0']:.3f}",
+                  f"{BL[sz]['m1']:.3f}", f"{BL[sz]['keep']:.0f}%"] for sz in BL],
+                note="BLiMP accuracy, 67 paradigms, chance = 0.500. \"Margin retained\" is the share of "
+                     "the parents' above-chance margin the aligned merge keeps.") if BL else ""
+
+t_conf = table(["substrate", "predictor", "AUROC held out by seed", "perm p", "BH q"],
+               [[c["sub"], c["pred"], f"{c['auroc']:.3f}",
+                 ("—" if c["p"] != c["p"] else f"{c['p']:.3f}"),
+                 ("—" if c["q"] != c["q"] else f"{c['q']:.3f}")] for c in conf],
+               note="Outcome: the share of the naive merge's Δfloor that alignment removes, split at the "
+                    "within-substrate median. Null: 2,000 seed-cluster permutations, which preserve the "
+                    "dependence between pairs built from 9 shared seeds.") if conf else ""
+
+cov = []
+for sz in ["14m", "31m", "70m", "160m", "410m"]:
+    n = len([r for r in set1 if r["size"] == sz])
+    tot = 36 if sz != "410m" else 15
+    cov.append([f"SET 1 Δfloor · pythia-{sz}", f"{n}/{tot}",
+                "complete" if n >= tot else ("partial" if n else "not run")])
+nb = {}
+for b in blimp: nb[b["size"]] = nb.get(b["size"], 0) + 1
+cov.append(["BLiMP accuracy · SET 1", ", ".join(f"{k} {v}/36" for k, v in sorted(nb.items(), key=lambda kv: int(kv[0][:-1]))), "ran"])
+nr = {}
+for r_ in rep: nr[r_["size"]] = nr.get(r_["size"], 0) + 1
+cov.append(["REPAIR rung", ", ".join(f"{k} {v}/36" for k, v in sorted(nr.items(), key=lambda kv: int(kv[0][:-1]))) or "0", "ran" if rep else "not run"])
+ns = {}
+for r_ in slp: ns[r_["size"]] = ns.get(r_["size"], 0) + 1
+cov.append(["SLERP rung", ", ".join(f"{k} {v}/36" for k, v in sorted(ns.items(), key=lambda kv: int(kv[0][:-1]))) or "0", "ran" if slp else "not run"])
+nc = {}
+for r_ in crb: nc[r_["size"]] = nc.get(r_["size"], 0) + 1
+cov.append(["Corpus robustness (Pile, WikiText)", ", ".join(f"{k} {v}/36" for k, v in sorted(nc.items(), key=lambda kv: int(kv[0][:-1]))) or "0", "ran" if crb else "not run"])
+cov.append(["SET 4 Δfloor · Goldfish, both anchoring directions", f"{len(set4)}/4 and {len(load('set4_reverse.jsonl'))}/4", "complete" if len(set4) == 4 else "partial"])
+cov.append(["MultiBLiMP accuracy · SET 4", f"{len(mb)}/4", "ran" if mb else "not run"])
+cov.append(["Jointly-trained bilingual ceiling (B-GPT)", f"{len(bgc)}/4", "ran" if bgc else "not run"])
+cov.append(["Bilingual × bilingual merge (B-GPT en_X × X_en)", f"{len(bgm)}/4", "ran" if bgm else "not run"])
+cov.append(["Task arithmetic / TIES on SET 4", "—", "not applicable: no shared ancestor"])
+cov.append(["Post-merge finetuning", "—", "out of scope: this audit is training-free"])
+cov.append(["Any task beyond minimal-pair grammaticality", "—", "not run"])
+t_cov = table(["cell", "n", "status"], cov)
+
+CSS = """
+:root{
+  --ground:#F4F6F5; --surface:#FFFFFF; --ink:#131A19; --muted:#5C6764; --faint:#7C8784;
+  --rule:#DBE2DF; --rule-soft:#E9EEEC; --accent:#0F5F58; --accent-soft:#E3EFEC;
+  --warn:#A4402F; --warn-soft:#F6E9E6; --shadow:0 1px 2px rgba(19,26,25,.05);
+}
+@media (prefers-color-scheme:dark){
+  :root:not([data-theme="light"]){
+    --ground:#0E1312; --surface:#161C1B; --ink:#E7EDEB; --muted:#98A3A0; --faint:#7C8784;
+    --rule:#28302E; --rule-soft:#1E2523; --accent:#5CC4B7; --accent-soft:#16302C;
+    --warn:#E28572; --warn-soft:#2E1B17; --shadow:none;
+  }
+}
+:root[data-theme="dark"]{
+  --ground:#0E1312; --surface:#161C1B; --ink:#E7EDEB; --muted:#98A3A0; --faint:#7C8784;
+  --rule:#28302E; --rule-soft:#1E2523; --accent:#5CC4B7; --accent-soft:#16302C;
+  --warn:#E28572; --warn-soft:#2E1B17; --shadow:none;
+}
+*{box-sizing:border-box}
+body{
+  margin:0; background:var(--ground); color:var(--ink);
+  font-family:"IBM Plex Sans","Helvetica Neue",Arial,sans-serif;
+  font-size:16.5px; line-height:1.62; -webkit-font-smoothing:antialiased;
+}
+.wrap{max-width:1080px;margin:0 auto;padding:0 28px 96px}
+.col{max-width:68ch}
+h1,h2,h3{font-family:Spectral,Georgia,"Times New Roman",serif;font-weight:600;text-wrap:balance;margin:0}
+h1{font-size:clamp(2.2rem,5.2vw,3.5rem);line-height:1.08;letter-spacing:-.015em}
+h2{font-size:clamp(1.35rem,2.6vw,1.8rem);line-height:1.2;margin-bottom:.5rem}
+h3{font-size:1.06rem;line-height:1.32;font-weight:600}
+p{margin:0 0 1rem}
+a{color:var(--accent);text-decoration:none;border-bottom:1px solid color-mix(in srgb,var(--accent) 35%,transparent)}
+a:hover{border-bottom-color:var(--accent)}
+a:focus-visible,summary:focus-visible{outline:2px solid var(--accent);outline-offset:3px;border-radius:2px}
+.eyebrow{font-family:"IBM Plex Mono",ui-monospace,Menlo,monospace;font-size:.7rem;letter-spacing:.16em;
+  text-transform:uppercase;color:var(--accent);margin:0 0 1.1rem}
+header.hero{padding:80px 0 40px;border-bottom:1px solid var(--rule)}
+.lede{font-size:1.16rem;color:var(--muted);margin-top:1.3rem;max-width:64ch}
+.meta{display:flex;flex-wrap:wrap;gap:10px 26px;margin-top:2rem;
+  font-family:"IBM Plex Mono",ui-monospace,monospace;font-size:.74rem;color:var(--faint)}
+.meta b{color:var(--ink);font-weight:500}
+section{padding:56px 0 8px;border-bottom:1px solid var(--rule-soft)}
+section:last-of-type{border-bottom:none}
+.kicker{font-family:"IBM Plex Mono",ui-monospace,monospace;font-size:.7rem;letter-spacing:.14em;
+  text-transform:uppercase;color:var(--faint);margin:0 0 .6rem}
+.stats{display:grid;grid-template-columns:repeat(auto-fit,minmax(178px,1fr));gap:1px;
+  background:var(--rule);border:1px solid var(--rule);margin:34px 0 8px}
+.stat{background:var(--surface);padding:20px 22px}
+.stat .v{font-family:"IBM Plex Mono",ui-monospace,monospace;font-size:1.72rem;font-weight:500;
+  letter-spacing:-.02em;font-variant-numeric:tabular-nums;line-height:1.1}
+.stat .v.bad{color:var(--warn)}
+.stat .k{font-size:.78rem;color:var(--muted);margin-top:.5rem;line-height:1.4}
+ol.finds{list-style:none;margin:34px 0 0;padding:0;display:flex;flex-direction:column;gap:0}
+li.find{display:grid;grid-template-columns:56px 1fr;gap:22px;padding:26px 0;border-top:1px solid var(--rule-soft)}
+li.find:first-child{border-top:1px solid var(--rule)}
+.fnum{font-family:"IBM Plex Mono",ui-monospace,monospace;font-size:.86rem;color:var(--accent);
+  padding-top:.22rem;font-variant-numeric:tabular-nums}
+.fbody{max-width:66ch}
+.fbody h3{margin-bottom:.45rem}
+.fbody p{margin:0;color:var(--muted)}
+.fbody b{color:var(--ink);font-weight:600;font-variant-numeric:tabular-nums}
+.tw{overflow-x:auto;border:1px solid var(--rule);background:var(--surface);margin:26px 0 0}
+table{border-collapse:collapse;width:100%;font-size:.85rem;
+  font-family:"IBM Plex Mono",ui-monospace,monospace;font-variant-numeric:tabular-nums}
+th,td{padding:9px 15px;text-align:right;white-space:nowrap;border-bottom:1px solid var(--rule-soft)}
+th:first-child,td:first-child{text-align:left}
+thead th{font-size:.68rem;letter-spacing:.07em;text-transform:uppercase;color:var(--faint);
+  font-weight:500;border-bottom:1px solid var(--rule);background:var(--surface);position:sticky;top:0}
+tbody tr:last-child td{border-bottom:none}
+.tnote{font-size:.78rem;color:var(--faint);margin:.65rem 0 0;max-width:74ch;line-height:1.55}
+.fig{margin:30px 0 0;padding:0}
+.fig img{display:block;width:100%;height:auto;border:1px solid var(--rule);background:#fff}
+.fig figcaption{font-size:.78rem;color:var(--faint);margin-top:.6rem;max-width:74ch;line-height:1.55}
+.callout{border-left:2px solid var(--warn);background:var(--warn-soft);padding:18px 22px;margin:28px 0 0;max-width:70ch}
+.callout p{margin:0;font-size:.94rem}
+.callout strong{color:var(--warn)}
+.note{border-left:2px solid var(--accent);background:var(--accent-soft);padding:18px 22px;margin:28px 0 0;max-width:70ch}
+.note p{margin:0;font-size:.94rem}
+details{border-top:1px solid var(--rule-soft);padding:14px 0}
+summary{cursor:pointer;font-family:"IBM Plex Mono",ui-monospace,monospace;font-size:.8rem;
+  color:var(--accent);list-style:none}
+summary::-webkit-details-marker{display:none}
+summary::before{content:"+ ";color:var(--faint)}
+details[open] summary::before{content:"– "}
+details .col{padding-top:12px}
+footer{padding:52px 0 0;color:var(--faint);font-size:.82rem;border-top:1px solid var(--rule)}
+@media (max-width:640px){
+  .wrap{padding:0 18px 64px}
+  li.find{grid-template-columns:38px 1fr;gap:14px}
+  header.hero{padding:52px 0 30px}
+}
+@media (prefers-reduced-motion:reduce){*{animation:none!important;transition:none!important}}
+"""
+
+BODY = f"""
+<link rel="preconnect" href="https://fonts.googleapis.com">
+<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
+<link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=IBM+Plex+Mono:wght@400;500&family=IBM+Plex+Sans:wght@400;500;600&family=Spectral:wght@500;600&display=swap">
+<style>{CSS}</style>
+<div class="wrap">
+<header class="hero">
+  <p class="eyebrow">Evaluation audit · training-free · real models</p>
+  <h1>Merging without composition</h1>
+  <p class="lede">Does representational alignment predict and enable model merging? Tested on the
+  models the claim is about: {sum(S1[s]['n'] for s in sizes)} PolyPythia seed pairs across five
+  scales, and the Goldfish and B-GPT bilingual models — with a likelihood metric and an accuracy
+  metric measured on the same merges.</p>
+  <div class="meta">
+    <span><b>{sum(S1[s]['n'] for s in sizes)}</b> seed pairs</span>
+    <span><b>{len(sizes)}</b> model scales</span>
+    <span><b>7</b> merge operators</span>
+    <span><b>2</b> metric families</span>
+    <span>generated {time.strftime('%Y-%m-%d %H:%M UTC')}</span>
+  </div>
+</header>
+
+<section>
+  <p class="kicker">The short version</p>
+  <h2>Alignment reduces the obstruction. It does not enable the merge.</h2>
+  <div class="col">
+    <p>The manuscript's thesis — that representational alignment predicts and enables merging — was
+    demonstrated on one substrate while the bilingual composition models it is <em>about</em> only
+    ever got a naive merge that failed. This puts both on the same real models, and adds the accuracy
+    measurement the thesis needs and did not have.</p>
+  </div>
+  <div class="stats">
+    <div class="stat"><div class="v bad">+{S1[sizes[0]]['d0']:.0f}</div><div class="k">nats/token that a naive average costs at pythia-{sizes[0]}, against a parent floor of {S1[sizes[0]]['floor']:.1f}</div></div>
+    <div class="stat"><div class="v">{S1[sizes[0]]['resc']:.0f}% → {S1[sizes[-1]]['resc']:.0f}%</div><div class="k">of that penalty alignment removes, from {sizes[0]} to {sizes[-1]}</div></div>
+    <div class="stat"><div class="v">{BL[list(BL)[0]]['m0']:.2f} → {BL[list(BL)[0]]['m1']:.2f}</div><div class="k">BLiMP accuracy, naive → aligned merge, against parents at {BL[list(BL)[0]]['par']:.2f} and chance at 0.50</div></div>
+    <div class="stat"><div class="v">{len(sig)} / {len(tested)}</div><div class="k">pre-merge predictor cells that survive correction, held out by seed pair</div></div>
+  </div>
+  <div class="callout"><p><strong>Δfloor is a likelihood metric, not benchmark accuracy — and here
+  they come apart.</strong> We measured both on the same merges. In the seed setting a ~70% likelihood
+  rescue buys about 0.03 accuracy; in the bilingual setting a merge the likelihood metric calls
+  destroyed still scores {mb_e0:.2f} on MultiBLiMP-English. Neither number may stand in for the other.</p></div>
+</section>
+
+<section>
+  <p class="kicker">Findings</p>
+  <h2>Nine things the grid shows</h2>
+  <ol class="finds">{find_html}</ol>
+</section>
+
+<section>
+  <p class="kicker">Set 1 · PolyPythia seed pairs</p>
+  <h2>The pure-coordinate case</h2>
+  <div class="col"><p><code>EleutherAI/pythia-&lt;size&gt;-seed{{1..9}}</code>: same data, same
+  architecture, same tokenizer, different initialisation. C(9,2) = 36 pairs per size. Whatever stops
+  the merge here is a coordinate problem and nothing else — which is what makes the residual so
+  awkward for the thesis.</p></div>
+  {t_scale}
+  {img("set1_scale_trend.png", "Naive merge penalty and alignment rescue against model size",
+       "Both the obstruction and alignment's purchase on it shrink with scale — and the purchase shrinks faster.")}
+  {img("set1_dfloor_by_rung.png", "Delta-floor by merge rung for each model size",
+       "Every rung on every size. Task arithmetic and TIES are shown to document that the shared-base operators degenerate when the base is not shared: two PolyPythia seeds have no common ancestor.")}
+  <div class="note"><p>One rung is <b>not</b> an alignment. Applying the Procrustes residual map to a
+  PolyPythia parent costs that parent +27 nats/token on its own — LayerNorm subtracts the mean over
+  the residual axis and applies a learned elementwise gain, and neither commutes with a general
+  rotation. The permutation family is exact to float32 noise on both architectures. Every coordinate
+  claim here rests on the permutation rung.</p></div>
+</section>
+
+<section>
+  <p class="kicker">The accuracy test</p>
+  <h2>Does the likelihood rescue transfer?</h2>
+  <div class="col"><p>PolyPythia parents are English language models, so BLiMP applies directly to
+  their merges. Same pairs, same alignment, same merges as the table above.</p></div>
+  {t_blimp}
+  {img("set1_blimp_dissociation.png", "Likelihood rescue against accuracy rescue, and parents against merges",
+       "Left: each point is a seed pair. The size of the likelihood rescue carries no information about the size of the accuracy rescue. Right: parents against merges at each scale.")}
+</section>
+
+<section>
+  <p class="kicker">Set 4 · Goldfish and B-GPT</p>
+  <h2>The composition models themselves</h2>
+  <div class="col"><p>Merging a monolingual English model with a monolingual partner-language model
+  is the operation the manuscript is about. It fails, and unit alignment does not rescue it — but the
+  reason is not the one the coordinate story predicts. The two parents' tokenizers share 13–28% of
+  their surface forms, and the merged model lives in one parent's token-id space. The alignment group
+  acts on the residual basis; the obstruction is on the vocabulary axis.</p></div>
+  {img("set4_joint_ceiling.png", "Bilingual ceiling versus parents versus merges, likelihood and accuracy",
+       "What success would look like. A jointly-trained bilingual model of the same budget is good at both languages at once; no merge of two monolinguals comes close, on either metric. All arms re-scored at a matched 128-token context.")}
+  {img("set4_dfloor.png", "Delta-floor by rung for each Goldfish language pair",
+       "Nine rungs, four language pairs, and no rung meaningfully better than the naive average.")}
+  {img("set4_likelihood_vs_accuracy.png", "MultiBLiMP accuracy against delta-floor for every Goldfish rung",
+       "The other direction of the dissociation. Every merge sits about a nat per byte above the English parent — by the likelihood metric, destroyed — and every one of them still scores far above chance on MultiBLiMP-English.")}
+</section>
+
+<section>
+  <p class="kicker">P0-2 · Predictor validation</p>
+  <h2>Do the pre-merge predictors predict the rescue?</h2>
+  <div class="col"><p>The confirmatory family is the five predictors the brief itself names, on the
+  one outcome it asks about, fixed before looking at the results. Held out by seed: each fold drops
+  every pair touching one seed and fits on the pairs touching neither, so the predictor's direction
+  never sees the held-out data.</p></div>
+  {t_conf}
+  {img("set1_roc.png", "ROC curves for the coordinate share predictor at each model size",
+       "The same predictor, the same outcome, four complete 36-pair grids of the same model family differing only in size.")}
+  {img("set1_rescue_vs_predictor.png", "Realised rescue against coordinate share and against CKA",
+       "The clusters separate by scale, not by predictor value. Within a substrate the relationship is weak; between substrates it is confounded with size.")}
+</section>
+
+<section>
+  <p class="kicker">Coverage</p>
+  <h2>What ran, and what did not</h2>
+  {t_cov}
+  <details><summary>Threats to validity</summary><div class="col">
+  <p><b>BLiMP and MultiBLiMP are minimal-pair grammaticality benchmarks.</b> They are a real accuracy
+  measurement and not a general one. A merge that scores 0.68 on MultiBLiMP-English is not thereby a
+  usable model — agreement minimal pairs are forgiving of a degraded model, because the two candidates
+  differ in one inflected token.</p>
+  <p><b>PolyPythia's <code>-seed{{n}}</code> repos reseed initialisation and data order together.</b>
+  The 160M ablations separate them only at n=3 pairs each, and both of those families turn out to sit
+  in the same basin.</p>
+  <p><b>The alignment search is the permutation group plus its orthogonal relaxation</b>, plus
+  embedding-row Procrustes for the cross-tokenizer case. It is not the full symmetry group. A better
+  aligner could raise the aligned rungs; nothing here bounds how far. What is bounded is the claim
+  that the aligners already in the codebase do the job on these substrates.</p>
+  <p><b>The largest scales carry the fewest pairs.</b> The complete 36-pair grids are 14m, 31m, 70m
+  and 160m; 410m is partial and directional.</p>
+  <p><b>Everything is training-free by construction.</b> No claim is made about what post-merge
+  finetuning would recover — that is the obvious next experiment and out of scope for this audit.</p>
+  </div></details>
+</section>
+
+<footer>
+  <p>Full report, per-pair records, predictor tables and every script:
+  <a href="{HF}">{HF.replace('https://', '')}</a>.
+  Merge operators, aligners, quotient metrics and the linear-mode-connectivity barrier are imported
+  unmodified from <code>mergeschool.core</code>; the GPT-2 Conv1D symmetry factors and the evaluation
+  harness are new here.</p>
+</footer>
+</div>
+"""
+
+open("/root/compose-audit/compose_audit.html", "w", encoding="utf-8").write(
+    "<title>Merging Without Composition</title>\n" + BODY)
+print("artifact html written:", len(BODY), "chars")

code/make_report.py

@@ -28,7 +28,13 @@ def fmt(x, n=3):
         return str(x)
 
 
-set1 = load("set1_*.jsonl")
+set1 = load("set1_*.jsonl") + load("set1x_*.jsonl")
+_seen, _ded = set(), []
+for _r in set1:
+    _k = (_r["size"], tuple(_r["pair"]))
+    if _k in _seen: continue
+    _seen.add(_k); _ded.append(_r)
+set1 = _ded
 set4 = load("set4_goldfish.jsonl")
 VOCAB = {"14m": 50304, "70m": 50304, "160m": 50304}
 sizes = sorted({r["size"] for r in set1}, key=lambda s: int(s[:-1]))
@@ -139,7 +145,24 @@ if set1:
                   f"rescue it.** Goldfish eng×{{nld,spa,ell,pol}}: naive Δfloor on English text "
                   f"+{d0e:.2f} nats/byte against a 0.81 floor; the best M1 rung +{bst:.2f}. The binding "
                   f"constraint is the **vocabulary**, not the coordinate frame — the English tokenizer "
-                  f"UNK-s 45% of Greek and 11% of Polish, and no permutation or rotation can address that.")
+                  f"UNK-s 45% of Greek and 11% of Polish, and no permutation or rotation can address "
+                  f"that. Anchoring on the partner language instead (whose tokenizers handle English "
+                  f"at <0.1% UNK) removes that wall and the merge still fails.")
+    _bgm2 = load("bgpt_merge.jsonl")
+    if _bgm2:
+        _rk2 = list(_bgm2[0]["rungs"])
+        _n0 = float(np.mean([r["rungs"]["M0_naive_avg"]["multiblimp_mean"] for r in _bgm2]))
+        _nb = max(float(np.mean([r["rungs"][k]["multiblimp_mean"] for r in _bgm2])) for k in _rk2 if k.startswith("M1"))
+        _f0 = float(np.mean([r["rungs"]["M0_naive_avg"]["delta_floor_mean"] for r in _bgm2]))
+        _fb = min(float(np.mean([r["rungs"][k]["delta_floor_mean"] for r in _bgm2])) for k in _rk2 if k.startswith("M1"))
+        _ce = float(np.mean([0.5 * (r["ceiling_mb_eng"] + r["ceiling_mb_x"]) for r in _bgm2]))
+        hl.append(f"5b. **Give alignment a shared vocabulary and it finally does something — still not "
+                  f"enough.** Merging two *bilingual* B-GPT models of the same language pair (~94% "
+                  f"tokenizer overlap instead of 13–28%), vocabulary transport plus unit alignment "
+                  f"moves MultiBLiMP from {_n0:.3f} to {_nb:.3f} and Δfloor from +{_f0:.2f} to "
+                  f"+{_fb:.2f} nats/byte. The parents are at {_ce:.2f} and Δfloor 0. This is the "
+                  f"clean decomposition: vocabulary is the wall in SET 4, and independent training is "
+                  f"the wall behind it.")
     if _mb:
         hl.append(f"6. **…and the accuracy dissociation runs the other way there.** The same "
                   f"likelihood-destroyed Goldfish merges retain "
@@ -162,11 +185,27 @@ if set1:
               f"five-predictor family the audit brief itself names: **{len(_sg)} of {len(_tt)} cells "
               f"significant**"
               + (" (" + "; ".join(f"{c[0]}, {c[1]}, AUROC {c[2]:.2f}, q={c[3]:.3f}" for c in _sg) + ")" if _sg else "")
-              + ". It does not replicate across substrates — the same predictor sits below 0.5 at the "
-                "largest size — and nothing survives BH across the wider exploratory family. Reported "
-                "as the negative transfer result it is.")
+              + ". The carrying predictor is the coordinate share, whose held-out AUROC across the "
+              + "substrates is "
+              + " · ".join(f"{c[0].split('-')[1]}: {c[2]:.2f}"
+                           for c in sorted([c for c in _cf if "coordinate share" in c[1]],
+                                           key=lambda c: int(c[0].split('-')[1][:-1])))
+              + " — i.e. it does not replicate. Nothing survives BH across the wider exploratory "
+                "family either. Reported as the negative transfer result it is.")
+    _abl = load("abl_*.jsonl")
+    if _abl:
+        _wc_a = float(np.mean([r["predictors"]["weight_cosine"] for r in _abl]))
+        _m160 = [r for r in set1 if r["size"] == "160m"]
+        _wc_m = float(np.mean([r["predictors"]["weight_cosine"] for r in _m160])) if _m160 else float("nan")
+        _d_a = float(np.mean([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in _abl]))
+        hl.append(f"8. **The residual obstruction is not coordinate.** A same-basin control (the 160M "
+                  f"Pythia data-seed / weight-seed ablations, weight cosine {_wc_a:.2f} against "
+                  f"{_wc_m:.2f} for two PolyPythia seeds) still pays ~{_d_a:.1f} nats/token to a naive "
+                  f"average, and alignment removes only a few percent of it — correctly, since there is "
+                  f"no coordinate mismatch left. Merging is not free even inside a basin, and what "
+                  f"remains after alignment is not something the permutation group describes.")
     if _rp:
-        hl.append("8. **This is not an under-trying artifact.** REPAIR-style statistics correction on "
+        hl.append("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.")
     L.append("\n## Headline findings\n")
@@ -202,8 +241,10 @@ if set1:
    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.
+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.
 """)
 
 # ---------------- alignment health
@@ -236,6 +277,12 @@ gain, and neither commutes with a general rotation (an RMSNorm model would be mu
 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*
@@ -303,11 +350,16 @@ if set4:
                  "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:\n")
         L.append(md_table(["text", "UNK rate, English tokenizer", "UNK rate, own tokenizer",
+                           "UNK rate, partner tokenizer on ENGLISH text",
                            "bytes/token, English tok", "bytes/token, own tok"],
                           [[k, f"{v['eng_tok_unk_rate']:.1%}", f"{v['own_tok_unk_rate']:.1%}",
+                            (f"{v['partner_tok_unk_rate_on_ENGLISH_text']:.1%}"
+                             if 'partner_tok_unk_rate_on_ENGLISH_text' in v else "—"),
                             fmt(v['eng_tok_bytes_per_token'], 2), fmt(v['own_tok_bytes_per_token'], 2)]
                            for k, v in diag.items()]))
-        L.append("\nAt a 46.5% UNK rate the English parent's *apparent* likelihood on Greek text is an "
+        L.append("\n**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) "
@@ -348,13 +400,19 @@ if set4:
     _b.append(["**mean of the 4**"] + ["**" + fmt(float(np.mean([r["rungs"][k]["delta_floor_eng"] for r in set4]))) + "**"
                                        for k in rung_keys])
     L.append(md_table(["pair"] + rung_keys, _b))
-    L.append("\nAveraged over the four pairs the best M1 rung removes **"
-             + fmt(100 * (1 - min(np.mean([r["rungs"][k]["delta_floor_mean"] for r in set4]) for k in rung_keys if k.startswith("M1"))
-                          / np.mean([r["rungs"]["M0_naive_avg"]["delta_floor_mean"] for r in set4])), 1)
-             + "%** of the naive merge's Δfloor. 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.\n")
+    _e0 = np.mean([r["rungs"]["M0_naive_avg"]["delta_floor_eng"] for r in set4])
+    _eb = min(np.mean([r["rungs"][k]["delta_floor_eng"] for r in set4]) for k in rung_keys if k.startswith("M1"))
+    _m0 = np.mean([r["rungs"]["M0_naive_avg"]["delta_floor_mean"] for r in set4])
+    _mb = min(np.mean([r["rungs"][k]["delta_floor_mean"] for r in set4]) for k in rung_keys if k.startswith("M1"))
+    L.append(f"""
+**On the clean English cell, every M1 rung is *worse* than the naive merge**: naive {_e0:.3f},
+best M1 {_eb:.3f} nats/byte averaged over the four pairs. Averaged over both languages the best M1
+rung removes {100 * (1 - _mb / _m0):.1f}% 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.
+""")
     L.append("\n**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):\n")
     L.append(md_table(hdr, body))
@@ -419,9 +477,15 @@ if blimp:
     L.append("""
 **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
+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 that the merged model retains does not track it
+at all: it sits at roughly a fifth at 14M, 31M and 70M and drops at 160M. Whatever the likelihood
+rescue is buying, it is not this benchmark, and the amount of it makes almost no difference.
 """)
     if corr_rows:
         L.append("\nPair by pair, does the size of the likelihood rescue predict the size of the "
@@ -472,6 +536,64 @@ alignment were all tried on the same pairs; the best of them recovers most of th
 14M, a quarter of it at 160M, and grammatical competence in none of them.
 """)
 
+# ---------------- corpus robustness
+crb = load("corpus_*.jsonl")
+if crb:
+    L.append("\n### Robustness: is the Δfloor an artifact of the held-out corpus?\n")
+    L.append("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**:\n")
+    _cs = list(crb[0]["rungs"]["M0_naive_avg"].keys())
+    body = []
+    for sz in sorted({r["size"] for r in crb}, key=lambda x: int(x[:-1])):
+        sub = [r for r in crb if r["size"] == sz]
+        for c in _cs:
+            fl = np.mean([min(r["parent_nll"]["a"][c], r["parent_nll"]["b"][c]) for r in sub])
+            d0 = np.array([r["rungs"]["M0_naive_avg"][c]["delta_floor"] for r in sub])
+            d1 = np.array([r["rungs"]["M1_perm_avg"][c]["delta_floor"] for r in sub])
+            body.append([f"pythia-{sz}", len(sub), c, fmt(fl, 2), fmt(d0.mean(), 2), fmt(d1.mean(), 2),
+                         fmt(np.mean(1 - d1 / d0) * 100, 1) + "%"])
+    L.append(md_table(["substrate", "n pairs", "corpus", "parent floor", "naive Δfloor",
+                       "Δfloor permutation-aligned", "rescue"], body))
+    L.append("\n**It is not a corpus artifact.** The parent floors move with domain, as they should, "
+             "but the naive Δfloor, the aligned Δfloor and the rescue fraction are stable across all "
+             "three corpora — including the in-distribution Pile sample. The merge penalty is a "
+             "property of the merge, not of the evaluation set.\n")
+
+# ---------------- SLERP
+slp = load("slerp_*.jsonl")
+if slp:
+    L.append("\n## The operator practitioners actually use · SLERP\n")
+    L.append("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.\n")
+    rk = ["M0_naive_avg", "M1_perm_avg", "M6_slerp", "M7_perm_slerp"]
+    body = []
+    for sz in sorted({r["size"] for r in slp}, key=lambda x: int(x[:-1])):
+        sub = [r for r in slp if r["size"] == sz]
+        ce = np.mean([r["blimp_ceiling"] for r in sub])
+        for k in rk:
+            if k not in sub[0]["rungs"]: continue
+            d = np.array([r["rungs"][k]["delta_floor"] for r in sub])
+            a = np.array([r["rungs"][k]["blimp_acc"] for r in sub])
+            body.append([f"pythia-{sz}", len(sub), k, fmt(d.mean(), 2), fmt(a.mean())])
+        body.append([f"pythia-{sz}", len(sub), "**parents**", "0.00", fmt(ce)])
+    L.append(md_table(["substrate", "n pairs", "rung", "mean Δfloor (nats/tok)", "BLiMP accuracy"], body))
+    L.append("""
+**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 adds to it. Applied *after* unit alignment it comes back to roughly
+where the aligned average already was. 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 accuracy arm
 mb = load("set4_multiblimp.jsonl")
 if mb:
@@ -553,6 +675,55 @@ aligner might close; the joint model also has a *shared vocabulary*, which is ex
 alignment group cannot act on.
 """)
 
+bgm = load("bgpt_merge.jsonl")
+if bgm:
+    L.append("\n## SET 4c · merging two BILINGUAL models of the same language pair\n")
+    L.append("""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.)\n""")
+    rk = list(bgm[0]["rungs"])
+    L.append(md_table(["pair", "vocab overlap", "parent A / B, nats/byte (eng, X)", "parent A / B, MultiBLiMP (eng, X)"],
+                      [[f"en–{r['lang'].split('_')[0]}", f"{r['vocab_overlap']:.0%}",
+                        f"{r['parents']['A']['nats_per_byte_eng']:.2f}/{r['parents']['A']['nats_per_byte_x']:.2f} · "
+                        f"{r['parents']['B']['nats_per_byte_eng']:.2f}/{r['parents']['B']['nats_per_byte_x']:.2f}",
+                        f"{r['parents']['A']['multiblimp_eng']:.2f}/{r['parents']['A']['multiblimp_x']:.2f} · "
+                        f"{r['parents']['B']['multiblimp_eng']:.2f}/{r['parents']['B']['multiblimp_x']:.2f}"] for r in bgm]))
+    L.append("\n**Δfloor, mean over the two languages (nats/UTF-8 byte, lower better):**\n")
+    _b = [[f"en–{r['lang'].split('_')[0]}"] + [fmt(r["rungs"][k]["delta_floor_mean"]) for k in rk] for r in bgm]
+    _b.append(["**mean**"] + ["**" + fmt(float(np.mean([r["rungs"][k]["delta_floor_mean"] for r in bgm]))) + "**" for k in rk])
+    L.append(md_table(["pair"] + rk, _b))
+    L.append("\n**MultiBLiMP, mean over the two languages (accuracy, higher better; parent ceiling in the last column):**\n")
+    _b = [[f"en–{r['lang'].split('_')[0]}"] + [fmt(r["rungs"][k]["multiblimp_mean"]) for k in rk]
+          + [fmt(0.5 * (r["ceiling_mb_eng"] + r["ceiling_mb_x"]))] for r in bgm]
+    _b.append(["**mean**"] + ["**" + fmt(float(np.mean([r["rungs"][k]["multiblimp_mean"] for r in bgm]))) + "**" for k in rk]
+              + ["**" + fmt(float(np.mean([0.5 * (r["ceiling_mb_eng"] + r["ceiling_mb_x"]) for r in bgm]))) + "**"])
+    L.append(md_table(["pair"] + rk + ["parent ceiling"], _b))
+    _m0 = float(np.mean([r["rungs"]["M0_naive_avg"]["multiblimp_mean"] for r in bgm]))
+    _mb = max(float(np.mean([r["rungs"][k]["multiblimp_mean"] for r in bgm])) for k in rk if k.startswith("M1"))
+    _d0 = float(np.mean([r["rungs"]["M0_naive_avg"]["delta_floor_mean"] for r in bgm]))
+    _db = min(float(np.mean([r["rungs"][k]["delta_floor_mean"] for r in bgm])) for k in rk if k.startswith("M1"))
+    L.append(f"""
+**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 {_m0:.3f} (naive) to {_mb:.3f} (best M1) and Δfloor from {_d0:+.3f} to {_db:+.3f}
+nats/byte. Both move in the right direction, and both leave the merge far from parents that sit near
+{float(np.mean([0.5 * (r['ceiling_mb_eng'] + r['ceiling_mb_x']) for r in bgm])):.2f} 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.
+""")
+
 rev = load("set4_reverse.jsonl")
 if rev:
     L.append("\n## SET 4 · reverse direction (the partner language is the anchor)\n")
@@ -689,16 +860,20 @@ That is a real effect and it should not be rounded down to zero. It should also
 The predictor that carries it is the **coordinate share** — exactly the quantity the manuscript's
 thesis is about — and the honest summary is:
 
-- **It does not replicate across substrates.** The same predictor's held-out AUROC across the sizes
-  we ran is not stable, and at the largest size it sits *below* 0.5, i.e. pointing the wrong way. A
-  quantity that predicts the rescue on one substrate and anti-predicts it on another is not a
-  validated instrument for "representational alignment predicts merging".
+- **It does not replicate across substrates.** The same predictor's held-out AUROC ranges from ~0.48
+  (chance, and slightly the wrong way) to 0.81 across four complete 36-pair grids of the *same*
+  model family differing only in size. A quantity that lands anywhere in that range 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 is likewise partial.** Fitting on the other sizes and testing on a
-  held-out one, the coordinate share transfers to some substrates and not to others (table above).
+- **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
@@ -723,41 +898,57 @@ negative transfer result from the synthetic/S3 setting to real models, and it is
 
 abl = load("abl_*.jsonl")
 if abl:
-    L.append("\n## Control · is the obstruction the INIT seed or the DATA order?\n")
-    L.append("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.\n")
+    L.append("\n## Control · same-basin vs different-basin pairs\n")
+    L.append("""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.\n""")
     body = []
-    for sz in sorted({r["size"] for r in abl}):
-        sub = [r for r in abl if r["size"] == sz]
+    def _row(label, sub):
         d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in sub])
         dp = np.array([r["rungs"]["M1_perm_avg"]["delta_floor"] for r in sub])
-        do = np.array([r["rungs"]["M1_orth_avg"]["delta_floor"] for r in sub])
+        wc = np.array([r["predictors"]["weight_cosine"] for r in sub])
+        dr = np.array([r["predictors"]["d_raw"] for r in sub])
         cs = np.array([r["predictors"]["coord_share_bnd_perm"] for r in sub])
-        body.append([sz, len(sub), fmt(float(np.mean([r["floor"] for r in sub])), 2), fmt(d0.mean(), 2),
-                     fmt(dp.mean(), 2), fmt(do.mean(), 2),
-                     fmt(np.mean(1 - np.minimum(dp, do) / d0) * 100, 1) + "%", fmt(cs.mean(), 4)])
-    main160 = [r for r in set1 if r["size"] == "160m"]
-    if main160:
-        d0 = np.array([r["rungs"]["M0_naive_avg"]["delta_floor"] for r in main160])
-        dp = np.array([r["rungs"]["M1_perm_avg"]["delta_floor"] for r in main160])
-        do = np.array([r["rungs"]["M1_orth_avg"]["delta_floor"] for r in main160])
-        cs = np.array([r["predictors"]["coord_share_bnd_perm"] for r in main160])
-        body.append(["160m (init+data, main grid)", len(main160),
-                     fmt(float(np.mean([r["floor"] for r in main160])), 2), fmt(d0.mean(), 2),
-                     fmt(dp.mean(), 2), fmt(do.mean(), 2),
-                     fmt(np.mean(1 - np.minimum(dp, do) / d0) * 100, 1) + "%", fmt(cs.mean(), 4)])
-    L.append(md_table(["seed variant", "n pairs", "parent floor", "naive Δfloor", "Δfloor perm",
-                       "Δfloor Procrustes", "rescue, best", "weight coordinate share"], body))
+        ck = np.array([r["predictors"]["cka_mean"] for r in sub])
+        return [label, len(sub), fmt(wc.mean()), fmt(dr.mean()), fmt(ck.mean()), fmt(cs.mean(), 4),
+                fmt(d0.mean(), 2), fmt(dp.mean(), 2), fmt(np.mean(1 - dp / d0) * 100, 1) + "%"]
+    for sz in sorted({r["size"] for r in abl}):
+        body.append(_row(f"`pythia-{sz}-seed{{1,2,3}}`", [r for r in abl if r["size"] == sz]))
+    _m160 = [r for r in set1 if r["size"] == "160m"]
+    if _m160:
+        body.append(_row("`pythia-160m-seed{1..9}` (main grid)", _m160))
+    L.append(md_table(["pairs", "n", "weight cosine", "d_raw", "CKA", "coordinate share",
+                       "naive Δfloor", "Δfloor perm", "rescue"], body))
     L.append("""
-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 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.
 """)
 
 L.append("\n## Coverage — what ran and what did not\n")
@@ -779,6 +970,18 @@ cov.append(["SET 1 accuracy · BLiMP", ", ".join(f"pythia-{k}: {v}/36" for k, v
             "67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges"])
 nr = {}
 for r_ in rep: nr[r_["size"]] = nr.get(r_["size"], 0) + 1
+_slp = load("slerp_*.jsonl")
+_ns = {}
+for r_ in _slp: _ns[r_["size"]] = _ns.get(r_["size"], 0) + 1
+_crb = load("corpus_*.jsonl")
+_nc = {}
+for r_ in _crb: _nc[r_["size"]] = _nc.get(r_["size"], 0) + 1
+cov.append(["SET 1 · corpus robustness", ", ".join(f"pythia-{k}: {v}/36" for k, v in sorted(_nc.items(), key=lambda kv: int(kv[0][:-1]))) or "0",
+            "RAN" if _crb else "**NOT RUN**",
+            "same pairs and merges re-scored on FLORES-200 eng, NeelNanda/pile-10k and WikiText-103 validation"])
+cov.append(["SET 1 · SLERP rung", ", ".join(f"pythia-{k}: {v}/36" for k, v in sorted(_ns.items(), key=lambda kv: int(kv[0][:-1]))) or "0",
+            "RAN" if _slp else "**NOT RUN**",
+            "M6 SLERP and M7 permutation-aligned SLERP on the same pairs; Δfloor and BLiMP"])
 cov.append(["SET 1 · REPAIR rung", ", ".join(f"pythia-{k}: {v}/36" for k, v in sorted(nr.items(), key=lambda kv: int(kv[0][:-1]))) or "0",
             "RAN" if rep else "**NOT RUN**", "M4 = permutation-aligned average + pre-activation statistics repair; M5 = naive + repair; Δfloor and BLiMP on the same merges"])
 cov.append(["SET 4 Δfloor · English-anchored", f"{len(set4)}/4 language pairs ({', '.join(r['lang'] for r in set4) or '—'})",
@@ -792,6 +995,12 @@ bg = load("bgpt_ceiling.jsonl")
 cov.append(["SET 4 · jointly-trained bilingual ceiling", f"{len(bg)}/4 language pairs",
             "RAN" if bg else "**NOT RUN**",
             "`catherinearnett/B-GPT_en_X_simultaneous` vs the Goldfish parents and merges, all scored at a matched 128-token context"])
+_bgm = load("bgpt_merge.jsonl")
+cov.append(["SET 4c · bilingual×bilingual merge (B-GPT en_X × X_en)", f"{len(_bgm)}/4 language pairs",
+            "RAN" if _bgm else "**NOT RUN**",
+            "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"])
+cov.append(["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)"])
 cov.append(["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."])
 cov.append(["SET 1 · pythia-410m full grid", f"{len([r for r in set1 if r['size'] == '410m'])}/36 possible pairs", "partial",
@@ -841,26 +1050,35 @@ L.append("""
 
 L.append("\n## Files\n")
 L.append("""```
-results/set1_{14m,31m,70m,160m,410m}.jsonl  SET 1 per-pair raw records (predictors, rungs, barriers)
+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        init-seed-only vs data-order-only control
+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_auroc.csv                 P0-2: held-out-by-seed AUROC, seed-cluster null, BH q
+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
+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
-code/*.py                                   every script that produced the above
+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

code/set1_corpus_robustness.py

@@ -0,0 +1,123 @@
+"""Robustness: is SET 1's Δfloor an artifact of the held-out corpus?
+
+The main SET 1 tables score on FLORES-200 English devtest, which is genuinely held out from
+PolyPythia training but out-of-domain for the Pile. A reviewer's first objection is that the merge
+penalty is inflated by domain shift. This re-scores a subset of the same pairs and the same merges on
+a **Pile sample** (`NeelNanda/pile-10k`, in-distribution for Pythia) and on **WikiText-103
+validation**, and reports the three side by side."""
+import os, sys, json, time, itertools, argparse, gc
+sys.path.insert(0, "/root/compose-audit")
+from common import *
+from transformers import AutoModelForCausalLM, AutoTokenizer
+from datasets import load_dataset
+
+ap = argparse.ArgumentParser()
+ap.add_argument("--size", default="14m")
+ap.add_argument("--seeds", default="1,2,3,4,5,6")
+ap.add_argument("--blocks", type=int, default=48)
+ap.add_argument("--bs", type=int, default=16)
+ap.add_argument("--acts_rows", type=int, default=2048)
+A = ap.parse_args()
+SEEDS = [int(s) for s in A.seeds.split(",")]
+OUT = f"/root/compose-audit/results/corpus_{A.size}.jsonl"
+DEV = "cuda"
+
+
+def log(*a): print(f"[{time.strftime('%H:%M:%S')}]", *a, flush=True)
+
+
+def neox_head_match(sd_a, sd_b, d, nh, nl):
+    hd, perms = d // nh, {}
+    for L in range(nl):
+        qk = f"gpt_neox.layers.{L}.attention.query_key_value.weight"
+        de = f"gpt_neox.layers.{L}.attention.dense.weight"
+        if qk not in sd_a: continue
+        Aq = np.asarray(sd_a[qk], float).reshape(nh, 3 * hd, d)
+        Bq = np.asarray(sd_b[qk], float).reshape(nh, 3 * hd, d)
+        Ad = np.asarray(sd_a[de], float).reshape(d, nh, hd)
+        Bd = np.asarray(sd_b[de], float).reshape(d, nh, hd)
+        perms[L] = AL._assignment(np.einsum("ixy,jxy->ij", Aq, Bq) + np.einsum("xiy,xjy->ij", Ad, Bd))
+    return perms
+
+
+def neox_apply_head(sd, perms, d, nh):
+    hd, o = d // nh, dict(sd)
+    for L, h in perms.items():
+        qk = f"gpt_neox.layers.{L}.attention.query_key_value.weight"
+        qb = f"gpt_neox.layers.{L}.attention.query_key_value.bias"
+        de = f"gpt_neox.layers.{L}.attention.dense.weight"
+        o[qk] = np.asarray(sd[qk], float).reshape(nh, 3 * hd, d)[h].reshape(3 * d, d)
+        if qb in sd: o[qb] = np.asarray(sd[qb], float).reshape(nh, 3 * hd)[h].reshape(3 * d)
+        o[de] = np.asarray(sd[de], float).reshape(d, nh, hd)[:, h].reshape(d, d)
+    return o
+
+
+def align_perm(sd_a, sd_b, d, aa, ab, nh, nl):
+    sd, _ = AL.align_weights_full(sd_a, sd_b, d, acts_a=aa, acts_b=ab, n_heads=None,
+                                  method="permutation", strict=True, accept_each=True)
+    hp = neox_head_match(sd_a, sd, d, nh, nl)
+    if hp:
+        cand = neox_apply_head(sd, hp, d, nh)
+        if AL.block_normalised_distance(sd_a, cand) <= AL.block_normalised_distance(sd_a, sd):
+            sd = cand
+    return sd
+
+
+tok = AutoTokenizer.from_pretrained(f"EleutherAI/pythia-{A.size}")
+CORPORA = {}
+CORPORA["flores_eng"] = make_blocks(tok, flores_lines("eng_Latn"), 512, A.blocks)
+try:
+    d = load_dataset("NeelNanda/pile-10k", split="train")
+    CORPORA["pile_10k"] = make_blocks(tok, [x for x in d["text"][:400]], 512, A.blocks)
+except Exception as e:
+    log("pile load failed", type(e).__name__, str(e)[:150])
+try:
+    d = load_dataset("Salesforce/wikitext", "wikitext-103-raw-v1", split="validation")
+    CORPORA["wikitext103_val"] = make_blocks(tok, [x for x in d["text"] if x.strip()][:4000], 512, A.blocks)
+except Exception as e:
+    log("wikitext load failed", type(e).__name__, str(e)[:150])
+log("corpora:", {k: tuple(v.shape) for k, v in CORPORA.items()})
+
+shell = AutoModelForCausalLM.from_pretrained(f"EleutherAI/pythia-{A.size}-seed{SEEDS[0]}",
+                                             dtype=torch.float32).to(DEV).eval()
+cfg = shell.config
+D, NH, NL = cfg.hidden_size, cfg.num_attention_heads, cfg.num_hidden_layers
+
+
+def ev_all(sd):
+    sd_load(shell, sd, DEV)
+    return {k: nll_nats(shell, b, DEV, bs=A.bs) for k, b in CORPORA.items()}
+
+
+SDS, ACTS, PAR = {}, {}, {}
+for s in SEEDS:
+    m = AutoModelForCausalLM.from_pretrained(f"EleutherAI/pythia-{A.size}-seed{s}", dtype=torch.float32).to(DEV).eval()
+    SDS[s] = sd_np(m); ACTS[s] = capture_acts(m, CORPORA["flores_eng"], DEV, n_rows=A.acts_rows, bs=A.bs)
+    del m; torch.cuda.empty_cache()
+    PAR[s] = ev_all(SDS[s])
+    log(f"  seed{s} {PAR[s]}")
+
+done = set()
+if os.path.exists(OUT):
+    for l in open(OUT):
+        try: done.add(tuple(json.loads(l)["pair"]))
+        except Exception: pass
+fh = open(OUT, "a")
+for a, b in itertools.combinations(SEEDS, 2):
+    if (a, b) in done: continue
+    t0 = time.time()
+    sbp = align_perm(SDS[a], SDS[b], D, ACTS[a], ACTS[b], NH, NL)
+    rungs = {"M0_naive_avg": MG.average([SDS[a], SDS[b]]), "M1_perm_avg": MG.average([SDS[a], sbp])}
+    res = {}
+    for k, sd in rungs.items():
+        nl_ = ev_all(sd)
+        res[k] = {c: {"nll": v, "delta_floor": v - min(PAR[a][c], PAR[b][c])} for c, v in nl_.items()}
+    r = {"set": "set1_corpus_robustness", "size": A.size, "pair": [a, b],
+         "parent_nll": {"a": PAR[a], "b": PAR[b]}, "rungs": res, "secs": time.time() - t0}
+    fh.write(json.dumps(r) + "\n"); fh.flush()
+    log(f"pair {a},{b} " + " | ".join(
+        f"{c}: M0 {res['M0_naive_avg'][c]['delta_floor']:+.2f} M1 {res['M1_perm_avg'][c]['delta_floor']:+.2f}"
+        for c in CORPORA) + f" ({r['secs']:.0f}s)")
+    del rungs, sbp; gc.collect()
+fh.close()
+log("DONE corpus", A.size)

code/set1_slerp.py

@@ -0,0 +1,212 @@
+"""The operator practitioners actually use: SLERP.
+
+Every rung in the main SET 1 table is a lab operator. A census of community merges on the Hub finds
+SLERP on ~25% of them -- more than TIES, DARE-TIES and task arithmetic combined -- and it needs no
+shared base, which is exactly why it gets reached for when merging two models with no common
+ancestor. That is the PolyPythia seed case. This adds it, on the same pairs, before and after unit
+alignment, with both metrics.
+
+Rungs: M0 naive average - M1 permutation-aligned average - M6 SLERP - M7 permutation-aligned SLERP.
+"""
+import os, sys, json, time, glob, itertools, argparse, gc, csv
+sys.path.insert(0, "/root/compose-audit")
+from common import *
+from transformers import AutoModelForCausalLM, AutoTokenizer
+import pyarrow.parquet as pq
+
+ap = argparse.ArgumentParser()
+ap.add_argument("--size", default="14m")
+ap.add_argument("--seeds", default="1,2,3,4,5,6,7,8,9")
+ap.add_argument("--blocks", type=int, default=48)
+ap.add_argument("--bs", type=int, default=16)
+ap.add_argument("--n_per_paradigm", type=int, default=200)
+ap.add_argument("--acts_rows", type=int, default=2048)
+A = ap.parse_args()
+SEEDS = [int(s) for s in A.seeds.split(",")]
+OUT = f"/root/compose-audit/results/slerp_{A.size}.jsonl"
+DEV = "cuda"
+BLIMP = glob.glob("/root/hf_cache_brainalign/hub/datasets--nyu-mll--blimp/snapshots/*/")[0]
+
+
+def log(*a):
+    print(f"[{time.strftime('%H:%M:%S')}]", *a, flush=True)
+
+
+def neox_head_match(sd_a, sd_b, d, nh, nl):
+    hd, perms = d // nh, {}
+    for L in range(nl):
+        qk = f"gpt_neox.layers.{L}.attention.query_key_value.weight"
+        de = f"gpt_neox.layers.{L}.attention.dense.weight"
+        if qk not in sd_a: continue
+        Aq = np.asarray(sd_a[qk], float).reshape(nh, 3 * hd, d)
+        Bq = np.asarray(sd_b[qk], float).reshape(nh, 3 * hd, d)
+        g = np.einsum("ixy,jxy->ij", Aq, Bq)
+        Ad = np.asarray(sd_a[de], float).reshape(d, nh, hd)
+        Bd = np.asarray(sd_b[de], float).reshape(d, nh, hd)
+        perms[L] = AL._assignment(g + np.einsum("xiy,xjy->ij", Ad, Bd))
+    return perms
+
+
+def neox_apply_head(sd, perms, d, nh):
+    hd, out = d // nh, dict(sd)
+    for L, h in perms.items():
+        qk = f"gpt_neox.layers.{L}.attention.query_key_value.weight"
+        qb = f"gpt_neox.layers.{L}.attention.query_key_value.bias"
+        de = f"gpt_neox.layers.{L}.attention.dense.weight"
+        out[qk] = np.asarray(sd[qk], float).reshape(nh, 3 * hd, d)[h].reshape(3 * d, d)
+        if qb in sd: out[qb] = np.asarray(sd[qb], float).reshape(nh, 3 * hd)[h].reshape(3 * d)
+        out[de] = np.asarray(sd[de], float).reshape(d, nh, hd)[:, h].reshape(d, d)
+    return out
+
+
+def align_perm(sd_a, sd_b, d, aa, ab, nh, nl):
+    sd, _ = AL.align_weights_full(sd_a, sd_b, d, acts_a=aa, acts_b=ab, n_heads=None,
+                                  method="permutation", strict=True, accept_each=True)
+    hp = neox_head_match(sd_a, sd, d, nh, nl)
+    if hp:
+        cand = neox_apply_head(sd, hp, d, nh)
+        if AL.block_normalised_distance(sd_a, cand) <= AL.block_normalised_distance(sd_a, sd):
+            sd = cand
+    return sd
+
+
+# ------------------------------------------------------------------ REPAIR
+TARGETS = ("mlp.dense_h_to_4h", "attention.query_key_value")
+
+
+@torch.no_grad()
+def preact_stats(model, blocks, dev, bs, nl):
+    """{(layer, target): (mean, std)} of each Linear's OUTPUT (= pre-activation), per unit."""
+    acc = {}
+    hs = []
+
+    def mk(key):
+        def hook(mod, inp, out):
+            o = out.detach().float().reshape(-1, out.shape[-1])
+            s = acc.setdefault(key, [0.0, None, None])
+            s[0] += o.shape[0]
+            s[1] = o.sum(0) if s[1] is None else s[1] + o.sum(0)
+            s[2] = (o * o).sum(0) if s[2] is None else s[2] + (o * o).sum(0)
+        return hook
+
+    for L in range(nl):
+        blk = model.gpt_neox.layers[L]
+        hs.append(blk.mlp.dense_h_to_4h.register_forward_hook(mk((L, "mlp.dense_h_to_4h"))))
+        hs.append(blk.attention.query_key_value.register_forward_hook(mk((L, "attention.query_key_value"))))
+    for i in range(0, blocks.shape[0], bs):
+        model(blocks[i:i + bs].to(dev))
+    for h in hs: h.remove()
+    out = {}
+    for k, (n, s1, s2) in acc.items():
+        m = s1 / n
+        v = (s2 / n - m * m).clamp_min(1e-12)
+        out[k] = (m.cpu().numpy().astype(np.float64), v.sqrt().cpu().numpy().astype(np.float64))
+    return out
+
+
+def repair(sd_merged, stats_a, stats_b, shell, blocks, dev, bs, nl):
+    """Walk layers in order; after fixing layers < L the inputs to layer L are already corrected, so
+    layer L's own statistics are re-measured before it is corrected. Affine correction on the
+    Linear's weight/bias, so the model stays exactly a model of the same architecture."""
+    sd = {k: np.array(v, dtype=np.float64, copy=True) for k, v in sd_merged.items()}
+    for L in range(nl):
+        sd_load(shell, sd, dev)
+        cur = preact_stats(shell, blocks, dev, bs, nl)
+        for t in TARGETS:
+            mu_t = 0.5 * (stats_a[(L, t)][0] + stats_b[(L, t)][0])
+            sd_t = 0.5 * (stats_a[(L, t)][1] + stats_b[(L, t)][1])
+            mu_m, sd_m = cur[(L, t)]
+            g = sd_t / np.maximum(sd_m, 1e-8)
+            wk, bk = f"gpt_neox.layers.{L}.{t}.weight", f"gpt_neox.layers.{L}.{t}.bias"
+            sd[wk] = sd[wk] * g[:, None]
+            sd[bk] = (sd[bk] - mu_m) * g + mu_t
+    return sd
+
+
+# ------------------------------------------------------------------ BLiMP
+def load_blimp(n_per):
+    out = []
+    for d in sorted(glob.glob(BLIMP + "*/")):
+        f = glob.glob(d + "*.parquet")
+        if not f: continue
+        t = pq.read_table(f[0]).to_pydict()
+        out.append((os.path.basename(d.rstrip("/")), t["sentence_good"][:n_per], t["sentence_bad"][:n_per]))
+    return out
+
+
+tok = AutoTokenizer.from_pretrained(f"EleutherAI/pythia-{A.size}")
+if tok.pad_token is None: tok.pad_token = tok.eos_token
+
+
+def enc(sents, maxlen=48):
+    e = tok(sents, return_tensors="pt", padding=True, truncation=True, max_length=maxlen)
+    return e["input_ids"], e["attention_mask"]
+
+
+ENC = [(n, enc(g), enc(b)) for n, g, b in load_blimp(A.n_per_paradigm)]
+lines = flores_lines("eng_Latn")
+blocks = make_blocks(tok, lines, block=512, max_blocks=A.blocks)
+shell = AutoModelForCausalLM.from_pretrained(f"EleutherAI/pythia-{A.size}-seed{SEEDS[0]}",
+                                             dtype=torch.float32).to(DEV).eval()
+cfg = shell.config
+D, NH, NL = cfg.hidden_size, cfg.num_attention_heads, cfg.num_hidden_layers
+log(f"size={A.size} d={D} heads={NH} layers={NL} blimp_paradigms={len(ENC)}")
+
+
+@torch.no_grad()
+def bscore(ids, am):
+    o = []
+    for i in range(0, ids.shape[0], 128):
+        x, m = ids[i:i + 128].to(DEV), am[i:i + 128].to(DEV)
+        lp = torch.log_softmax(shell(x, attention_mask=m).logits.float()[:, :-1], -1)
+        o.append((lp.gather(-1, x[:, 1:].unsqueeze(-1)).squeeze(-1) * m[:, 1:].float()).sum(1).cpu())
+    return torch.cat(o).numpy()
+
+
+def evaluate(sd):
+    sd_load(shell, sd, DEV)
+    nll = nll_nats(shell, blocks, DEV, bs=A.bs)
+    cor = tot = 0
+    for name, (gi, gm), (bi, bm) in ENC:
+        sg, sb = bscore(gi, gm), bscore(bi, bm)
+        cor += int((sg > sb).sum()); tot += len(sg)
+    return nll, cor / tot
+
+
+SDS, ACTS, PAR, STATS = {}, {}, {}, {}
+for s in SEEDS:
+    m = AutoModelForCausalLM.from_pretrained(f"EleutherAI/pythia-{A.size}-seed{s}", dtype=torch.float32).to(DEV).eval()
+    SDS[s] = sd_np(m); ACTS[s] = capture_acts(m, blocks, DEV, n_rows=A.acts_rows, bs=A.bs)
+    del m; torch.cuda.empty_cache()
+    PAR[s] = evaluate(SDS[s])
+    log(f"  seed{s} nll={PAR[s][0]:.4f} blimp={PAR[s][1]:.4f}")
+
+done = set()
+if os.path.exists(OUT):
+    for l in open(OUT):
+        try: done.add(tuple(json.loads(l)["pair"]))
+        except Exception: pass
+fh = open(OUT, "a")
+for a, b in itertools.combinations(SEEDS, 2):
+    if (a, b) in done: continue
+    t0 = time.time()
+    sa, sb = SDS[a], SDS[b]
+    sbp = align_perm(sa, sb, D, ACTS[a], ACTS[b], NH, NL)
+    rungs = {"M0_naive_avg": MG.average([sa, sb]), "M1_perm_avg": MG.average([sa, sbp]),
+             "M6_slerp": MG.slerp(sa, sb, t=0.5), "M7_perm_slerp": MG.slerp(sa, sbp, t=0.5)}
+    floor = min(PAR[a][0], PAR[b][0]); ceil = max(PAR[a][1], PAR[b][1])
+    res = {}
+    for k, sd in rungs.items():
+        nll, acc = evaluate(sd)
+        res[k] = {"nll": nll, "delta_floor": nll - floor, "blimp_acc": acc,
+                  "blimp_delta_vs_ceiling": acc - ceil}
+    r = {"set": "set1_slerp", "size": A.size, "pair": [a, b], "floor": floor, "blimp_ceiling": ceil,
+         "parent_nll": {"a": PAR[a][0], "b": PAR[b][0]},
+         "parent_blimp": {"a": PAR[a][1], "b": PAR[b][1]}, "rungs": res, "secs": time.time() - t0}
+    fh.write(json.dumps(r) + "\n"); fh.flush()
+    log(f"pair {a},{b} floor={floor:.2f}/ceil={ceil:.3f} | " +
+        " | ".join(f"{k}: {v['delta_floor']:+.2f}n {v['blimp_acc']:.3f}" for k, v in res.items()) +
+        f" ({r['secs']:.0f}s)")
+    del rungs, sbp; gc.collect()
+fh.close()
+log("DONE slerp", A.size)

results/bgpt_merge.jsonl

@@ -0,0 +1,4 @@
+{"set": "bgpt_merge", "lang": "nld_Latn", "repo_a": "catherinearnett/B-GPT_en_nl_simultaneous", "repo_b": "catherinearnett/B-GPT_nl_en_simultaneous", "variant": "simultaneous", "context_tokens": 128, "vocab_anchors": 48188, "vocab_overlap": 0.941171875, "metric": "nats/UTF-8 byte (likelihood) + MultiBLiMP accuracy", "parents": {"A": {"nats_per_byte_eng": 0.8709063725074672, "nats_per_byte_x": 0.8975835804605808, "multiblimp_eng": 0.9662337662337662, "multiblimp_x": 0.9516666666666667}, "B": {"nats_per_byte_eng": 0.927153128608545, "nats_per_byte_x": 0.833092335361209, "multiblimp_eng": 0.9454545454545454, "multiblimp_x": 0.9683333333333334}}, "floor_eng": 0.8709063725074672, "floor_x": 0.833092335361209, "ceiling_mb_eng": 0.9662337662337662, "ceiling_mb_x": 0.9683333333333334, "align_info": {"perm": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}, "orth": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}}, "rungs": {"M0_naive_avg": {"nats_per_byte_eng": 1.6702439928481354, "nats_per_byte_x": 1.8469807178070992, "delta_floor_eng": 0.7993376203406682, "delta_floor_x": 1.0138883824458902, "multiblimp_eng": 0.6766233766233766, "multiblimp_x": 0.5833333333333334, "delta_floor_mean": 0.9066130013932792, "multiblimp_mean": 0.629978354978355}, "M1a_vocab_avg": {"nats_per_byte_eng": 1.6436264924719222, "nats_per_byte_x": 1.7647907463575732, "delta_floor_eng": 0.772720119964455, "delta_floor_x": 0.9316984109963642, "multiblimp_eng": 0.6727272727272727, "multiblimp_x": 0.6883333333333334, "delta_floor_mean": 0.8522092654804097, "multiblimp_mean": 0.680530303030303}, "M1b_vocab_perm_avg": {"nats_per_byte_eng": 1.6460716563914373, "nats_per_byte_x": 1.78234839545402, "delta_floor_eng": 0.7751652838839701, "delta_floor_x": 0.949256060092811, "multiblimp_eng": 0.6857142857142857, "multiblimp_x": 0.7041666666666667, "delta_floor_mean": 0.8622106719883906, "multiblimp_mean": 0.6949404761904763}, "M1c_vocab_orth_avg": {"nats_per_byte_eng": 1.6460716563914373, "nats_per_byte_x": 1.78234839545402, "delta_floor_eng": 0.7751652838839701, "delta_floor_x": 0.949256060092811, "multiblimp_eng": 0.6857142857142857, "multiblimp_x": 0.7041666666666667, "delta_floor_mean": 0.8622106719883906, "multiblimp_mean": 0.6949404761904763}, "M1g_emb_procrustes": {"nats_per_byte_eng": 1.732040051131688, "nats_per_byte_x": 1.645383775265831, "delta_floor_eng": 0.8611336786242209, "delta_floor_x": 0.8122914399046219, "multiblimp_eng": 0.6883116883116883, "multiblimp_x": 0.6391666666666667, "delta_floor_mean": 0.8367125592644213, "multiblimp_mean": 0.6637391774891774}}, "secs": 101.82178163528442}
+{"set": "bgpt_merge", "lang": "spa_Latn", "repo_a": "catherinearnett/B-GPT_en_es_simultaneous", "repo_b": "catherinearnett/B-GPT_es_en_simultaneous", "variant": "simultaneous", "context_tokens": 128, "vocab_anchors": 48150, "vocab_overlap": 0.9404296875, "metric": "nats/UTF-8 byte (likelihood) + MultiBLiMP accuracy", "parents": {"A": {"nats_per_byte_eng": 0.8717946141865981, "nats_per_byte_x": 0.8886904678891461, "multiblimp_eng": 0.9675324675324676, "multiblimp_x": 0.8791666666666667}, "B": {"nats_per_byte_eng": 0.9462042091572577, "nats_per_byte_x": 0.8179411284174111, "multiblimp_eng": 0.9532467532467532, "multiblimp_x": 0.9083333333333333}}, "floor_eng": 0.8717946141865981, "floor_x": 0.8179411284174111, "ceiling_mb_eng": 0.9675324675324676, "ceiling_mb_x": 0.9083333333333333, "align_info": {"perm": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}, "orth": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}}, "rungs": {"M0_naive_avg": {"nats_per_byte_eng": 1.7313491015943847, "nats_per_byte_x": 1.9586783855838876, "delta_floor_eng": 0.8595544874077866, "delta_floor_x": 1.1407372571664767, "multiblimp_eng": 0.6285714285714286, "multiblimp_x": 0.6175, "delta_floor_mean": 1.0001458722871317, "multiblimp_mean": 0.6230357142857144}, "M1a_vocab_avg": {"nats_per_byte_eng": 1.7187136031903096, "nats_per_byte_x": 1.8605896518136928, "delta_floor_eng": 0.8469189890037115, "delta_floor_x": 1.0426485233962817, "multiblimp_eng": 0.6753246753246753, "multiblimp_x": 0.6891666666666667, "delta_floor_mean": 0.9447837561999965, "multiblimp_mean": 0.682245670995671}, "M1b_vocab_perm_avg": {"nats_per_byte_eng": 1.7420982826962468, "nats_per_byte_x": 1.87197194890501, "delta_floor_eng": 0.8703036685096487, "delta_floor_x": 1.0540308204875988, "multiblimp_eng": 0.6636363636363637, "multiblimp_x": 0.6958333333333333, "delta_floor_mean": 0.9621672444986238, "multiblimp_mean": 0.6797348484848484}, "M1c_vocab_orth_avg": {"nats_per_byte_eng": 1.7420982826962468, "nats_per_byte_x": 1.87197194890501, "delta_floor_eng": 0.8703036685096487, "delta_floor_x": 1.0540308204875988, "multiblimp_eng": 0.6636363636363637, "multiblimp_x": 0.6958333333333333, "delta_floor_mean": 0.9621672444986238, "multiblimp_mean": 0.6797348484848484}, "M1g_emb_procrustes": {"nats_per_byte_eng": 1.6396049267684156, "nats_per_byte_x": 1.7412632107964323, "delta_floor_eng": 0.7678103125818175, "delta_floor_x": 0.9233220823790212, "multiblimp_eng": 0.7298701298701299, "multiblimp_x": 0.6733333333333333, "delta_floor_mean": 0.8455661974804194, "multiblimp_mean": 0.7016017316017316}}, "secs": 82.30049467086792}
+{"set": "bgpt_merge", "lang": "ell_Grek", "repo_a": "catherinearnett/B-GPT_en_el_simultaneous", "repo_b": "catherinearnett/B-GPT_el_en_simultaneous", "variant": "simultaneous", "context_tokens": 128, "vocab_anchors": 46742, "vocab_overlap": 0.9129296875, "metric": "nats/UTF-8 byte (likelihood) + MultiBLiMP accuracy", "parents": {"A": {"nats_per_byte_eng": 0.8753055350819807, "nats_per_byte_x": 0.5819531108222833, "multiblimp_eng": 0.9675324675324676, "multiblimp_x": 0.927007299270073}, "B": {"nats_per_byte_eng": 0.9859717774411291, "nats_per_byte_x": 0.4837813179685353, "multiblimp_eng": 0.9415584415584416, "multiblimp_x": 0.9425182481751825}}, "floor_eng": 0.8753055350819807, "floor_x": 0.4837813179685353, "ceiling_mb_eng": 0.9675324675324676, "ceiling_mb_x": 0.9425182481751825, "align_info": {"perm": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}, "orth": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}}, "rungs": {"M0_naive_avg": {"nats_per_byte_eng": 1.7119019494685757, "nats_per_byte_x": 1.6706673613656065, "delta_floor_eng": 0.8365964143865949, "delta_floor_x": 1.1868860433970712, "multiblimp_eng": 0.6246753246753247, "multiblimp_x": 0.5593065693430657, "delta_floor_mean": 1.011741228891833, "multiblimp_mean": 0.5919909470091952}, "M1a_vocab_avg": {"nats_per_byte_eng": 1.6434728982704692, "nats_per_byte_x": 1.3925533965844863, "delta_floor_eng": 0.7681673631884884, "delta_floor_x": 0.908772078615951, "multiblimp_eng": 0.6597402597402597, "multiblimp_x": 0.5885036496350365, "delta_floor_mean": 0.8384697209022197, "multiblimp_mean": 0.6241219546876482}, "M1b_vocab_perm_avg": {"nats_per_byte_eng": 1.641348809914926, "nats_per_byte_x": 1.3919947739009324, "delta_floor_eng": 0.7660432748329453, "delta_floor_x": 0.9082134559323971, "multiblimp_eng": 0.6636363636363637, "multiblimp_x": 0.5894160583941606, "delta_floor_mean": 0.8371283653826712, "multiblimp_mean": 0.6265262110152621}, "M1c_vocab_orth_avg": {"nats_per_byte_eng": 1.641348809914926, "nats_per_byte_x": 1.3919947739009324, "delta_floor_eng": 0.7660432748329453, "delta_floor_x": 0.9082134559323971, "multiblimp_eng": 0.6636363636363637, "multiblimp_x": 0.5894160583941606, "delta_floor_mean": 0.8371283653826712, "multiblimp_mean": 0.6265262110152621}, "M1g_emb_procrustes": {"nats_per_byte_eng": 1.6182294308418255, "nats_per_byte_x": 1.3401340834841218, "delta_floor_eng": 0.7429238957598447, "delta_floor_x": 0.8563527655155865, "multiblimp_eng": 0.6350649350649351, "multiblimp_x": 0.593978102189781, "delta_floor_mean": 0.7996383306377156, "multiblimp_mean": 0.614521518627358}}, "secs": 77.6815595626831}
+{"set": "bgpt_merge", "lang": "pol_Latn", "repo_a": "catherinearnett/B-GPT_en_pl_simultaneous", "repo_b": "catherinearnett/B-GPT_pl_en_simultaneous", "variant": "simultaneous", "context_tokens": 128, "vocab_anchors": 47243, "vocab_overlap": 0.92271484375, "metric": "nats/UTF-8 byte (likelihood) + MultiBLiMP accuracy", "parents": {"A": {"nats_per_byte_eng": 0.8812636806964327, "nats_per_byte_x": 1.070125592872553, "multiblimp_eng": 0.9727272727272728, "multiblimp_x": 0.8925}, "B": {"nats_per_byte_eng": 0.942140913339622, "nats_per_byte_x": 0.9121878294188179, "multiblimp_eng": 0.9506493506493506, "multiblimp_x": 0.9491666666666667}}, "floor_eng": 0.8812636806964327, "floor_x": 0.9121878294188179, "ceiling_mb_eng": 0.9727272727272728, "ceiling_mb_x": 0.9491666666666667, "align_info": {"perm": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}, "orth": {"residual": false, "mlp": 12, "heads": 12, "rejected": ["residual"]}}, "rungs": {"M0_naive_avg": {"nats_per_byte_eng": 1.7825667558179592, "nats_per_byte_x": 2.4543135036792747, "delta_floor_eng": 0.9013030751215265, "delta_floor_x": 1.5421256742604568, "multiblimp_eng": 0.6298701298701299, "multiblimp_x": 0.6225, "delta_floor_mean": 1.2217143746909915, "multiblimp_mean": 0.626185064935065}, "M1a_vocab_avg": {"nats_per_byte_eng": 1.7335835231187322, "nats_per_byte_x": 2.3853252567459253, "delta_floor_eng": 0.8523198424222995, "delta_floor_x": 1.4731374273271074, "multiblimp_eng": 0.6311688311688312, "multiblimp_x": 0.6116666666666667, "delta_floor_mean": 1.1627286348747035, "multiblimp_mean": 0.6214177489177489}, "M1b_vocab_perm_avg": {"nats_per_byte_eng": 1.7200141561567022, "nats_per_byte_x": 2.363797599732352, "delta_floor_eng": 0.8387504754602695, "delta_floor_x": 1.4516097703135342, "multiblimp_eng": 0.6311688311688312, "multiblimp_x": 0.6091666666666666, "delta_floor_mean": 1.1451801228869019, "multiblimp_mean": 0.6201677489177488}, "M1c_vocab_orth_avg": {"nats_per_byte_eng": 1.7200141561567022, "nats_per_byte_x": 2.363797599732352, "delta_floor_eng": 0.8387504754602695, "delta_floor_x": 1.4516097703135342, "multiblimp_eng": 0.6311688311688312, "multiblimp_x": 0.6091666666666666, "delta_floor_mean": 1.1451801228869019, "multiblimp_mean": 0.6201677489177488}, "M1g_emb_procrustes": {"nats_per_byte_eng": 1.7070266299615326, "nats_per_byte_x": 2.053772839882701, "delta_floor_eng": 0.8257629492651, "delta_floor_x": 1.1415850104638832, "multiblimp_eng": 0.6480519480519481, "multiblimp_x": 0.6166666666666667, "delta_floor_mean": 0.9836739798644916, "multiblimp_mean": 0.6323593073593075}}, "secs": 82.07555818557739}

results/blimp_31m.jsonl

@@ -29,3 +29,8 @@
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+{"set": "set1_blimp", "size": "31m", "pair": [8, 9], "metric": "BLiMP accuracy (chance=0.5) -- ACCURACY, not likelihood", "n_per_paradigm": 200, "n_paradigms": 67, "parent_acc": {"a": 0.6827611940298507, "b": 0.6915671641791045}, "ceiling": 0.6915671641791045, "rungs": {"M0_naive_avg": {"blimp_acc": 0.5675373134328359, "delta_vs_best_parent": -0.1240298507462686}, "M1_perm_avg": {"blimp_acc": 0.5632089552238806, "delta_vs_best_parent": -0.12835820895522387}, "M1_orth_avg": {"blimp_acc": 0.566044776119403, "delta_vs_best_parent": -0.1255223880597015}}, "per_paradigm": {"M0_naive_avg": {"adjunct_island": 0.525, "anaphor_gender_agreement": 0.19, "anaphor_number_agreement": 0.51, "animate_subject_passive": 0.59, "animate_subject_trans": 0.62, "causative": 0.435, "complex_NP_island": 0.47, "coordinate_structure_constraint_complex_left_branch": 0.7, "coordinate_structure_constraint_object_extraction": 0.32, "determiner_noun_agreement_1": 0.49, "determiner_noun_agreement_2": 0.515, 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"wh_vs_that_no_gap_long_distance": 0.91, "wh_vs_that_with_gap": 0.135, "wh_vs_that_with_gap_long_distance": 0.11}}, "secs": 10.724910974502563}

results/blimp_pairs.csv

@@ -35,11 +35,78 @@ size,pair,ceiling,parent_mean,M0,M1best,acc_M0_naive_avg,acc_M1_perm_avg,acc_M1_
 14m,(7, 8),0.6624626865671642,0.6456716417910449,0.5300746268656716,0.531044776119403,0.5300746268656716,0.5198507462686567,0.531044776119403
 14m,(7, 9),0.6624626865671642,0.6515298507462687,0.5402985074626866,0.5307462686567164,0.5402985074626866,0.5307462686567164,0.5002985074626866
 14m,(8, 9),0.6405970149253731,0.6347388059701493,0.5158955223880597,0.5726865671641791,0.5158955223880597,0.5254477611940298,0.5726865671641791
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+160m,(1, 5),0.780497512437811,0.7739303482587065,0.5464676616915423,0.5736318407960199,0.5464676616915423,0.5736318407960199,0.5218905472636816
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+160m,(2, 8),0.7754228855721393,0.771592039800995,0.5016915422885572,0.5464676616915423,0.5016915422885572,0.5449751243781095,0.5464676616915423
+160m,(2, 9),0.7850746268656716,0.7764179104477612,0.532636815920398,0.5711442786069652,0.532636815920398,0.5597014925373134,0.5711442786069652
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+160m,(3, 7),0.7707462686567165,0.7669651741293533,0.517910447761194,0.5609950248756219,0.517910447761194,0.5290547263681592,0.5609950248756219
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+160m,(3, 9),0.7850746268656716,0.777910447761194,0.5154228855721393,0.5339303482587064,0.5154228855721393,0.5339303482587064,0.5228855721393035
+160m,(4, 5),0.767363184079602,0.7660199004975125,0.542089552238806,0.5502487562189055,0.542089552238806,0.5350248756218905,0.5502487562189055
+160m,(4, 6),0.7720398009950249,0.7683582089552239,0.5816915422885572,0.5760199004975124,0.5816915422885572,0.5671641791044776,0.5760199004975124
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+160m,(4, 8),0.7754228855721393,0.7700497512437812,0.5611940298507463,0.5402985074626866,0.5611940298507463,0.5402985074626866,0.5349253731343283
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+160m,(5, 9),0.7850746268656716,0.7762189054726368,0.5346268656716417,0.5495522388059702,0.5346268656716417,0.5293532338308458,0.5495522388059702
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+160m,(6, 8),0.7754228855721393,0.7737313432835822,0.5287562189054726,0.5575124378109453,0.5287562189054726,0.5575124378109453,0.5438805970149254
+160m,(6, 9),0.7850746268656716,0.7785572139303483,0.582089552238806,0.5467661691542288,0.582089552238806,0.5467661691542288,0.5288557213930348
+160m,(7, 8),0.7754228855721393,0.7693034825870647,0.5481592039800995,0.5197014925373135,0.5481592039800995,0.48517412935323384,0.5197014925373135
+160m,(7, 9),0.7850746268656716,0.7741293532338309,0.5200995024875622,0.5492537313432836,0.5200995024875622,0.5492537313432836,0.5357213930348259
+160m,(8, 9),0.7850746268656716,0.7802487562189055,0.529452736318408,0.5432835820895522,0.529452736318408,0.5432835820895522,0.5327363184079602
 31m,(1, 2),0.6994029850746268,0.6902985074626866,0.48641791044776117,0.5532835820895522,0.48641791044776117,0.5532835820895522,0.5169402985074627
 31m,(1, 3),0.6914179104477612,0.6863059701492538,0.5235820895522388,0.5397014925373135,0.5235820895522388,0.5397014925373135,0.52
 31m,(1, 4),0.698134328358209,0.6896641791044776,0.4791044776119403,0.5487313432835821,0.4791044776119403,0.5487313432835821,0.5338059701492537
 31m,(1, 5),0.6811940298507463,0.6734701492537314,0.5269402985074627,0.5494029850746268,0.5269402985074627,0.5161194029850746,0.5494029850746268
 31m,(1, 6),0.7037313432835821,0.6924626865671641,0.5271641791044777,0.5443283582089552,0.5271641791044777,0.5443283582089552,0.5419402985074627
+31m,(1, 7),0.7023134328358209,0.6917537313432836,0.5172388059701493,0.5412686567164179,0.5172388059701493,0.5412686567164179,0.5198507462686567
+31m,(1, 8),0.6827611940298507,0.6819776119402985,0.49350746268656714,0.5408208955223881,0.49350746268656714,0.49186567164179107,0.5408208955223881
+31m,(1, 9),0.6915671641791045,0.6863805970149254,0.5115671641791045,0.551044776119403,0.5115671641791045,0.5273880597014925,0.551044776119403
+31m,(2, 3),0.6994029850746268,0.695410447761194,0.5644776119402986,0.5724626865671641,0.5644776119402986,0.5471641791044776,0.5724626865671641
+31m,(2, 4),0.6994029850746268,0.698768656716418,0.52,0.5409701492537313,0.52,0.5167910447761194,0.5409701492537313
+31m,(2, 5),0.6994029850746268,0.6825746268656716,0.5067164179104477,0.5075373134328358,0.5067164179104477,0.5075373134328358,0.493134328358209
+31m,(2, 6),0.7037313432835821,0.7015671641791045,0.5195522388059701,0.527910447761194,0.5195522388059701,0.5237313432835821,0.527910447761194
+31m,(2, 7),0.7023134328358209,0.7008582089552239,0.5526119402985075,0.5405970149253732,0.5526119402985075,0.5173134328358209,0.5405970149253732
+31m,(2, 8),0.6994029850746268,0.6910820895522387,0.5214925373134328,0.5435074626865671,0.5214925373134328,0.5145522388059701,0.5435074626865671
+31m,(2, 9),0.6994029850746268,0.6954850746268657,0.5398507462686567,0.5300746268656716,0.5398507462686567,0.5300746268656716,0.5267910447761194
+31m,(3, 4),0.698134328358209,0.6947761194029851,0.5102985074626866,0.5549253731343283,0.5102985074626866,0.5549253731343283,0.5483582089552239
+31m,(3, 5),0.6914179104477612,0.6785820895522388,0.5257462686567164,0.5375373134328358,0.5257462686567164,0.5375373134328358,0.5258208955223881
+31m,(3, 6),0.7037313432835821,0.6975746268656717,0.55,0.5476119402985075,0.55,0.5476119402985075,0.5214179104477612
+31m,(3, 7),0.7023134328358209,0.6968656716417911,0.4811194029850746,0.5595522388059702,0.4811194029850746,0.5216417910447761,0.5595522388059702
+31m,(3, 8),0.6914179104477612,0.687089552238806,0.5251492537313432,0.5443283582089552,0.5251492537313432,0.5033582089552239,0.5443283582089552
+31m,(3, 9),0.6915671641791045,0.6914925373134329,0.5460447761194029,0.5208208955223881,0.5460447761194029,0.5156716417910447,0.5208208955223881
+31m,(4, 5),0.698134328358209,0.6819402985074627,0.478955223880597,0.5496268656716418,0.478955223880597,0.5496268656716418,0.5193283582089552
+31m,(4, 6),0.7037313432835821,0.7009328358208955,0.5673880597014925,0.5645522388059702,0.5673880597014925,0.5645522388059702,0.5524626865671641
+31m,(4, 7),0.7023134328358209,0.7002238805970149,0.5031343283582089,0.5564179104477612,0.5031343283582089,0.5504477611940298,0.5564179104477612
+31m,(4, 8),0.698134328358209,0.6904477611940298,0.5686567164179105,0.5655970149253732,0.5686567164179105,0.5655970149253732,0.5270149253731343
+31m,(4, 9),0.698134328358209,0.6948507462686567,0.5026865671641791,0.5452985074626866,0.5026865671641791,0.5452985074626866,0.5103731343283582
+31m,(5, 6),0.7037313432835821,0.6847388059701492,0.5142537313432836,0.5357462686567164,0.5142537313432836,0.5167910447761194,0.5357462686567164
+31m,(5, 7),0.7023134328358209,0.6840298507462687,0.5302985074626866,0.558955223880597,0.5302985074626866,0.5176119402985074,0.558955223880597
+31m,(5, 8),0.6827611940298507,0.6742537313432835,0.5747014925373134,0.5361940298507463,0.5747014925373134,0.5276119402985074,0.5361940298507463
+31m,(5, 9),0.6915671641791045,0.6786567164179105,0.5350746268656716,0.5345522388059701,0.5350746268656716,0.5345522388059701,0.48134328358208955
+31m,(6, 7),0.7037313432835821,0.7030223880597015,0.5069402985074627,0.5400746268656716,0.5069402985074627,0.5400746268656716,0.5277611940298508
+31m,(6, 8),0.7037313432835821,0.6932462686567165,0.5024626865671642,0.5443283582089552,0.5024626865671642,0.5423880597014925,0.5443283582089552
+31m,(6, 9),0.7037313432835821,0.6976492537313432,0.5343283582089552,0.5555970149253732,0.5343283582089552,0.5555970149253732,0.5409701492537313
+31m,(7, 8),0.7023134328358209,0.6925373134328359,0.5417164179104478,0.576044776119403,0.5417164179104478,0.5673134328358209,0.576044776119403
+31m,(7, 9),0.7023134328358209,0.6969402985074626,0.5711940298507463,0.5625373134328359,0.5711940298507463,0.5625373134328359,0.552910447761194
+31m,(8, 9),0.6915671641791045,0.6871641791044776,0.5675373134328359,0.566044776119403,0.5675373134328359,0.5632089552238806,0.566044776119403
 70m,(1, 2),0.7305223880597015,0.721044776119403,0.5678358208955224,0.543955223880597,0.5678358208955224,0.5375373134328358,0.543955223880597
 70m,(1, 3),0.7305223880597015,0.7224253731343284,0.542910447761194,0.5558955223880597,0.542910447761194,0.5305223880597015,0.5558955223880597
 70m,(1, 4),0.7305223880597015,0.7176492537313433,0.5120149253731343,0.5324626865671642,0.5120149253731343,0.5324626865671642,0.521044776119403
@@ -74,3 +141,5 @@ size,pair,ceiling,parent_mean,M0,M1best,acc_M0_naive_avg,acc_M1_perm_avg,acc_M1_
 70m,(6, 8),0.7256716417910448,0.7182089552238806,0.4824626865671642,0.542089552238806,0.4824626865671642,0.542089552238806,0.5407462686567164
 70m,(6, 9),0.7256716417910448,0.7231716417910448,0.5320149253731343,0.5605970149253732,0.5320149253731343,0.5355223880597015,0.5605970149253732
 70m,(7, 8),0.7194776119402985,0.7151119402985074,0.48253731343283585,0.5730597014925373,0.48253731343283585,0.5573880597014925,0.5730597014925373
+70m,(7, 9),0.7206716417910448,0.7200746268656717,0.5115671641791045,0.5614925373134328,0.5115671641791045,0.5614925373134328,0.5282835820895523
+70m,(8, 9),0.7206716417910448,0.7157089552238807,0.5497014925373135,0.5550746268656717,0.5497014925373135,0.5550746268656717,0.5436567164179105

results/corpus_14m.jsonl

@@ -0,0 +1,36 @@
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results/corpus_160m.jsonl

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results/predictor_auroc.csv

@@ -1,153 +1,191 @@
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results/predictor_confirmatory.csv

@@ -1,21 +1,26 @@
 substrate,predictor,n_pairs,spearman,auroc_heldout_by_seed,perm_null_mean,perm_p,n_null_draws,bh_q_within_confirmatory_family
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results/predictor_transfer_across_size.csv

@@ -1,41 +1,51 @@
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results/repair_160m.jsonl

@@ -0,0 +1,33 @@
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results/repair_31m.jsonl

@@ -0,0 +1,36 @@
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results/repair_70m.jsonl

@@ -8,3 +8,29 @@
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results/rung_summary.csv

@@ -14,16 +14,16 @@ SET1,pythia-70m,M1_perm_avg,36,14.619996948640328,10.993783677497825,8.768724295
 SET1,pythia-70m,M1_orth_avg,36,13.32290112143661,9.696687850294106,9.897506325678817,6.302425177985364,36,50.352146584420055
 SET1,pythia-70m,M2_task_arith,36,95.14443668687035,91.51822341572785,90.58194202639585,45.13919447608346,0,-357.7705684270056
 SET1,pythia-70m,M3_ties,36,151.39140910954373,147.76519583840124,147.74675279431924,112.97038222261294,0,-650.7491348516683
-SET1,pythia-160m,M0_naive_avg,30,12.095408945898566,8.841640902903059,8.384317834783207,6.883626142826566,0,0.0
-SET1,pythia-160m,M1_perm_avg,30,9.957645551130343,6.703877508134834,6.3827374303410895,5.496568773124083,27,22.815902213090038
-SET1,pythia-160m,M1_orth_avg,30,9.415541867967223,6.161773824971717,6.135199500156708,5.1328521549351755,30,29.38927635543068
-SET1,pythia-160m,M2_task_arith,30,30.306501689395795,27.052733646400284,26.96526263511344,17.881782666111178,0,-205.14897710111987
-SET1,pythia-160m,M3_ties,30,60.28103130860648,57.02726326561098,57.471641226990585,49.302846651021284,0,-555.4684743615128
-SET1,pythia-410m,M0_naive_avg,3,9.456917753010165,6.485910978439605,6.501884166819552,6.191101432546477,0,0.0
-SET1,pythia-410m,M1_perm_avg,3,8.72035732547157,5.749350550901011,5.639203474090834,5.560742920081131,3,11.230594113482429
-SET1,pythia-410m,M1_orth_avg,3,8.848747265030442,5.877740490459883,5.806495382827789,5.680337108355756,3,9.236708388901816
-SET1,pythia-410m,M2_task_arith,3,13.294903188872581,10.323896414302022,10.365064766542318,7.524678269477739,0,-60.6508073657252
-SET1,pythia-410m,M3_ties,3,13.026077977209718,10.05507120263916,10.165132068452381,9.429044898942024,0,-55.15870961848408
+SET1,pythia-160m,M0_naive_avg,36,12.247216669469587,8.994957778111155,8.47036671498517,6.883626142826566,0,0.0
+SET1,pythia-160m,M1_perm_avg,36,10.02288783853742,6.770628947178989,6.435096218161387,5.496568773124083,33,23.470654062334585
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+SET1,pythia-160m,M3_ties,36,61.54713634035592,58.29487744899749,57.96688460557195,49.302846651021284,0,-557.4068020335034
+SET1,pythia-410m,M0_naive_avg,14,9.434523058741904,6.450848737330442,6.462185834174209,5.951437196775115,0,0.0
+SET1,pythia-410m,M1_perm_avg,14,8.960686010812715,5.9770116894012535,5.866069915632136,5.560742920081131,11,7.098760479108755
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 SET4,goldfish eng-nld_Latn,M0_naive_avg,1,1.6997519931043927,1.6892323678609804,1.6892323678609804,1.6892323678609804,0,0.0
 SET4,goldfish eng-nld_Latn,M1a_vocab_avg,1,1.866523052069927,1.7633057297477746,1.7633057297477746,1.7633057297477746,0,-4.385030934529799
 SET4,goldfish eng-nld_Latn,M1b_vocab_perm_avg,1,1.8689461892935666,1.7661259814597123,1.7661259814597123,1.7661259814597123,0,-4.551985568219941

results/set1_160m.jsonl

@@ -28,3 +28,9 @@
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results/set1_410m.jsonl

@@ -1,3 +1,11 @@
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results/set1_pairs.csv

@@ -62,6 +62,15 @@ SET1_polypythia,pythia-160m,160m,4-7,4,7,3.2518446711411446,8.330261588796478,5.
 SET1_polypythia,pythia-160m,160m,4-8,4,8,3.2340771102158756,8.91856906838613,6.9614408310145555,M1_orth_avg,1.9571282373715748,0.21944419809552804,12.152646178602005,8.91856906838613,12.273053850446429,9.038976740230552,10.195517941230431,6.9614408310145555,26.684272183830725,23.45019507361485,70.07817086594912,66.84409375573324,8.898539444238471,9.01894783273835,-0.0070530324637820664,0.1991967017675047,1.4221580231609028,1.3310335201429462,0.06407480851911404,1.0000000000000002,1.3342808513105935,0.061791425720042426,1.189659594047577,1.113779219190694,0.07588037485688304,0.0637832664373473,1.189659594047577,1.0555664773890157,0.13409311665856127,0.11271553419943975,1.189659594047577,1.113779219190694,1.0555664773890157,0.0637832664373473,0.11271553419943975,0.9128514992425608,0.8870407324180893,0.003918728603039878,0.9960812713969601,0.003918728603038768,0.9960812713969612,0.004659772925401429,0.9953402270745986,0.5658540641227808,12,12,1
 SET1_polypythia,pythia-160m,160m,4-9,4,9,3.262358126108427,13.08598993529079,6.160650622821366,M1_orth_avg,6.925339312469424,0.5292178388272261,16.348348061399218,13.08598993529079,10.698082134448386,7.4357240083399585,9.423008748929794,6.160650622821366,42.591483457681015,39.32912533157259,62.245552914016635,58.98319478790821,13.08010081908941,7.429834772696001,0.03161099443751422,0.198844620318614,1.3926834761794986,1.3306865199238942,0.044516185706229935,1.0000000000000009,1.2979315969696825,0.0680354731211041,1.193857643425369,1.132963438133865,0.06089420529150402,0.05100625323869334,1.193857643425369,1.0599208049643605,0.13393683846100846,0.11218828241256822,1.193857643425369,1.132963438133865,1.0599208049643605,0.05100625323869334,0.11218828241256822,0.7211211159755844,0.8792108760076334,0.27289764096798597,0.727102359032014,0.2728976409679881,0.7271023590320119,0.27214817102079025,0.7278518289792097,0.5774673146699185,12,12,1
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 SET1_polypythia,pythia-31m,31m,1-2,1,2,3.9511041908736955,19.60127408599356,8.787993409317924,M1_orth_avg,10.813280676675635,0.5516621332489023,23.552378276867255,19.60127408599356,12.897065980715917,8.945961789842222,12.739097600191618,8.787993409317924,90.13433881686237,86.18323462598867,89.54899757420091,85.59789338332722,19.598162168937034,8.942849275572815,0.0418169739856449,0.202500492518182,1.3844040182473478,1.2022347064534529,0.13158681237036632,1.0000000000000004,1.1447916595301444,0.17307979141851387,1.215116893695873,1.1383532608261917,0.07676363286968124,0.06317386686658487,1.215116893695873,1.0945424823383594,0.12057441135751357,0.09922865197831056,1.215116893695873,1.1383532608261917,1.0945424823383594,0.06317386686658487,0.09922865197831056,0.5501635420889374,0.8108135480975568,0.8943283411131033,0.10567165888689661,0.8943283411131034,0.10567165888689654,0.8544468854471462,0.14555311455285383,0.3198016875095634,6,6,1
 SET1_polypythia,pythia-31m,31m,1-3,1,3,3.95732802498675,17.72417500216589,6.736627288838267,M1_perm_avg,10.987547713327622,0.6199187105738319,21.68150302715264,17.72417500216589,10.693955313825017,6.736627288838267,14.383636494516471,10.426308469529722,103.62520384866275,99.667875823676,98.38614797374429,94.42881994875754,17.708979915810502,6.721433994121514,0.05345081828266005,0.1941663517554338,1.3759572500291595,1.1294448994079922,0.17915698370421257,1.0,1.1147426884281002,0.18984206202301968,1.1898805647187838,1.0838501353228367,0.10603042939594709,0.08911014478247765,1.1898805647187838,1.054922959503422,0.13495760521536182,0.1134211358828755,1.1898805647187838,1.0838501353228367,1.054922959503422,0.08911014478247765,0.1134211358828755,0.7451908747560669,0.8038675188398995,0.2951430349369193,0.7048569650630807,0.2951430349369193,0.7048569650630807,0.36046482892840914,0.6395351710715909,0.36653318423012365,6,6,1
 SET1_polypythia,pythia-31m,31m,1-4,1,4,3.8991993843770385,17.00205059014188,6.586537898014514,M1_orth_avg,10.415512692127367,0.6126033231642355,20.90124997451892,17.00205059014188,17.241835224029682,13.342635839652644,10.485737282391552,6.586537898014514,86.96320276826484,83.0640033838878,56.837163140084805,52.93796375570776,16.972986269837023,13.31357116102006,0.05278835878757829,0.19081268958684366,1.3869007103870605,1.3750422599056789,0.008550324037307749,1.0000000000000009,1.325702871989061,0.04412560894926671,1.2461347583684763,1.209735019244704,0.03639973912377226,0.029210114619890107,1.2461347583684763,1.1511016002268264,0.09503315814164992,0.07626234442418871,1.2461347583684763,1.209735019244704,1.1511016002268264,0.029210114619890107,0.07626234442418871,0.5482096806235741,0.7630480174610721,0.9070490606409585,0.09295093935904157,0.9070490606409584,0.09295093935904165,0.8822422887258773,0.11775771127412271,0.3758342622161702,6,0,1
@@ -101,6 +110,14 @@ SET1_polypythia,pythia-31m,31m,8-9,8,9,3.953362212955602,20.609523825449486,5.68
 SET1_polypythia,pythia-410m,410m,1-2,1,2,2.966551938091161,6.191101432546477,5.639203474090834,M1_perm_avg,0.5518979584556423,0.08914374355980141,9.157653370637638,6.191101432546477,8.605755412181995,5.639203474090834,8.77304732091895,5.806495382827789,16.04849814497717,13.081946206886009,13.131684006543543,10.165132068452381,6.187760305186928,5.635862705059013,0.0427151081634782,0.21880007698572485,1.3847279773716792,1.3303970349305332,0.03923582344618351,1.0000000000000002,1.3274184900141912,0.04138681986209726,1.160589700833997,1.0650788340658717,0.09551086676812526,0.0822951183346633,1.160589700833997,1.0526234334466773,0.10796626738731963,0.09302707693316194,1.160589700833997,1.0650788340658717,1.0526234334466773,0.0822951183346633,0.09302707693316194,0.3091908430110828,0.9199221561893456,0.817137042183511,0.18286295781648898,0.8171370421835108,0.18286295781648917,0.7986525561206986,0.2013474438793014,0.47795609904941544,24,24,1
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 SET1_polypythia,pythia-70m,70m,1-3,1,3,3.578833135217914,20.71179135516043,10.563843091951036,M1_orth_avg,10.147948263209393,0.4899599503101884,24.29062449037834,20.71179135516043,27.663672639432484,24.08483950421457,14.14267622716895,10.563843091951036,84.06302236219831,80.48418922698039,124.66854717058057,121.08971403536265,20.685701871649236,24.058752489183277,-0.03963725521855644,0.1960134587844177,1.4475533367870448,1.3379341616984488,0.07572720970123568,0.9999999999999999,1.307247158076424,0.09692643106473788,1.2118348278280333,1.1427831521553735,0.0690516756726598,0.05698109518474629,1.2118348278280333,1.0763403649770777,0.13549446285095557,0.11180934871611319,1.2118348278280333,1.1427831521553735,1.0763403649770777,0.05698109518474629,0.11180934871611319,0.5346528047650446,0.7809718654448193,0.9051293370412379,0.09487066295876209,0.9051293370412379,0.09487066295876208,0.930894116581892,0.06910588341810799,0.48330722438050994,6,6,1
 SET1_polypythia,pythia-70m,70m,1-4,1,4,3.578833135217914,27.890989618369822,13.275441826050839,M1_orth_avg,14.615547792318983,0.5240239945696569,31.469822753587735,27.890989618369822,34.52885860037508,30.950025465157168,16.854274961268754,13.275441826050839,95.8927985363666,92.31396540114868,136.30908043868232,132.7302473034644,27.8399529603285,30.898992669092465,0.04355576957983617,0.17713822481673977,1.3940391987417349,1.3549455544588296,0.0280434325793646,0.9999999999999996,1.3368282505776277,0.04103969832107019,1.2372319633224234,1.1658744835860315,0.07135747973639184,0.05767510204373538,1.2372319633224234,1.1101203702159828,0.1271115931064406,0.10273869159110566,1.2372319633224234,1.1658744835860315,1.1101203702159828,0.05767510204373538,0.10273869159110566,0.5033392721168221,0.760755588678183,0.9580342341608327,0.04196576583916734,0.9580342341608327,0.041965765839167384,0.9705700834471602,0.029429916552839816,0.528244572757333,6,6,1
@@ -137,3 +154,6 @@ SET1_polypythia,pythia-70m,70m,6-9,6,9,3.631728518810135,16.430689941724765,9.04
 SET1_polypythia,pythia-70m,70m,7-8,7,8,3.6366048814110403,22.94067096150318,7.189522720207519,M1_orth_avg,15.751148241295661,0.6866036424012061,26.577275842914222,22.94067096150318,11.196601205764841,7.559996324353801,10.826127601618559,7.189522720207519,99.52662773157208,95.89002285016103,168.91501549249836,165.2784106110873,22.93331950984589,7.552646584706764,0.050997599795640995,0.2021025785262535,1.3783390918902083,1.2739011932286661,0.07577083119533345,1.0000000000000007,1.2892946575095274,0.06460270546238975,1.195081297909044,1.0879032252432266,0.10717807266581736,0.0896826624710301,1.195081297909044,1.0490014332119622,0.14607986469708178,0.12223424879350737,1.195081297909044,1.0879032252432266,1.0490014332119622,0.0896826624710301,0.12223424879350737,0.8622754448136462,0.7826939580676212,0.08430709663430969,0.9156929033656903,0.08430709663430835,0.9156929033656916,0.0686139208329587,0.9313860791670413,0.5479097840215689,6,6,1
 SET1_polypythia,pythia-70m,70m,7-9,7,9,3.631728518810135,18.61637951078869,7.041663242646159,M1_perm_avg,11.57471626814253,0.6217490496170146,22.248108029598825,18.61637951078869,10.673391761456294,7.041663242646159,14.283389136904763,10.651660618094628,96.22974763535551,92.59801911654537,156.36456804468364,152.7328395258735,18.60658987783095,7.0318754809554385,0.04863949587011176,0.19046681259249384,1.3794879332973322,1.3068144069986487,0.052681523733937294,1.0000000000000024,1.2570374083266864,0.08876520193834347,1.2010867317220326,1.0718377203589586,0.12924901136307398,0.1076100567506611,1.2010867317220326,1.0632100792639636,0.13787665245806902,0.11479325249092652,1.2010867317220326,1.0718377203589586,1.0632100792639636,0.1076100567506611,0.11479325249092652,0.6317034921464805,0.7721638524956678,0.6428467432067481,0.35715325679325194,0.6428467432067482,0.35715325679325177,0.6503441025969965,0.3496558974030035,0.547966688025233,6,0,1
 SET1_polypythia,pythia-70m,70m,8-9,8,9,3.631728518810135,23.211640539001344,7.333266843632787,M1_perm_avg,15.878373695368557,0.6840694292455947,26.84336905781148,23.211640539001344,10.964995362442922,7.333266843632787,12.58635061205561,8.954622093245474,93.61738115622961,89.98565263741948,153.05546722113502,149.4237387023249,23.209202357700892,7.330827866048495,-0.01701731389289497,0.18116254416912528,1.4264379475826996,1.2682465843688688,0.11089957574523894,1.0000000000000018,1.2862945451097594,0.0982471075663915,1.211153521585096,1.1101678643388733,0.10098565724622266,0.08337973299541564,1.211153521585096,1.0658534217597864,0.14530009982530956,0.11996835845809886,1.211153521585096,1.1101678643388733,1.0658534217597864,0.08337973299541564,0.11996835845809886,0.6410276021855338,0.7876314453326478,0.6300119448619816,0.3699880551380183,0.6300119448619816,0.3699880551380183,0.651777351333674,0.3482226486663261,0.5161361277534802,6,6,1
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results/set1x_410m.jsonl

@@ -0,0 +1,3 @@
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results/slerp_14m.jsonl

@@ -0,0 +1,36 @@
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results/slerp_31m.jsonl

@@ -0,0 +1,36 @@
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results/slerp_70m.jsonl

@@ -0,0 +1 @@
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