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RESULTS_COMPOSE_AUDIT.md

@@ -1,31 +1,33 @@
 # Compose-audit: putting the alignment map and the merging payoff on the SAME real models
 
-_Generated 2026-08-26 20:43 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 20:50 UTC · training-free · code: `/root/compose-audit` · operators/aligners/metrics imported unmodified from `mergeschool.core` (`/root/mergeability`, treated as read-only)._
 
 ## Read this first: what substrate, and what metric
 
 | | SET 1 | SET 4 |
 |---|---|---|
-| **Substrate** | `EleutherAI/pythia-{14m,70m,160m}-seed{1..9}` (PolyPythia) — real reseeded LMs | `goldfish-models/eng_latn_1000mb` × `{nld,spa,ell,pol}_*_1000mb` — the real bilingual-composition models, GPT-2 arch, 125M |
+| **Substrate** | `EleutherAI/pythia-{14m,31m,70m,160m,410m}-seed{1..9}` (PolyPythia) — real reseeded LMs | `goldfish-models/eng_latn_1000mb` × `{nld,spa,ell,pol}_*_1000mb` — the real bilingual-composition models, GPT-2 arch, 125M |
 | **What varies between the two parents** | the init/data-order **seed only**. Same data, same architecture, same tokenizer → the merge obstruction is *purely coordinate* | the **language** and the **tokenizer**. Independently initialised, independently trained |
 | **Held-out corpus** | FLORES-200 devtest `eng_Latn` | FLORES-200 devtest, `eng_Latn` + the partner language |
-| **Metric** | Δfloor in **nats/token** vs the better parent | Δfloor in **nats per UTF-8 byte** vs the better parent (bytes, because the two parents use different tokenizers and nats/token is not comparable across them) |
-| **What the metric is** | a **likelihood** metric | a **likelihood** metric |
+| **Metric** | Δfloor in **nats/token** vs the better parent; **BLiMP accuracy** on the same merges | Δfloor in **nats per UTF-8 byte** vs the better parent (bytes, because the two parents use different tokenizers and nats/token is not comparable across them); **MultiBLiMP 1.0 accuracy** on the same merges |
+| **What the metric is** | Δfloor is a **likelihood** metric; BLiMP is an **accuracy** metric | Δfloor is a **likelihood** metric; MultiBLiMP is an **accuracy** metric |
 
-> **Δfloor is a likelihood metric, not benchmark accuracy.** Nothing below shows that a likelihood
-> rescue transfers to BLiMP/MultiBLiMP accuracy, or to any downstream task. The audit's sharpest
-> point — *recovery is not success* — is **not** settled by these numbers and must not be written up
-> as if it were. **We tested that transfer directly on SET 1 with BLiMP — see the accuracy section
-> below — and it does not hold.** SET 4 has no accuracy benchmark in this window (see Coverage).
+> **Δfloor is a likelihood metric, not benchmark accuracy — and here they come apart.** The audit's
+> sharpest point is that a likelihood rescue has not been shown to transfer to accuracy. We tested
+> that transfer directly, on the same merges, with BLiMP (SET 1) and MultiBLiMP 1.0 (SET 4), and it
+> **does not hold in either direction**: in SET 1 a ~70% Δfloor rescue buys ~0.03 BLiMP accuracy over
+> the naive merge, and in SET 4 a merge whose Δfloor says it is destroyed still scores 0.68 on
+> MultiBLiMP-English. Neither metric may be reported as a proxy for the other. Every table below
+> states which one it is.
 
 
 ## Headline findings
 
-1. **Naive averaging of two seed-only-different real LMs is catastrophic, at every size.** Δfloor 14m: +32.4 · 31m: +20.4 · 70m: +20.2 · 160m: +8.7 · 410m: +6.2 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 / 20 / 1 pairs.
-2. **Unit alignment removes a large fraction of that gap and still does not produce a usable model.** Best of permutation / Procrustes removes 14m: 72% · 31m: 57% · 70m: 55% · 160m: 30% · 410m: 9% — leaving 9.0 · 8.1 · 8.7 · 6.0 · 5.6 nats/token above the better parent.
-3. **The rescue shrinks monotonically with scale** (14m: 72% → 410m: 9%) 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: +8.8 · 410m: +6.3 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 / 23 / 2 pairs.
+2. **Unit alignment removes a large fraction of that gap and still does not produce a usable model.** Best of permutation / Procrustes removes 14m: 72% · 31m: 57% · 70m: 55% · 160m: 31% · 410m: 8% — leaving 9.0 · 8.1 · 8.7 · 5.9 · 5.8 nats/token above the better parent.
+3. **The rescue shrinks monotonically with scale** (14m: 72% → 410m: 8%) 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 +0.89 nats/byte against a 0.81 floor; the best M1 rung +0.89. 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.
 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 predict the realised rescue.** Held out by seed pair on a complete 36-pair grid with a seed-cluster permutation null, no predictor survives BH correction. 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.
@@ -75,30 +77,30 @@ 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 — 20 seed pairs · mean parent floor **3.254** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+### pythia-160m — 23 seed pairs · mean parent floor **3.255** nats/token · uniform-over-vocabulary reference **10.826** nats/token
 
 | rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
 |---|---|---|---|---|---|---|---|
-| M0_naive_avg | 20 | 11.92 | 8.66 | 8.30 | 6.88 | 0/20 | 0.0% |
-| M1_perm_avg | 20 | 9.89 | 6.64 | 6.36 | 5.50 | 18/20 | 22.2% |
-| M1_orth_avg | 20 | 9.42 | 6.17 | 6.04 | 5.16 | 20/20 | 28.2% |
-| M2_task_arith | 20 | 30.09 | 26.83 | 27.23 | 17.88 | 0/20 | -209.4% |
-| M3_ties | 20 | 59.75 | 56.50 | 56.80 | 49.69 | 0/20 | -559.8% |
+| M0_naive_avg | 23 | 12.03 | 8.77 | 8.32 | 6.88 | 0/23 | 0.0% |
+| M1_perm_avg | 23 | 9.84 | 6.59 | 6.34 | 5.50 | 21/23 | 23.7% |
+| M1_orth_avg | 23 | 9.41 | 6.16 | 6.11 | 5.15 | 23/23 | 29.2% |
+| M2_task_arith | 23 | 30.47 | 27.22 | 27.31 | 17.88 | 0/23 | -209.7% |
+| M3_ties | 23 | 60.06 | 56.81 | 57.09 | 49.69 | 0/23 | -555.4% |
 
-Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.66**, permutation-aligned **6.63** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.76**, permutation-aligned **6.58** nats/token.
 
 
-### pythia-410m — 1 seed pairs · mean parent floor **2.967** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+### pythia-410m — 2 seed pairs · mean parent floor **2.970** nats/token · uniform-over-vocabulary reference **10.826** nats/token
 
 | rung | n | mean nats/tok | mean Δfloor | median Δfloor | best Δfloor | beats naive | % of naive Δfloor removed |
 |---|---|---|---|---|---|---|---|
-| M0_naive_avg | 1 | 9.16 | 6.19 | 6.19 | 6.19 | 0/1 | 0.0% |
-| M1_perm_avg | 1 | 8.61 | 5.64 | 5.64 | 5.64 | 1/1 | 8.9% |
-| M1_orth_avg | 1 | 8.77 | 5.81 | 5.81 | 5.81 | 1/1 | 6.2% |
-| M2_task_arith | 1 | 16.05 | 13.08 | 13.08 | 13.08 | 0/1 | -111.3% |
-| M3_ties | 1 | 13.13 | 10.17 | 10.17 | 10.17 | 0/1 | -64.2% |
+| M0_naive_avg | 2 | 9.32 | 6.35 | 6.35 | 6.19 | 0/2 | 0.0% |
+| M1_perm_avg | 2 | 8.81 | 5.84 | 5.84 | 5.64 | 2/2 | 7.9% |
+| M1_orth_avg | 2 | 8.95 | 5.98 | 5.98 | 5.81 | 2/2 | 5.8% |
+| M2_task_arith | 2 | 14.69 | 11.72 | 11.72 | 10.37 | 0/2 | -85.4% |
+| M3_ties | 2 | 12.77 | 9.80 | 9.80 | 9.43 | 0/2 | -54.6% |
 
-Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.19**, permutation-aligned **5.64** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.31**, permutation-aligned **5.83** nats/token.
 
 
 **What this says.**
@@ -128,8 +130,8 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.19**, permuta
 | 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 | 20 | 3.25 | 8.66 | 22.2% | 28.2% | 30.4% | 0.755 | 0.771 | 0.0941 |
-| pythia-410m | 1 | 2.97 | 6.19 | 8.9% | 6.2% | 8.9% | 0.309 | 0.183 | 0.0823 |
+| pythia-160m | 23 | 3.26 | 8.77 | 23.7% | 29.2% | 31.3% | 0.766 | 0.786 | 0.0925 |
+| pythia-410m | 2 | 2.97 | 6.35 | 7.9% | 5.8% | 7.9% | 0.381 | 0.342 | 0.0484 |
 
 The coordinator flagged this from the first two pairs and asked whether it survives the full grid.
 **It does, monotonically, across every size we ran.** The naive merge's Δfloor shrinks with scale
@@ -162,7 +164,7 @@ exactly the direction the field is scaling.
 
 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 nats/byte.
+Uniform-over-vocabulary reference (a model that has learned nothing), mean over the two languages, in the same units: **eng-nld_Latn** 3.093, **eng-spa_Latn** 2.920, **eng-ell_Grek** 2.964, **eng-pol_Latn** 3.221 nats/byte.
 
 
 **PRIMARY — Δfloor on ENGLISH text vs the English parent (nats/UTF-8 byte).** This cell has no tokenizer artifact: the merge is asked only to retain what the English parent already had.
@@ -170,12 +172,22 @@ Uniform-over-vocabulary reference (a model that has learned nothing), mean over
 | pair | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1d_vocab_perm_forced | M1e_vocab_orth_forced | M1g_emb_procrustes | M1h_emb_proc_units | M1f_perm_novocab |
 |---|---|---|---|---|---|---|---|---|---|
 | eng–nld_Latn | 0.889 | 1.056 | 1.058 | 1.058 | 1.167 | 0.990 | 1.085 | 0.975 | 0.891 |
+| eng–spa_Latn | 0.892 | 1.034 | 1.033 | 1.033 | 1.131 | 1.054 | 0.973 | 0.970 | 0.891 |
+| eng–ell_Grek | 0.983 | 1.054 | 1.054 | 1.054 | 1.080 | 1.041 | 0.965 | 1.006 | 0.983 |
+| eng–pol_Latn | 0.859 | 0.976 | 0.976 | 0.976 | 1.093 | 0.985 | 1.057 | 0.972 | 0.859 |
+| **mean of the 4** | **0.906** | **1.030** | **1.030** | **1.030** | **1.118** | **1.018** | **1.020** | **0.981** | **0.906** |
+
+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.
+
 
 **Δfloor vs the better parent, mean over the two languages, nats/UTF-8 byte** (lower is better; 0 would mean the merge matches the better parent):
 
 | pair | vocab overlap | floor eng | floor X (own tok) | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1d_vocab_perm_forced | M1e_vocab_orth_forced | M1g_emb_procrustes | M1h_emb_proc_units | M1f_perm_novocab |
 |---|---|---|---|---|---|---|---|---|---|---|---|---|
 | eng–nld_Latn | 27.8% | 0.811 | 0.792 | 1.689 | 1.763 | 1.766 | 1.766 | 2.004 | 1.601 | 1.732 | 1.559 | 1.691 |
+| eng–spa_Latn | 23.1% | 0.811 | 0.746 | 1.643 | 1.637 | 1.635 | 1.635 | 1.831 | 1.632 | 1.503 | 1.426 | 1.643 |
+| eng–ell_Grek | 12.9% | 0.811 | 0.428 | 0.844 | 0.942 | 0.943 | 0.943 | 1.491 | 1.353 | 1.078 | 1.202 | 0.844 |
+| eng–pol_Latn | 15.5% | 0.811 | 0.799 | 1.789 | 1.687 | 1.687 | 1.687 | 2.065 | 1.656 | 1.693 | 1.693 | 1.789 |
 
 **Split by language, and Δ vs naive:**
 
@@ -190,6 +202,33 @@ Uniform-over-vocabulary reference (a model that has learned nothing), mean over
 | eng–nld_Latn | M1g_emb_procrustes | 1.085 | 2.380 | 0.043 |
 | eng–nld_Latn | M1h_emb_proc_units | 0.975 | 2.143 | -0.130 |
 | eng–nld_Latn | M1f_perm_novocab | 0.891 | 2.491 | 0.002 |
+| eng–spa_Latn | M0_naive_avg | 0.892 | 2.395 | 0.000 |
+| eng–spa_Latn | M1a_vocab_avg | 1.034 | 2.240 | -0.007 |
+| eng–spa_Latn | M1b_vocab_perm_avg | 1.033 | 2.238 | -0.008 |
+| eng–spa_Latn | M1c_vocab_orth_avg | 1.033 | 2.238 | -0.008 |
+| eng–spa_Latn | M1d_vocab_perm_forced | 1.131 | 2.531 | 0.187 |
+| eng–spa_Latn | M1e_vocab_orth_forced | 1.054 | 2.210 | -0.011 |
+| eng–spa_Latn | M1g_emb_procrustes | 0.973 | 2.032 | -0.141 |
+| eng–spa_Latn | M1h_emb_proc_units | 0.970 | 1.883 | -0.217 |
+| eng–spa_Latn | M1f_perm_novocab | 0.891 | 2.396 | -0.000 |
+| eng–ell_Grek | M0_naive_avg | 0.983 | 0.706 | 0.000 |
+| eng–ell_Grek | M1a_vocab_avg | 1.054 | 0.829 | 0.097 |
+| eng–ell_Grek | M1b_vocab_perm_avg | 1.054 | 0.831 | 0.098 |
+| eng–ell_Grek | M1c_vocab_orth_avg | 1.054 | 0.831 | 0.098 |
+| eng–ell_Grek | M1d_vocab_perm_forced | 1.080 | 1.901 | 0.646 |
+| eng–ell_Grek | M1e_vocab_orth_forced | 1.041 | 1.665 | 0.509 |
+| eng–ell_Grek | M1g_emb_procrustes | 0.965 | 1.191 | 0.234 |
+| eng–ell_Grek | M1h_emb_proc_units | 1.006 | 1.397 | 0.358 |
+| eng–ell_Grek | M1f_perm_novocab | 0.983 | 0.704 | -0.001 |
+| eng–pol_Latn | M0_naive_avg | 0.859 | 2.719 | 0.000 |
+| eng–pol_Latn | M1a_vocab_avg | 0.976 | 2.399 | -0.101 |
+| eng–pol_Latn | M1b_vocab_perm_avg | 0.976 | 2.399 | -0.101 |
+| eng–pol_Latn | M1c_vocab_orth_avg | 0.976 | 2.399 | -0.101 |
+| eng–pol_Latn | M1d_vocab_perm_forced | 1.093 | 3.037 | 0.276 |
+| eng–pol_Latn | M1e_vocab_orth_forced | 0.985 | 2.327 | -0.133 |
+| eng–pol_Latn | M1g_emb_procrustes | 1.057 | 2.329 | -0.096 |
+| eng–pol_Latn | M1h_emb_proc_units | 0.972 | 2.414 | -0.096 |
+| eng–pol_Latn | M1f_perm_novocab | 0.859 | 2.719 | 0.000 |
 
 **Rungs.** `M0_naive_avg` = straight weight average in raw index space (the merge the manuscript
 reports as failing). `M1a_vocab_avg` = English/partner embedding + unembedding rows transported into
@@ -209,7 +248,7 @@ 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-70m | 19 | 0.718 | 0.723 | 0.518 | 0.537 | 0.543 | 23.6% |
+| pythia-70m | 27 | 0.716 | 0.722 | 0.518 | 0.538 | 0.543 | 24.2% |
 
 **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
@@ -223,7 +262,7 @@ Pair by pair, does the size of the likelihood rescue predict the size of the acc
 | substrate | n | Spearman(Δfloor rescue, BLiMP rescue) | mean Δfloor rescue (nats/tok) | mean BLiMP rescue (acc) |
 |---|---|---|---|---|
 | pythia-14m | 36 | 0.139 | 23.44 | 0.0257 |
-| pythia-70m | 19 | 0.309 | 9.91 | 0.0314 |
+| pythia-70m | 27 | 0.206 | 10.94 | 0.0322 |
 
 ## Did we try hard enough? · REPAIR on top of the alignment
 
@@ -231,11 +270,11 @@ The obvious objection to a negative merging result is that averaging is a weak m
 
 | substrate | n pairs | rung | mean Δfloor (nats/tok) | median Δfloor | BLiMP accuracy | % of the parents' above-chance margin retained |
 |---|---|---|---|---|---|---|
-| pythia-14m | 1 | M0_naive_avg | 23.83 | 23.83 | 0.473 | -14.5% |
-| pythia-14m | 1 | M1_perm_avg | 5.66 | 5.66 | 0.527 | 14.6% |
-| pythia-14m | 1 | M4_perm_repair | 5.16 | 5.16 | 0.531 | 17.1% |
-| pythia-14m | 1 | M5_naive_repair | 22.05 | 22.05 | 0.497 | -1.6% |
-| pythia-14m | 1 | **parents** | 0.00 | 0.00 | 0.684 | 100.0% |
+| pythia-14m | 27 | M0_naive_avg | 32.25 | 30.70 | 0.512 | 7.2% |
+| pythia-14m | 27 | M1_perm_avg | 9.53 | 9.06 | 0.534 | 20.6% |
+| pythia-14m | 27 | M4_perm_repair | 7.72 | 7.10 | 0.532 | 19.0% |
+| pythia-14m | 27 | M5_naive_repair | 32.11 | 30.98 | 0.509 | 5.4% |
+| pythia-14m | 27 | **parents** | 0.00 | 0.00 | 0.666 | 100.0% |
 
 REPAIR does help the likelihood — it takes a further bite out of the aligned merge's Δfloor, and it
 is the best training-free merge in this report. It does **not** change the conclusion. The repaired
@@ -304,68 +343,120 @@ alignment were all tried on the same pairs; the best of them recovers most of th
   accuracy standing. Whichever of the two you report, the other does not follow from it.
 
 
+## SET 4 · what would SUCCESS look like? The jointly-trained bilingual ceiling
+
+A merge that fails is only interpretable against what a bilingual model of the same budget actually achieves. B-GPT (Arnett et al.) trains English+X **jointly** with one shared tokenizer — the target the composition literature is trying to reach without joint training. B-GPT's context window is 128 tokens, so **every arm in this table, including the Goldfish parents and merges, is re-scored at a matched 128-token context**; these numbers are therefore not directly comparable to the 512-token SET 4 tables above, only to each other.
+
+
+**nats/byte, English**  (lower is better)
+
+| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
+|---|---|---|---|---|---|
+| eng–nld_Latn | 0.871 | 0.848 | 1.473 | 1.697 | 1.835 |
+| eng–spa_Latn | 0.872 | 0.848 | 1.609 | 1.685 | 1.834 |
+
+**nats/byte, partner**  (lower is better)
+
+| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
+|---|---|---|---|---|---|
+| eng–nld_Latn | 0.898 | 2.336 | 0.823 | 3.281 | 3.302 |
+| eng–spa_Latn | 0.889 | 1.940 | 0.777 | 3.126 | 2.969 |
+
+**MultiBLiMP-English**  (higher is better, chance 0.500)
+
+| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
+|---|---|---|---|---|---|
+| eng–nld_Latn | 0.966 | 0.962 | 0.694 | 0.673 | 0.601 |
+| eng–spa_Latn | 0.968 | 0.962 | 0.656 | 0.677 | 0.727 |
+
+**MultiBLiMP-partner**  (higher is better, chance 0.500)
+
+| pair | bgpt_joint_bilingual | goldfish_eng_parent | goldfish_partner_parent | merge_M0_naive | merge_M1a_vocab |
+|---|---|---|---|---|---|
+| eng–nld_Latn | 0.952 | 0.598 | 0.970 | 0.655 | 0.646 |
+| eng–spa_Latn | 0.879 | 0.502 | 0.926 | 0.500 | 0.532 |
+
+This is the cleanest single statement the audit can make about SET 4. A jointly trained bilingual
+model of the same parameter budget is **good at both languages at once** — near the monolingual
+parents on likelihood and on MultiBLiMP. The merge of two monolingual models is not close, on either
+metric, under any rung, in either anchoring direction. The gap is not a coordinate gap that a better
+aligner might close; the joint model also has a *shared vocabulary*, which is exactly the axis the
+alignment group cannot act on.
+
+
+## SET 4 · reverse direction (the partner language is the anchor)
+
+Identical rungs, but the merged model lives in the **partner** language's tokenizer and residual basis and English is transported into it. If the failure were an artifact of anchoring on English it would not survive the swap.
+
+| anchor | floor (anchor lang) | floor (English) | M0_naive_avg | M1a_vocab_avg | M1b_vocab_perm_avg | M1c_vocab_orth_avg | M1e_vocab_orth_forced | M1g_emb_procrustes |
+|---|---|---|---|---|---|---|---|---|
+| nld_Latn | 0.792 | 0.811 | 1.342 | 1.335 | 1.337 | 1.337 | 1.384 | 1.425 |
+
+Δfloor, mean over the two languages, nats/UTF-8 byte. The failure is symmetric: anchoring on the partner language does not make the merge work either.
+
+
 ## P0-2 · Do the pre-merge predictors predict the realised rescue?
 
 Showing, per substrate and per outcome, the **six predictors with the largest |AUROC − 0.5|** plus the multivariate ridge. The full table (every predictor, both outcomes, every substrate) is `results/predictor_auroc.csv`; selecting the extremes here is deliberately generous to the positive claim.
 
 | substrate | outcome | predictor | n | Spearman | AUROC (held out by seed) | null mean | perm p | BH q |
 |---|---|---|---|---|---|---|---|---|
-| pythia-14m | rescue_frac | bnd_perm | 36 | 0.012 | 0.296 | 0.497 | 0.981 | 1.000 |
-| pythia-14m | rescue_frac | qmd_orth | 36 | 0.093 | 0.676 | 0.497 | 0.037 | 0.232 |
-| pythia-14m | rescue_frac | qmd_perm | 36 | 0.077 | 0.664 | 0.498 | 0.051 | 0.232 |
-| pythia-14m | rescue_frac | qmd_act_perm | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.232 |
-| pythia-14m | rescue_frac | qmd_act_procrustes | 36 | -0.207 | 0.657 | 0.500 | 0.055 | 0.232 |
-| pythia-14m | rescue_frac | cka_last | 36 | -0.478 | 0.651 | 0.499 | 0.067 | 0.253 |
-| pythia-14m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.254 | 0.620 | 0.501 | 0.114 | 0.311 |
-| pythia-31m | rescue_frac | bnd_perm | 36 | -0.490 | 0.750 | 0.506 | 0.011 | 0.232 |
-| pythia-31m | rescue_frac | coord_share_bnd_perm | 36 | 0.427 | 0.710 | 0.505 | 0.025 | 0.232 |
-| pythia-31m | rescue_frac | weight_cosine | 36 | 0.274 | 0.704 | 0.504 | 0.029 | 0.232 |
-| pythia-31m | rescue_frac | d_raw | 36 | -0.321 | 0.704 | 0.505 | 0.025 | 0.232 |
-| pythia-31m | rescue_frac | bnd_raw | 36 | -0.391 | 0.701 | 0.506 | 0.032 | 0.232 |
-| pythia-31m | rescue_frac | qmd_perm | 36 | -0.493 | 0.691 | 0.505 | 0.048 | 0.232 |
-| pythia-31m | rescue_frac | MULTIVARIATE_ridge_all | 36 | 0.403 | 0.707 | 0.505 | 0.035 | 0.232 |
-| pythia-70m | rescue_frac | coord_share_bnd_perm | 33 | 0.444 | 0.768 | — | — | — |
-| pythia-70m | rescue_frac | bnd_perm | 33 | -0.386 | 0.750 | — | — | — |
-| pythia-70m | rescue_frac | coord_share_perm | 33 | 0.389 | 0.728 | — | — | — |
-| pythia-70m | rescue_frac | coord_share_orth | 33 | 0.383 | 0.724 | — | — | — |
-| pythia-70m | rescue_frac | qmd_act_perm | 33 | -0.498 | 0.724 | — | — | — |
-| pythia-70m | rescue_frac | qmd_act_procrustes | 33 | -0.498 | 0.724 | — | — | — |
-| pythia-70m | rescue_frac | MULTIVARIATE_ridge_all | 33 | 0.465 | 0.732 | — | — | — |
-| pythia-160m | rescue_frac | qmd_act_perm | 15 | -0.079 | 0.214 | — | — | — |
-| pythia-160m | rescue_frac | qmd_act_procrustes | 15 | -0.079 | 0.214 | — | — | — |
-| pythia-160m | rescue_frac | qmd_act_ot | 15 | -0.111 | 0.232 | — | — | — |
-| pythia-160m | rescue_frac | weight_cosine | 15 | 0.364 | 0.714 | — | — | — |
-| pythia-160m | rescue_frac | d_raw | 15 | -0.393 | 0.714 | — | — | — |
-| pythia-160m | rescue_frac | bnd_perm | 15 | -0.264 | 0.696 | — | — | — |
-| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 15 | 0.100 | 0.411 | — | — | — |
+| 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 | 23 | -0.592 | 0.803 | — | — | — |
+| pythia-160m | rescue_frac | coord_share_orth | 23 | 0.445 | 0.795 | — | — | — |
+| pythia-160m | rescue_frac | qmd_perm | 23 | -0.610 | 0.773 | — | — | — |
+| pythia-160m | rescue_frac | coord_share_perm | 23 | 0.485 | 0.773 | — | — | — |
+| pythia-160m | rescue_frac | bnd_orth | 23 | -0.302 | 0.750 | — | — | — |
+| pythia-160m | rescue_frac | coord_share_bnd_orth | 23 | 0.265 | 0.750 | — | — | — |
+| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 23 | 0.342 | 0.598 | — | — | — |
 | 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 | 0.232 |
-| pythia-14m | dfloor_M1best | coord_share_perm | 36 | -0.445 | 0.735 | 0.495 | 0.016 | 0.232 |
-| pythia-14m | dfloor_M1best | qmd_orth | 36 | 0.438 | 0.725 | 0.496 | 0.021 | 0.232 |
-| pythia-14m | dfloor_M1best | coord_share_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 | 0.228 |
-| pythia-31m | dfloor_M1best | qmd_orth | 36 | 0.289 | 0.670 | 0.502 | 0.101 | 0.298 |
-| pythia-31m | dfloor_M1best | coord_share_orth | 36 | -0.271 | 0.670 | 0.503 | 0.103 | 0.298 |
-| pythia-31m | dfloor_M1best | qmd_perm | 36 | 0.243 | 0.633 | 0.503 | 0.166 | 0.372 |
-| pythia-31m | dfloor_M1best | coord_share_perm | 36 | -0.230 | 0.633 | 0.503 | 0.166 | 0.372 |
-| pythia-31m | dfloor_M1best | bnd_raw | 36 | 0.163 | 0.633 | 0.503 | 0.132 | 0.346 |
-| pythia-31m | dfloor_M1best | bnd_orth | 36 | 0.114 | 0.611 | 0.501 | 0.186 | 0.405 |
-| pythia-31m | dfloor_M1best | MULTIVARIATE_ridge_all | 36 | -0.111 | 0.500 | 0.501 | 0.516 | 0.701 |
-| pythia-70m | dfloor_M1best | cka_last | 33 | 0.590 | 0.776 | — | — | — |
-| pythia-70m | dfloor_M1best | coord_share_bnd_perm | 33 | 0.507 | 0.739 | — | — | — |
-| pythia-70m | dfloor_M1best | bnd_perm | 33 | -0.467 | 0.728 | — | — | — |
-| pythia-70m | dfloor_M1best | coord_share_bnd_orth | 33 | 0.295 | 0.673 | — | — | — |
-| pythia-70m | dfloor_M1best | cka_mean | 33 | 0.432 | 0.662 | — | — | — |
-| pythia-70m | dfloor_M1best | bnd_orth | 33 | -0.233 | 0.651 | — | — | — |
-| pythia-70m | dfloor_M1best | MULTIVARIATE_ridge_all | 33 | 0.388 | 0.647 | — | — | — |
-| pythia-160m | dfloor_M1best | cka_last | 15 | 0.521 | 0.768 | — | — | — |
-| pythia-160m | dfloor_M1best | qmd_act_perm | 15 | -0.143 | 0.268 | — | — | — |
-| pythia-160m | dfloor_M1best | qmd_act_procrustes | 15 | -0.143 | 0.268 | — | — | — |
-| pythia-160m | dfloor_M1best | qmd_act_ot | 15 | -0.189 | 0.286 | — | — | — |
-| pythia-160m | dfloor_M1best | bnd_perm | 15 | -0.636 | 0.696 | — | — | — |
-| pythia-160m | dfloor_M1best | coord_share_bnd_perm | 15 | 0.496 | 0.696 | — | — | — |
-| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 15 | 0.507 | 0.679 | — | — | — |
+| 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 | bnd_perm | 23 | -0.591 | 0.818 | — | — | — |
+| pythia-160m | dfloor_M1best | coord_share_bnd_perm | 23 | 0.445 | 0.773 | — | — | — |
+| pythia-160m | dfloor_M1best | bnd_orth | 23 | -0.587 | 0.765 | — | — | — |
+| pythia-160m | dfloor_M1best | coord_share_bnd_orth | 23 | 0.489 | 0.742 | — | — | — |
+| pythia-160m | dfloor_M1best | cka_last | 23 | 0.386 | 0.712 | — | — | — |
+| pythia-160m | dfloor_M1best | cka_mean | 23 | -0.324 | 0.697 | — | — | — |
+| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 23 | 0.585 | 0.735 | — | — | — |
 
 ### Does a predictor fitted on one substrate transfer to another?
 
@@ -373,49 +464,49 @@ 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 | 0.352 | 0.500 | 0.925 | 0.992 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 15 | 0.571 | 0.496 | 0.346 | 0.630 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.667 | 0.498 | 0.041 | 0.328 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 33 | 0.559 | 0.502 | 0.291 | 0.583 |
-| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.501 | 0.463 | 0.740 |
-| coord_share_bnd_perm | rescue_frac | pythia-160m | 15 | 0.696 | 0.497 | 0.130 | 0.400 |
-| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.501 | 0.026 | 0.260 |
-| coord_share_bnd_perm | rescue_frac | pythia-70m | 33 | 0.768 | 0.502 | 0.005 | 0.140 |
-| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.501 | 0.067 | 0.344 |
-| qmd_act_perm | rescue_frac | pythia-160m | 15 | 0.429 | 0.500 | 0.693 | 0.977 |
-| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.497 | 0.387 | 0.672 |
-| qmd_act_perm | rescue_frac | pythia-70m | 33 | 0.724 | 0.495 | 0.007 | 0.140 |
-| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.495 | 0.129 | 0.400 |
-| cka_mean | rescue_frac | pythia-160m | 15 | 0.304 | 0.502 | 0.915 | 0.992 |
-| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.346 | 0.630 |
-| cka_mean | rescue_frac | pythia-70m | 33 | 0.298 | 0.497 | 0.972 | 0.992 |
-| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.506 | 0.242 | 0.566 |
-| weight_cosine | rescue_frac | pythia-160m | 15 | 0.714 | 0.505 | 0.081 | 0.344 |
-| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.500 | 0.018 | 0.240 |
-| weight_cosine | rescue_frac | pythia-70m | 33 | 0.467 | 0.496 | 0.627 | 0.962 |
-
-**SET 4, held out by language pair.** n = 1 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.
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-14m | 36 | 0.349 | 0.500 | 0.932 | 0.977 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 23 | 0.720 | 0.500 | 0.037 | 0.209 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.701 | 0.496 | 0.019 | 0.152 |
+| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 36 | 0.556 | 0.500 | 0.291 | 0.612 |
+| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.507 | 0.480 | 0.799 |
+| coord_share_bnd_perm | rescue_frac | pythia-160m | 23 | 0.606 | 0.499 | 0.198 | 0.497 |
+| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.500 | 0.011 | 0.152 |
+| coord_share_bnd_perm | rescue_frac | pythia-70m | 36 | 0.806 | 0.495 | 0.001 | 0.040 |
+| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.494 | 0.045 | 0.209 |
+| qmd_act_perm | rescue_frac | pythia-160m | 23 | 0.500 | 0.497 | 0.507 | 0.812 |
+| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.498 | 0.399 | 0.725 |
+| qmd_act_perm | rescue_frac | pythia-70m | 36 | 0.676 | 0.504 | 0.031 | 0.206 |
+| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.498 | 0.155 | 0.442 |
+| cka_mean | rescue_frac | pythia-160m | 23 | 0.455 | 0.498 | 0.649 | 0.928 |
+| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.500 | 0.338 | 0.675 |
+| cka_mean | rescue_frac | pythia-70m | 36 | 0.346 | 0.502 | 0.937 | 0.977 |
+| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.505 | 0.232 | 0.545 |
+| weight_cosine | rescue_frac | pythia-160m | 23 | 0.636 | 0.498 | 0.141 | 0.433 |
+| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.497 | 0.014 | 0.152 |
+| weight_cosine | rescue_frac | pythia-70m | 36 | 0.494 | 0.504 | 0.528 | 0.813 |
+
+**SET 4, held out by language pair.** n = 4 language pairs. This is far too few for an AUROC or a permutation null; only the rank correlation is reported, and it should be read as descriptive, not inferential.
 
 | predictor | Spearman vs realised rescue |
 |---|---|
 | weight_cosine | -0.400 |
-| d_raw | -0.400 |
-| qmd_perm | -0.400 |
-| coord_share_perm | 0.000 |
-| qmd_orth | -0.400 |
-| coord_share_orth | 0.000 |
-| bnd_raw | 0.200 |
-| bnd_perm | 0.200 |
-| bnd_orth | 0.200 |
-| coord_share_bnd_perm | 0.000 |
-| coord_share_bnd_orth | 0.000 |
+| d_raw | 0.400 |
+| qmd_perm | 0.400 |
+| coord_share_perm | 0.800 |
+| qmd_orth | 0.400 |
+| coord_share_orth | 0.800 |
+| bnd_raw | 0.800 |
+| bnd_perm | 0.800 |
+| bnd_orth | 0.800 |
+| coord_share_bnd_perm | 0.800 |
+| coord_share_bnd_orth | 0.800 |
 | cka_mean | -0.400 |
-| cka_last | 0.400 |
+| cka_last | -0.400 |
 | qmd_act_perm | 0.400 |
 | qmd_act_procrustes | 0.400 |
 | qmd_act_ot | 0.400 |
-| vocab_overlap | -0.200 |
-| weight_cosine_body | -0.200 |
+| vocab_overlap | -0.800 |
+| weight_cosine_body | -0.800 |
 
 ### What P0-2 comes to
 
@@ -447,7 +538,7 @@ SET 1's main grid uses `pythia-<size>-seed{n}`, which reseeds **both** the initi
 |---|---|---|---|---|---|---|---|
 | 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) | 20 | 3.25 | 8.66 | 6.64 | 6.17 | 30.4% | 0.0941 |
+| 160m (init+data, main grid) | 23 | 3.26 | 8.77 | 6.59 | 6.16 | 31.3% | 0.0925 |
 
 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,
@@ -462,14 +553,23 @@ init-plus-data-order number, not an init-only one.
 
 | cell | n | status | what was measured |
 |---|---|---|---|
-| SET 1 · pythia-14m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
-| SET 1 · pythia-70m | 36/36 seed pairs | complete | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
-| SET 1 · pythia-160m | 20/36 seed pairs | partial | M0 naive · M1 permutation · M1 Procrustes · M2 task-arithmetic · M3 TIES; barrier for M0 and M1-perm |
-| SET 4 · goldfish eng×X | 1/4 language pairs (nld_Latn) | partial | M0 naive · M1a vocab-transport · M1b/c vocab+unit-aligned (perm/Procrustes) · M1d/e forced-residual · M1f unit-aligned only |
-| BLiMP accuracy · SET 1 (English) | pythia-14m: 36/36 pairs, pythia-70m: 19/36 pairs | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges as the Δfloor tables |
-| MultiBLiMP / any accuracy benchmark · SET 4 (Goldfish) | 0 | **NOT RUN** | No multilingual benchmark harness was close to wired inside this window; deliberately not built from scratch. SET 4's numbers are likelihood only and say nothing about accuracy. |
-| B-GPT joint bilingual reference | 0 | **NOT RUN** | Out of window; the merged models are not compared against a jointly-trained bilingual ceiling. |
-| Goldfish 160m/other tiers, other language pairs | 0 | NOT RUN | Only the 1000mb tier and the four audit languages. |
+| 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 | 23/36 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 | 2/15 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-70m: 27/36 | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges |
+| SET 1 · REPAIR rung | pythia-14m: 27/36 | 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) | 1/4 language pairs | partial | 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 | 2/4 language pairs | RAN | `catherinearnett/B-GPT_en_X_simultaneous` vs the Goldfish parents and merges, all scored at a matched 128-token context |
+| SET 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 | 2/36 possible pairs | partial | 6 seeds only (15 possible pairs) and a reduced eval budget; the per-pair alignment cost is ~9 min at this width. Treat 410m as directional. |
+| Goldfish other tiers / other languages | 0 | NOT RUN | Only the 1000mb tier and the four audit languages. |
+| Any downstream task beyond BLiMP/MultiBLiMP | 0 | NOT RUN | Both benchmarks are minimal-pair grammaticality tests. They do not speak to reasoning, generation quality or instruction following. |
 
 ## Threats to validity, stated plainly
 
@@ -491,15 +591,31 @@ init-plus-data-order number, not an init-only one.
 ## Files
 
 ```
-results/set1_{14m,70m,160m}.jsonl   per-pair raw records (predictors, rungs, barriers, align info)
-results/set1_pairs.csv              per-pair flat table, SET 1
-results/set4_goldfish.jsonl         per-language-pair raw records, SET 4
-results/set4_pairs.csv              per-language-pair flat table, SET 4
-results/rung_summary.csv            rung x substrate x metric summary
-results/predictor_auroc.csv         SET 1 predictor table: held-out AUROC, permutation null, BH q
-results/set4_predictors.csv         SET 4 predictor rank correlations (n=4, descriptive)
-figs/set1_dfloor_by_rung.png        Δfloor by rung, per size
-figs/set1_rescue_vs_predictor.png   realised rescue vs coordinate share / CKA
-figs/set1_roc.png                   held-out-by-seed ROC
-figs/set4_dfloor.png                Δfloor by rung, Goldfish
+results/set1_{14m,31m,70m,160m,410m}.jsonl  SET 1 per-pair raw records (predictors, rungs, barriers)
+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/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/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/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_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_blimp_dissociation.png            likelihood rescue vs accuracy rescue
+figs/set4_dfloor.png                        Δfloor by rung, Goldfish
+code/*.py                                   every script that produced the above
 ```
+
+**Reproducing.** `common.py` holds the corpora and evaluation; `gpt2_align.py` holds the GPT-2
+(Conv1D) symmetry factors that `mergeschool.core.alignment`'s row-major aligners do not cover; the
+`set1_*`/`set4_*` scripts are the drivers, each with a resumable JSONL ledger; `analyze.py` builds
+the tables and figures and `make_report.py` writes this document. Merge operators, aligners, quotient
+metrics and the barrier are imported unmodified from `mergeschool.core`.
+