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@@ -5,7 +5,7 @@ tags: [model-merging, alignment, polypythia, goldfish, multilingual]
 
 # Compose-audit: putting the alignment map and the merging payoff on the SAME real models
 
-_Generated 2026-08-26 20:54 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 20:59 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
 
@@ -28,13 +28,13 @@ _Generated 2026-08-26 20:54 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: +6.3 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 / 25 / 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 · 6.0 · 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.)
+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 / 28 / 3 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: 32% · 410m: 11% — leaving 9.0 · 8.1 · 8.7 · 6.0 · 5.7 nats/token above the better parent.
+3. **The rescue shrinks monotonically with scale** (14m: 72% → 410m: 11%) 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.
 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.
+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.
 
 
@@ -82,30 +82,30 @@ 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 — 25 seed pairs · mean parent floor **3.254** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+### pythia-160m — 28 seed pairs · mean parent floor **3.254** 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 | 25 | 12.01 | 8.76 | 8.33 | 6.88 | 0/25 | 0.0% |
-| M1_perm_avg | 25 | 9.98 | 6.72 | 6.37 | 5.50 | 22/25 | 22.1% |
-| M1_orth_avg | 25 | 9.40 | 6.15 | 6.11 | 5.13 | 25/25 | 29.3% |
-| M2_task_arith | 25 | 30.22 | 26.96 | 27.14 | 17.88 | 0/25 | -207.2% |
-| M3_ties | 25 | 60.16 | 56.91 | 57.09 | 49.30 | 0/25 | -556.6% |
+| M0_naive_avg | 28 | 12.10 | 8.84 | 8.38 | 6.88 | 0/28 | 0.0% |
+| M1_perm_avg | 28 | 9.97 | 6.72 | 6.38 | 5.50 | 25/28 | 22.6% |
+| M1_orth_avg | 28 | 9.38 | 6.12 | 6.04 | 5.13 | 28/28 | 29.8% |
+| M2_task_arith | 28 | 30.32 | 27.07 | 26.97 | 17.88 | 0/28 | -205.4% |
+| M3_ties | 28 | 60.19 | 56.93 | 57.41 | 49.30 | 0/28 | -554.6% |
 
-Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.75**, permutation-aligned **6.72** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **8.84**, permutation-aligned **6.71** nats/token.
 
 
-### pythia-410m — 2 seed pairs · mean parent floor **2.970** nats/token · uniform-over-vocabulary reference **10.826** nats/token
+### pythia-410m — 3 seed pairs · mean parent floor **2.971** 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 | 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% |
+| 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% |
 
-Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.31**, permutation-aligned **5.83** nats/token.
+Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.38**, permutation-aligned **5.90** nats/token.
 
 
 **What this says.**
@@ -135,8 +135,8 @@ Linear-mode-connectivity barrier (`eval.merge_barrier`): naive **6.31**, 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 | 25 | 3.25 | 8.76 | 22.1% | 29.3% | 31.3% | 0.769 | 0.791 | 0.0900 |
-| pythia-410m | 2 | 2.97 | 6.35 | 7.9% | 5.8% | 7.9% | 0.381 | 0.342 | 0.0484 |
+| pythia-160m | 28 | 3.25 | 8.84 | 22.6% | 29.8% | 31.5% | 0.751 | 0.765 | 0.0874 |
+| pythia-410m | 3 | 2.97 | 6.49 | 11.2% | 9.2% | 11.2% | 0.410 | 0.372 | 0.0333 |
 
 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
@@ -253,7 +253,8 @@ 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 | 32 | 0.717 | 0.722 | 0.515 | 0.539 | 0.541 | 24.0% |
+| pythia-31m | 11 | 0.688 | 0.695 | 0.514 | 0.530 | 0.535 | 22.8% |
+| pythia-70m | 35 | 0.717 | 0.722 | 0.515 | 0.540 | 0.542 | 24.4% |
 
 **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
@@ -267,7 +268,8 @@ 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 | 32 | 0.187 | 11.28 | 0.0352 |
+| pythia-31m | 11 | -0.327 | 14.16 | 0.0303 |
+| pythia-70m | 35 | 0.239 | 11.31 | 0.0370 |
 
 ## Did we try hard enough? · REPAIR on top of the alignment
 
@@ -280,6 +282,11 @@ 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 | 4 | M0_naive_avg | 20.95 | 19.69 | 0.544 | 19.0% |
+| pythia-70m | 4 | M1_perm_avg | 21.63 | 20.06 | 0.541 | 17.6% |
+| pythia-70m | 4 | M4_perm_repair | 21.67 | 20.37 | 0.532 | 13.7% |
+| pythia-70m | 4 | M5_naive_repair | 20.02 | 20.22 | 0.518 | 8.0% |
+| pythia-70m | 4 | **parents** | 0.00 | 0.00 | 0.731 | 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
@@ -430,6 +437,47 @@ follow that the English-anchored direction alone could not support:
 
 ## P0-2 · Do the pre-merge predictors predict the realised rescue?
 
+### The confirmatory test
+
+Outcome = **realised rescue**: the fraction of the naive merge's Δfloor that the best M1 rung removes.
+Label = above the within-substrate median. **Held out by seed**: fold *k* is every pair touching seed
+*k*, fitted on the pairs touching neither, so the predictor's direction never sees the held-out pairs.
+Null = a **seed-cluster permutation** (2000 draws): permute the seed identities and re-map each pair's
+outcome to the permuted pair, leaving the predictor vector untouched. That preserves the pair
+dependence structure a plain label shuffle destroys, and it is why the null means below sit at 0.50
+rather than drifting.
+
+The family below is the five predictors **the audit brief itself names** — weight cosine, coordinate
+share, QMD, CKA, task-vector cosine — on the one outcome it asks about. It was fixed from the brief,
+not selected after looking at the results, and BH is applied within this family only. The larger
+exploratory table follows it.
+
+
+| substrate | predictor | n | Spearman | AUROC (held out by seed) | null mean | perm p | BH q (within family) |
+|---|---|---|---|---|---|---|---|
+| pythia-14m | weight cosine | 36 | 0.095 | 0.549 | 0.501 | 0.316 | 0.517 |
+| 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 |
+
+### The exploratory table
+
 Showing, per substrate and per outcome, the **six predictors with the largest |AUROC − 0.5|** plus the multivariate ridge. The full table (every predictor, both outcomes, every substrate) is `results/predictor_auroc.csv`; selecting the extremes here is deliberately generous to the positive claim.
 
 | substrate | outcome | predictor | n | Spearman | AUROC (held out by seed) | null mean | perm p | BH q |
@@ -455,13 +503,13 @@ Showing, per substrate and per outcome, the **six predictors with the largest |A
 | 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 | 25 | -0.597 | 0.801 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_orth | 25 | 0.395 | 0.763 | — | — | — |
-| pythia-160m | rescue_frac | qmd_perm | 25 | -0.552 | 0.737 | — | — | — |
-| pythia-160m | rescue_frac | coord_share_perm | 25 | 0.379 | 0.718 | — | — | — |
-| pythia-160m | rescue_frac | bnd_orth | 25 | -0.242 | 0.705 | — | — | — |
-| pythia-160m | rescue_frac | task_vector_cosine | 25 | 0.052 | 0.301 | — | — | — |
-| pythia-160m | rescue_frac | MULTIVARIATE_ridge_all | 25 | 0.348 | 0.590 | — | — | — |
+| 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 | 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 |
@@ -483,13 +531,13 @@ Showing, per substrate and per outcome, the **six predictors with the largest |A
 | 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 | 25 | -0.449 | 0.763 | — | — | — |
-| pythia-160m | dfloor_M1best | cka_mean | 25 | -0.402 | 0.731 | — | — | — |
-| pythia-160m | dfloor_M1best | bnd_orth | 25 | -0.438 | 0.724 | — | — | — |
-| pythia-160m | dfloor_M1best | coord_share_bnd_perm | 25 | 0.335 | 0.724 | — | — | — |
-| pythia-160m | dfloor_M1best | cka_last | 25 | 0.395 | 0.724 | — | — | — |
-| pythia-160m | dfloor_M1best | d_raw | 25 | 0.103 | 0.282 | — | — | — |
-| pythia-160m | dfloor_M1best | MULTIVARIATE_ridge_all | 25 | 0.472 | 0.699 | — | — | — |
+| 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 | — | — | — |
 
 ### Does a predictor fitted on one substrate transfer to another?
 
@@ -497,26 +545,26 @@ 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 | 0.931 | 0.962 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-160m | 25 | 0.699 | 0.503 | 0.050 | 0.200 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-31m | 36 | 0.691 | 0.496 | 0.023 | 0.180 |
-| MULTIVARIATE_ridge_all | rescue_frac | pythia-70m | 36 | 0.580 | 0.501 | 0.217 | 0.502 |
-| coord_share_bnd_perm | rescue_frac | pythia-14m | 36 | 0.515 | 0.506 | 0.481 | 0.768 |
-| coord_share_bnd_perm | rescue_frac | pythia-160m | 25 | 0.583 | 0.500 | 0.255 | 0.515 |
-| coord_share_bnd_perm | rescue_frac | pythia-31m | 36 | 0.710 | 0.502 | 0.015 | 0.180 |
-| coord_share_bnd_perm | rescue_frac | pythia-70m | 36 | 0.806 | 0.498 | 0.002 | 0.080 |
-| qmd_act_perm | rescue_frac | pythia-14m | 36 | 0.657 | 0.495 | 0.046 | 0.200 |
-| qmd_act_perm | rescue_frac | pythia-160m | 25 | 0.442 | 0.505 | 0.693 | 0.952 |
-| qmd_act_perm | rescue_frac | pythia-31m | 36 | 0.525 | 0.497 | 0.407 | 0.707 |
-| qmd_act_perm | rescue_frac | pythia-70m | 36 | 0.676 | 0.500 | 0.027 | 0.180 |
-| cka_mean | rescue_frac | pythia-14m | 36 | 0.599 | 0.499 | 0.159 | 0.424 |
-| cka_mean | rescue_frac | pythia-160m | 25 | 0.410 | 0.505 | 0.782 | 0.955 |
-| cka_mean | rescue_frac | pythia-31m | 36 | 0.540 | 0.497 | 0.338 | 0.643 |
-| cka_mean | rescue_frac | pythia-70m | 36 | 0.346 | 0.502 | 0.938 | 0.962 |
-| weight_cosine | rescue_frac | pythia-14m | 36 | 0.580 | 0.506 | 0.226 | 0.502 |
-| weight_cosine | rescue_frac | pythia-160m | 25 | 0.673 | 0.499 | 0.072 | 0.231 |
-| weight_cosine | rescue_frac | pythia-31m | 36 | 0.704 | 0.501 | 0.018 | 0.180 |
-| weight_cosine | rescue_frac | pythia-70m | 36 | 0.494 | 0.499 | 0.518 | 0.768 |
+| 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 |
 
 **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.
 
@@ -543,24 +591,45 @@ Leave-one-**size**-out. Predictors are standardised *within* size first, so a pr
 
 ### What P0-2 comes to
 
-**Within a single substrate, nothing predicts the realised rescue.** On pythia-14m — 36 seed pairs,
-a complete grid, a properly structured seed-cluster null — every pre-merge predictor we computed
-(weight cosine, QMD in weight space and in representation space, coordinate share, CKA, task-vector
-cosine) lands between AUROC 0.30 and 0.68 held out by seed, and **not one survives BH correction**.
-The multivariate ridge over all of them does no better. This is a negative transfer result and it is
-reported as one: the alignment-derived quantities that predict mergeability in the synthetic/S3
-setting do **not** rank real reseeded-LM pairs by how much alignment will actually rescue them.
-
-**Across substrates the picture is only slightly better and it is not consistent.** The
-block-normalised coordinate share does transfer to some held-out sizes and not to others. Read
-against the whole family that is one predictor doing well on part of the grid, not a validated
-instrument, and it should not be quoted as a headline number.
-
-Two honest caveats in the other direction. First, the *within-substrate* variance in rescue is small
-relative to the *between*-substrate variance — every pair at a given size is rescued by roughly the
-same amount — so there may simply be little signal left for a within-size predictor to find. Second,
-the seed-cluster null is conservative by construction. Neither rescues the positive claim: on this
-substrate, at this n, the predictors do not predict.
+**The confirmatory family gives 1 significant cell out of
+15 tested** (BH q < 0.05 within the family):
+
+- pythia-70m · coordinate share (block-normalised / permutation) · AUROC 0.806 · q = 0.037
+
+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".
+- **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).
+
+One thing worth noticing before concluding, because it is partly a power story rather than a signal
+story: **detectability tracks how much the outcome varies at all.** The within-substrate standard
+deviation of the realised rescue is 0.067 at 14m, 0.143 at 31m, 0.127 at 70m and 0.095 at 160m
+(against a between-substrate spread of 0.143 in the means). 14m — where the rescue is both largest
+and most uniform across pairs — is the substrate where nothing predicts, and 70m, with roughly twice
+the spread, is where the one significant cell appears. So part of the null is that at some sizes
+every pair is rescued by nearly the same amount and there is very little left to rank. That is a
+caveat in the predictors' favour and it does not rescue the positive claim: a predictor that only
+resolves when the outcome happens to be dispersed is not the instrument the thesis needs.
+
+Against them: the seed-cluster null is
+conservative by construction, but so is the design that needs it; these are 36 pairs built from 9
+seeds, not 36 independent observations, and any analysis that treats them as independent will
+overstate its significance.
+
+**Verdict, stated as the audit asks.** On real reseeded LMs, the pre-merge alignment predictors do
+not reliably predict how much of the merge obstruction alignment will actually remove. The one
+substrate where the coordinate share does predict it does not generalise to the others. This is a
+negative transfer result from the synthetic/S3 setting to real models, and it is reported as one.
 
 
 ## Control · is the obstruction the INIT seed or the DATA order?
@@ -571,7 +640,7 @@ 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) | 25 | 3.25 | 8.76 | 6.72 | 6.15 | 31.3% | 0.0900 |
+| 160m (init+data, main grid) | 28 | 3.25 | 8.84 | 6.72 | 6.12 | 31.5% | 0.0874 |
 
 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,
@@ -589,18 +658,18 @@ 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 | 25/36 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 Δfloor · pythia-160m | 28/36 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 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: 32/36 | RAN | 67 paradigms from `nyu-mll/blimp`, minimal-pair sentence-logprob scoring, on the SAME merges |
-| SET 1 · REPAIR rung | pythia-14m: 36/36 | 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: 11/36, pythia-70m: 35/36 | 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: 4/36 | 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 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. |
+| 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. |
 | 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. |