E13b/c: harden real-weight speciation — full symmetry group + emergent-divergence null

E13c (the symmetry defense): alignment now runs modulo the FULL
function-preserving unit symmetry group of a ReLU MLP (per-unit positive
rescaling via canonicalise_scale, composed with Re-Basin permutations;
sanity gate recovers a permuted-and-rescaled copy exactly). Verdict: the
full group removes the independent-init barrier (residual 0.001) and
essentially none of the conflict barrier (0.502 -> 0.497) — the residual
is functional, not a missed symmetry (answers arXiv:2606.23607). The
cliff gains a hybrid-fitness readout: merged accuracy 0.97 -> 0.03 with
conflict. Floor proposition drafted (paper/si-notes.md S1): endpoint
invariance + max(eps_A, eps_B) >= mu(S)/2 for any merged model under any
alignment group.

E13b (emergent divergence): pre-registered second reading — with NO
conflicting training signal (disjoint class specialists; rolled-input
conventions), residual is 0.000 at every divergence to t_div=3200, and
the merge RESCUES the forgetting specialists (parents 0.535/0.474 ->
merged 0.955; a sustained Fisher-Muller rescue at zero barrier).
Speciation in real weights requires functional conflict; it does not
emerge from compatible specialisation on shared ancestry. LLM-scale
over-specialisation (cf. 2607.11997) deferred to Phase-3 llm_speciation.

3-panel figure, READMEs, +2 tests (149 green), make mnist wired.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v

results/speciation_real/README.md

@@ -1,54 +1,85 @@
-# E13 — Real-weight model speciation (Git Re-Basin residual)
+# E13 — Real-weight model speciation (the alignment residual, now modulo the full symmetry group)
 
 **Claim tested.** E12 predicts model *speciation* analytically: as two lineages diverge, recombination
 (merging) fails, via Bateson–Dobzhansky–Muller incompatibilities. E13 confirms it in **real trained
-weights**, and — decisively — separates the part of the incompatibility that is a mere **coordinate
-artefact** (removable by permuting hidden units; Git Re-Basin, Ainsworth et al. 2022) from the
-**residual** that permutation *cannot* remove, which is the true reproductive-isolation signal. This is
-the experiment that answers the mode-connectivity reviewer: if alignment removes the barrier, it was a
-coordinate artefact; the barrier that *survives* alignment is real speciation.
+weights**, separating the part of the merge barrier that is a mere **coordinate artefact** (removable
+by re-coordinating hidden units) from the **residual** that no alignment can remove — the true
+reproductive-isolation signal.
 
-**Setup.** Small no-BatchNorm MLPs (784–512–512–10) on MNIST — the clean Re-Basin regime. Two children
-are forked from a shared base and trained independently; we weight-average them and measure the
-**linear-mode-connectivity error barrier** before (`naive`) and after (`aligned`) in-house, deterministic
-Git Re-Basin weight-matching (`neural/rebasin.py`, scipy `linear_sum_assignment`). Statistically
-reproducible (seeded torch; NumPy/scipy alignment is deterministic). 3 replicates.
+**E13c hardening (2026 PNAS campaign).** Recent work shows symmetry groups *richer than permutations*
+remove more of the barrier between independently trained transformers (arXiv:2606.23607;
+neuron-identifiability LMC). We therefore align modulo the **full function-preserving unit symmetry
+group of a plain ReLU MLP** — per-unit positive rescaling (scale canonicalisation, exact) *composed
+with* Git Re-Basin permutation matching (`neural/rebasin.py`; the sanity gate recovers a permuted
+**and rescaled** copy to exact weight identity). Both residuals are reported: `residual` (permutation
+only) and `residual_scale` (full group).
+
+**Setup.** No-BatchNorm MLPs (784–512–512–10) on MNIST. Children forked/trained per condition;
+weight-average merge; linear-mode-connectivity error barrier before/after alignment; midpoint
+(merged-model) accuracy recorded alongside. 3 replicates (decomposition/cliff), 4 (emergent).
+Statistically reproducible (seeded); the alignment itself is deterministic NumPy/scipy.
 
 ### Results — the decomposition (mean over divergence, reps)
-| condition | naive barrier | removable (coordinate) | **residual (isolation)** |
-|---|---|---|---|
-| `shared` (same task, shared fork) | 0.00 | 0.00 | **0.00** |
-| `independent` (same task, different init) | 0.056 | 0.055 | **0.001** |
-| `conflict` (conflicting label maps) | 0.496 | 0.000 | **0.496** |
+| condition | naive barrier | residual (permutation) | **residual (full symmetry group)** | merged acc |
+|---|---|---|---|---|
+| `shared` (same task, shared fork) | 0.000 | 0.000 | **0.000** | 0.964 |
+| `independent` (same task, different init) | 0.044 | 0.001 | **0.001** | 0.960 (= parents) |
+| `conflict` (contradictory label maps) | 0.502 | 0.502 | **0.497** | **0.037 (inviable)** |
 
-- **`independent`**: two nets trained *from different random inits* on the *same task* have a real naive
-  barrier — which alignment **removes ~98%** of (residual 0.001). Same species, different basis: the
-  incompatibility is a coordinate artefact. (This reproduces the canonical Git Re-Basin result and
-  proves our alignment works.)
-- **`conflict`**: two nets that learned *conflicting* functions have a large barrier that alignment
-  **removes none** of (residual 0.496). Different species: genuine reproductive isolation. Because
-  alignment demonstrably works on `independent`, this residual cannot be dismissed as a failure to align.
-- The **residual after alignment** is therefore the clean discriminator: ~0 for compatible models (even
-  independently trained), large only for functionally incompatible ones.
+- **`independent`**: the barrier is a coordinate artefact — permutations already remove ~98%, and the
+  full symmetry group confirms (residual 0.001). The aligned merge performs **at parent level**
+  (0.960): same species, different basis.
+- **`conflict`**: the full symmetry group removes essentially nothing (0.502 → 0.497). The residual is
+  **functional**, not a missed symmetry — and the hybrid is functionally dead (accuracy 0.037).
+  Because the same aligner erased the independent-init barrier, this cannot be a failure to align.
+- Formal floor (SI note S1, `paper/si-notes.md`): for label maps conflicting on mass `μ(S)`, *any*
+  single merged model errs at rate ≥ `μ(S)/2` against at least one parent, under *any* alignment
+  group and merge operator — hybrid disadvantage is information-theoretic, and endpoints/chord are
+  invariant to all function-preserving transformations.
 
 ### Results — the isolation cliff (`speciation_real_cliff/`)
-Sweeping the fraction of classes on which child B learns a *conflicting* label map, the residual
-(after-alignment) barrier rises monotonically — the real-weight image of E12's cliff:
+Sweeping the fraction of conflicting classes (residual = full-symmetry alignment; `t_div=800`):
 
 | conflict fraction | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
 |---|---|---|---|---|---|---|
-| residual barrier | 0.00 | 0.13 | 0.19 | 0.28 | 0.40 | 0.49 |
+| residual barrier | 0.000 | 0.122 | 0.187 | 0.278 | 0.406 | 0.506 |
+| **merged (hybrid) accuracy** | 0.968 | 0.764 | 0.586 | 0.396 | 0.199 | 0.034 |
 
-residual = naive at every point (alignment removes nothing in the conflict condition), so the cliff is
-genuinely functional isolation, not a coordinate artefact.
+`residual_scale ≈ residual` at every point (±0.005): the cliff is functional isolation under the full
+symmetry group. Read as **hybrid fitness**, the merged model's accuracy falls 0.97 → 0.03 — the
+real-weight image of E12's *compatible → outbreeding depression → hybrid inviability* trajectory.
+
+### Results — emergent divergence does NOT speciate (`speciation_real_emergent/`, E13b)
+The conflict condition *imposes* contradiction; a true BDM incompatibility is *emergent*. Two
+pre-registered conditions with **no conflicting training signal anywhere**: `disjoint` (child A trains
+only on classes 0–4, child B on 5–9) and `augment` (same labels, inputs rolled ±3 px), swept to
+`t_div = 3200` (children trained 6.4× longer than the shared base):
+
+- **Residual barrier = 0.000 at every divergence, both conditions** (naive barrier is 0 too — the
+  children never leave the shared basin).
+- The `disjoint` parents decay to 0.535/0.474 on the full task (each forgets the other's classes),
+  while the **merged model holds ≈ 0.955 at every divergence** — a sustained ~40-point
+  **Fisher–Muller rescue** of two catastrophically-forgetting specialists, at zero barrier.
+  `augment` shows the same shape (parents 0.65/0.73, merge ≈ 0.90).
+
+**Honest conclusion (the pre-registered second reading):** in this regime — shared ancestry, same
+architecture, compatible tasks, divergence up to 3200 steps — **model speciation does not emerge
+spontaneously; reproductive isolation requires functional conflict.** Trained networks are *more*
+merge-compatible than the biological analogy predicts, and the design rule sharpens: *merge freely
+across divergently-specialised lineages of shared ancestry — the danger is conflicting conventions,
+not specialisation per se.* Scope caveat: small MLPs, one fork depth; whether long-horizon
+over-specialisation at LLM scale erodes mergeability (as the expert-training-duration literature
+suggests, arXiv:2607.11997) is exactly the Phase-3 `llm_speciation` question.
 
 ### Positioning
-The incumbents each hold one piece: Git Re-Basin / Entezari (barriers are coordinate artefacts),
-Frankle (the fork-instability protocol), Pari et al. 2024 (specialisation diverges representations,
-route don't fuse), Zhou et al. 2026 (predict mergeability from divergence metrics). E13's contribution
-is the synthesis they lack: a controlled decomposition where alignment cleanly partitions the merge
-barrier into a **removable coordinate artefact** and a **residual reproductive-isolation** term that
-rises with task conflict — the real-weight confirmation of E12's speciation prediction, and the direct
-answer to "isn't this just a loss barrier / permutation artefact?" **Falsifier (not triggered):**
-alignment failing to remove the independent-init barrier (then residual is meaningless), or conflict
-showing no residual — instead alignment removed 98% of the former and 0% of the latter.
+Git Re-Basin / Entezari (barriers as coordinate artefacts), the richer-symmetry LMC results
+(2606.23607 and neuron-identifiability, 2026), Frankle (fork instability), Pari 2024 (route don't
+fuse), Zhou 2026 / 2601.22285 (predict mergeability from divergence/geometry), 2603.09463
+(merge-collapse capacity theory). E13's contribution is the synthesis they lack: a controlled
+decomposition where alignment — *modulo the full symmetry group* — cleanly partitions the merge
+barrier into a removable coordinate artefact and a **functional reproductive-isolation residual** that
+rises with task conflict, is absent under compatible specialisation, and carries an
+information-theoretic floor. **Falsifiers (none triggered):** alignment failing on `independent`
+(would invalidate the residual); conflict showing no residual; the richer symmetry group dissolving
+the conflict residual (it removed 0.005 of 0.502); emergent conditions showing residual attributable
+to alignment failure.

results/speciation_real/manifest.json

@@ -1,8 +1,8 @@
 {
   "experiment": "speciation_real",
   "master_seed": 13,
-  "git_commit": "56f642e7f9ae01fe01d863bdffe98b226b9dbb7b",
-  "python": "3.14.5",
+  "git_commit": "f5f68f52498402ba7cc6a5193e5e357be6357446",
+  "python": "3.14.7",
   "libraries": {
     "numpy": "2.5.0",
     "scipy": "1.18.0",
@@ -12,7 +12,7 @@
     "torchvision": "0.27.1"
   },
   "rows": 45,
-  "results_sha256": "14b15c16ea8a43523fdc929641b8ad5741445435203d1511ecb698097da0a806",
+  "results_sha256": "dc77ac51b8dc92549e39edbed8d1a68469ad40de288f28672d87d1739436247a",
   "layer": "1.5",
   "tier": "speciation_real"
 }

results/speciation_real_cliff/manifest.json

@@ -1,8 +1,8 @@
 {
   "experiment": "speciation_real_cliff",
   "master_seed": 13,
-  "git_commit": "56f642e7f9ae01fe01d863bdffe98b226b9dbb7b",
-  "python": "3.14.5",
+  "git_commit": "f5f68f52498402ba7cc6a5193e5e357be6357446",
+  "python": "3.14.7",
   "libraries": {
     "numpy": "2.5.0",
     "scipy": "1.18.0",
@@ -12,7 +12,7 @@
     "torchvision": "0.27.1"
   },
   "rows": 18,
-  "results_sha256": "0252581d848376ad698f56d4e69edbcae40cf5a0f090203d6f723cfc5e25303c",
+  "results_sha256": "889945655a6efaba9d97eed409f24968c9f77764101bdfa05acdf00c8f8668b7",
   "layer": "1.5",
   "tier": "speciation_real"
 }

results/speciation_real_emergent/README.md

@@ -0,0 +1,16 @@
+# E13b — Emergent divergence (no imposed conflict): does model speciation arise spontaneously?
+
+Companion to `results/speciation_real/` (full legend and interpretation there; figure panel C of
+`speciation_real.png`). Pre-registered design: `shared` control, `disjoint` (complementary class
+specialists 0–4 vs 5–9), `augment` (same labels, inputs rolled ±3 px) — **no conflicting training
+signal anywhere** — swept over post-fork divergence `t_div ∈ [100, 3200]`, 4 replicates, with
+alignment modulo the full ReLU unit symmetry group (E13c).
+
+**Outcome (the pre-registered second reading):** residual barrier **0.000 at every divergence in both
+emergent conditions**; the merged model **rescues** the two forgetting `disjoint` specialists
+(parents → 0.535/0.474; merge ≈ 0.955 throughout — a sustained Fisher–Muller rescue at zero barrier).
+**Speciation requires functional conflict; it does not emerge from compatible specialisation on shared
+ancestry in this regime.** An honest bound on the biological analogy, and a positive design result:
+merging complementary specialists of shared ancestry is safe — the danger is conflicting conventions,
+not specialisation. LLM-scale over-specialisation is the open tier (`llm_speciation`, PNAS work order
+Phase 3).

results/speciation_real_emergent/manifest.json

@@ -0,0 +1,18 @@
+{
+  "experiment": "speciation_real_emergent",
+  "master_seed": 813,
+  "git_commit": "f5f68f52498402ba7cc6a5193e5e357be6357446",
+  "python": "3.14.7",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0",
+    "torch": "2.12.1",
+    "torchvision": "0.27.1"
+  },
+  "rows": 72,
+  "results_sha256": "95c626e0d1854690b0ad6ceaf696caa1cff005104a0814cc044c0b6b2604482b",
+  "layer": "1.5",
+  "tier": "speciation_real"
+}

results/speciation_real_emergent/resolved_config.yaml

@@ -0,0 +1,32 @@
+experiment: speciation_real_emergent
+seed: 813
+n_replicates: 4
+source_config:
+  experiment: speciation_real_emergent
+  kind: speciation_real
+  seed: 813
+  n_replicates: 4
+  speciation_real:
+    sizes:
+    - 784
+    - 512
+    - 512
+    - 10
+    conditions:
+    - shared
+    - disjoint
+    - augment
+    t_div:
+    - 100
+    - 200
+    - 400
+    - 800
+    - 1600
+    - 3200
+    base_steps: 500
+    lr: 0.05
+    batch: 128
+    n_eval: 2000
+    data_root: data
+  output:
+    dir: results/speciation_real_emergent