E12: model speciation — the merge-compatibility limit of the sexual society

New analytic result for the evolution-of-sex paper: how far can two lineages
diverge before recombination (model merging) stops working? Frames merge failure
as biological reproductive isolation via Bateson-Dobzhansky-Muller
incompatibilities. src/knowledge/speciation.py, kind: speciation, on the E7-E11
genotype machinery (pure seeded NumPy, bitwise-reproducible; no external
simulator whose separate RNG would break that).

- BDM construction (E12.yaml): ancestor + two lineages substituting disjoint loci
  (each parent adaptive, incompatibility-free), a fraction rho of cross-lineage
  pairs are BDMIs. Sweeping divergence d reproduces the predicted
  compatible -> outbreeding depression -> hybrid inviability curve; the isolation
  cliff moves to lower d as epistasis density rises (iso at d=20: 0.00/0.03/0.50
  for rho 0.1/0.25/0.5); incompatibilities snowball ~ (d/2)^2 (Orr-Turelli).
- NK variant (E12_nk.yaml): parents = hill-climbed local optima; the epistasis
  wedge — recombination gain flips 0 -> -0.13 and OD rate 0 -> 0.90 as ruggedness
  K rises. At matched divergence, mergeability is governed by epistasis, the axis
  no divergence-only ML merge predictor captures.

plot_E12.py (3-panel), +7 tests (138 green), README with honest positioning
(concedes the empirical phenomenon to Pari 2024 / Zhou 2026 + permutation
artefacts to Git Re-Basin; claims the predictive theory + the epistasis wedge).
Wired into make layer1.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

results/E12/README.md

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+# E12 — Model speciation: when two diverged models are too incompatible to merge
+
+**Claim tested.** The sexual society (E7–E11) recombines complementary parents. E12 asks the limit:
+**how far can two lineages diverge before recombination (model merging) stops working?** In biology the
+answer is *reproductive isolation* via **Bateson–Dobzhansky–Muller incompatibilities** (BDMIs) — alleles
+benign on their own lineage's background but deleterious *in combination*, which a recombinant inherits
+untested. A merged model is a single recombinant (an F2-like *hybrid-breakdown / recombination-load*
+object, not an F1), so the predicted signature as parental divergence grows is
+**compatible → outbreeding depression → hybrid inviability**, arriving earlier the more epistatic the
+capability landscape.
+
+**Setup.** Pure seeded NumPy on the E7–E11 genotype machinery (bitwise-reproducible; no external
+simulator, whose separate RNG would break that guarantee). Two landscapes:
+- **BDM** (`configs/layer1/E12.yaml`, headline): an ancestor; two lineages each substitute a *disjoint*
+  set of loci (each parent adaptive, neither carrying an incompatibility); a fraction `ρ` of
+  cross-lineage locus pairs are BDMIs (penalty `s`), biting only when a hybrid inherits *both* derived
+  alleles. Sweep divergence `d` (substitutions) for several `ρ`; `L=20`, 15 reps.
+- **NK** (`configs/layer1/E12_nk.yaml`): parents are *local optima* (hill-climbed) on a Kauffman NK
+  landscape; sweep ruggedness `K`. The emergent version.
+
+### Results
+- **The three-regime collapse (BDM).** Parent fitness rises linearly with divergence; hybrid fitness
+  *tracks it while compatible, then peels off, peaks, and crashes*. At dense epistasis (`ρ=0.5`) hybrids
+  peak near `d≈8` and fall to **−1.0** by `d=20` (below the ancestor = inviable); at sparse epistasis
+  (`ρ=0.1`) there is mild outbreeding depression and **no** isolation.
+- **The isolation cliff moves with epistasis density.** Reproductive-isolation rate (P hybrid inviable)
+  at `d=20`: `ρ=0.1`→0.00, `ρ=0.25`→0.03, `ρ=0.5`→**0.50** — the cliff arrives at lower divergence the
+  denser the epistasis.
+- **The Orr–Turelli snowball.** The number of incompatibilities grows ~`(d/2)²` (≈48 at `d=20`, `ρ=0.5`
+  ≈ `0.5·10²`), so hybrid fitness falls *super-linearly* — divergence is punished faster than it accrues.
+- **The epistasis wedge (NK).** At `K=0` (additive) recombination is neutral (no isolation — and the two
+  parents can't even diverge, since there is one peak); as ruggedness rises, recombining two adapted
+  local-optimum parents flips from a gain to **outbreeding depression** (recombination gain 0 → −0.13;
+  OD rate 0 → 0.90 across `K=0→10`). *At matched divergence, mergeability is governed by epistasis* —
+  the axis no divergence-only merge predictor captures.
+
+### Why it matters / positioning
+The ML *phenomenon* that "specialization/divergence eventually breaks merging" is known empirically
+(Pari et al. 2024; Zhou et al. 2026), and part of the apparent incompatibility is a permutation artefact
+(Git Re-Basin). E12's contribution is the **predictive theory** those lack: the functional form
+(compatible→OD→inviability), the **snowball** onset, and the **epistasis wedge** — merge failure as a
+Dobzhansky–Muller phenomenon whose onset is set by divergence *and* epistasis, not divergence alone. The
+design rule: *before merging, check divergence against the landscape's ruggedness; beyond the cliff,
+route (allopatry), don't merge.* **Falsifier (not triggered):** no OD/isolation progression as `d` and
+`ρ` grow — instead the full progression appears, and the additive control shows none. Real-weight
+confirmation (merging at increasing divergence *with* permutation alignment, isolating the residual
+epistatic incompatibility) is the flagged next step; here the analytic model is the anchor.

results/E12/manifest.json

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+{
+  "experiment": "E12",
+  "master_seed": 12,
+  "git_commit": "ae1779a9a83fc8f9f36019875efed522bf488b9c",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0"
+  },
+  "rows": 495,
+  "results_sha256": "0af2062c00f606ad1c2e6ca9f5974e981e0c15d699510576f5e7c6c84831f2bb"
+}

results/E12/resolved_config.yaml

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+experiment: E12
+seed: 12
+n_replicates: 15
+source_config:
+  experiment: E12
+  kind: speciation
+  seed: 12
+  n_replicates: 15
+  speciation:
+    landscape: bdm
+    L: 20
+    rho:
+    - 0.1
+    - 0.25
+    - 0.5
+    divergences:
+    - 0
+    - 2
+    - 4
+    - 6
+    - 8
+    - 10
+    - 12
+    - 14
+    - 16
+    - 18
+    - 20
+    s: 1.0
+    beta: 1.0
+    recomb_rate: 0.5
+    n_offspring: 500
+  output:
+    dir: results/E12

results/E12_nk/manifest.json

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+{
+  "experiment": "E12_nk",
+  "master_seed": 12,
+  "git_commit": "ae1779a9a83fc8f9f36019875efed522bf488b9c",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0"
+  },
+  "rows": 90,
+  "results_sha256": "c02706b6be6d2cd463d4af20efc1ff2d9cb2a98a1306d84cb07bbae517587e53"
+}

results/E12_nk/resolved_config.yaml

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+experiment: E12_nk
+seed: 12
+n_replicates: 15
+source_config:
+  experiment: E12_nk
+  kind: speciation
+  seed: 12
+  n_replicates: 15
+  speciation:
+    landscape: nk
+    L: 16
+    K:
+    - 0
+    - 2
+    - 4
+    - 6
+    - 8
+    - 10
+    n_pairs: 40
+    recomb_rate: 0.5
+    n_offspring: 200
+  output:
+    dir: results/E12_nk