society: make the sexual-transmission model rigorous (E9 epistasis, E10 directed sex)

Deepen the sexual-reproduction frame before entering the full society, on
the two facets GG chose: landscape robustness and directed recombination.
Adds a Kauffman NK landscape (genotype.nk_fitness, tunable ruggedness),
finite n-parent crossover (genotype.crossover, per-gap recombination rate),
and hill-climb (parents = local optima = trained models).

E9 (recomb_landscape) -- the "why sex?" test: E8's dramatic super-parent
result used an ADDITIVE landscape. On rugged/epistatic landscapes, blindly
recombining local optima causes OUTBREEDING DEPRESSION -- offspring fall
below the parents, worse with both ruggedness and recombination rate (K=8,
free recomb: ~ -0.23), and the optimal recombination rate shrinks as
ruggedness grows. Design rule: merge freely when skills are complementary/
additive; sparingly (and with selection) when entangled.

E10 (directed_sex) -- directed sex beats biological sex: biology is stuck
with 2 random-mating parents and no offspring preview; an AI can choose
complementary mates, evaluate many recombinant offspring, keep the fittest,
and use unbounded parents (iterated recombine-then-select). Random
("biological") sex craters with ruggedness (0.66->0.51); directed sex
tracks/exceeds the best parent at every ruggedness -- converting the
outbreeding-depression catastrophe into a win. No biological analog.

Complete sexual-transmission picture: dramatic super-parent offspring when
skills are complementary (E8); outbreeding-depression risk when entangled
(E9); directed sex resolves the risk (E10). configs/layer1/{E9,E10}.yaml,
figures/plot_{E9,E10}.py, READMEs, +5 tests (117 green).

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

results/E10/README.md

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+# E10 — directed sex beats biological sex (the distinctly-AI superpower)
+
+**Claim tested.** E9 showed that on rugged (epistatic) landscapes, blind recombination causes
+outbreeding depression — offspring worse than parents. Biology is largely stuck with this: two
+random-mating parents, no way to preview offspring. But an **AI is not** — it can choose mates,
+evaluate many recombinant offspring, and keep only the fittest, over rounds, with no two-parent
+limit. Does this **directed sex** rescue recombination where blind sex fails?
+
+**Setup.** Parents are local optima of a Kauffman NK landscape (`L=12`), swept over ruggedness `K`.
+Three strategies compared, all as deployed capability (fitness ∈ [0,1]): **best single parent**;
+**random sex** (blind mating, free recombination, no offspring selection — biology's default);
+**directed sex** (iterated recombine-then-select-offspring, `rate=0.2`, 5 rounds — the AI move).
+24 replicate landscapes.
+
+### Symbols
+- **random sex** — blind: random parents, free recombination, take the offspring as they come.
+- **directed sex** — choose complementary mates + generate many offspring + keep the fittest + repeat; unbounded parents.
+- **global optimum** — the landscape's best genotype (the ceiling).
+
+### The two panels
+1. **Capability vs ruggedness.** As `K` grows, **random sex (blue) craters** (0.66 → 0.51 — deep
+   outbreeding depression), while **directed sex (red) tracks the best parent and the global optimum**,
+   staying near the ceiling at every ruggedness.
+2. **Edge over the best parent.** Directed sex stays **≥ 0** (at or above the parents) across all `K`;
+   random sex falls to **≈ −0.2** (far below). Directed sex converts a catastrophe into a win.
+
+### Takeaway
+The move biology cannot make — **choose your mates, evaluate your offspring before you commit, and
+recombine as many parents as you like** — is exactly what makes AI sexual reproduction robust. Blind
+merging of entangled models is dangerous; *directed* merging (generate many candidate merges, keep
+the best) is safe and can exceed every parent. This is the practical payoff of the sexual-transmission
+model and the distinctly-AI superpower with no biological analog. **Falsifier (not triggered):** if
+directed sex did no better than random sex, or never recovered the best-parent level on rugged
+landscapes, the "AI beats biology" claim would fail.

results/E10/manifest.json

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+{
+  "experiment": "E10",
+  "master_seed": 20260705,
+  "git_commit": "62c68d6c8c4090e62cf9ee17ac7b7d1eff7a6955",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0"
+  },
+  "rows": 120,
+  "results_sha256": "b2d53d0a3949be0b67e3b8dffec56121d54e20c593e6302717a73a8a132f17cb"
+}

results/E10/resolved_config.yaml

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+experiment: E10
+seed: 20260705
+n_replicates: 24
+source_config:
+  experiment: E10
+  kind: directed_sex
+  seed: 20260705
+  n_replicates: 24
+  society:
+    L: 12
+    n_parents: 6
+    pop: 200
+    keep: 8
+    rounds: 5
+    rate: 0.2
+  sweep:
+  - param: K
+    values:
+    - 2
+    - 4
+    - 6
+    - 8
+    - 10
+  output:
+    dir: results/E10

results/E9/README.md

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+# E9 — landscape robustness: when recombination helps, and the outbreeding-depression risk
+
+**Claim tested.** E8 showed sexual recombination assembling super-parent offspring — but on an
+*additive* landscape, where recombination trivially helps. The honest, credibility-critical question
+(the classic "why sex?" problem): does the benefit survive **epistasis**, or does merging entangled
+models break them?
+
+**Setup.** Parents are **local optima** ("trained models") of a **Kauffman NK landscape** (`L=12`),
+whose ruggedness `K` (epistatic interactions per locus) is swept together with the **recombination
+rate**. `K=0` is additive/smooth; larger `K` is rugged (co-adapted allele blocks, many local optima).
+Fitness ∈ [0,1]. 24 replicate landscapes; 200 offspring per point.
+
+### Symbols
+- **NK landscape** — tunable-ruggedness fitness landscape; `K` = epistasis (0 = additive, high = rugged).
+- **recombination rate** — per-gap crossover probability (0 = clonal / copy a parent; 0.5 = free recombination, loci independent).
+- **outbreeding depression** — offspring *less* fit than parents because recombination broke co-adapted allele blocks.
+
+### The two panels
+1. **The risk.** Mean offspring fitness *minus* best parent, vs recombination rate, one curve per
+   ruggedness `K`. On the additive landscape (`K=0`) it's flat at 0; as `K` grows the curves plunge
+   **negative**, and deeper the higher the recombination rate — **outbreeding depression, worse the
+   more entangled the skills and the more you mix** (`K=8`, free recombination: ≈ −0.23).
+2. **With selection, an optimal rate re-emerges.** Best-of-brood fitness (offspring selection) vs
+   rate per `K`, with parents dotted. On rugged landscapes a **nonzero intermediate recombination
+   rate** is best — enough mixing to find new combinations, not so much that it shatters good blocks.
+
+### Takeaway
+Recombination is not a free lunch. **Merge freely when skills are complementary/additive; merge
+sparingly — and always *select* offspring — when they are entangled.** This is the celebrated
+population-genetics result (recombination load / outbreeding depression) reproduced for AI model
+merging, and it turns the sexual metaphor from a lucky demo into a law with a design rule. The rescue
+— directed sex with offspring selection — is E10. **Falsifier (not triggered):** if recombination
+rate had no effect, or free recombination never underperformed the parents on rugged landscapes, the
+epistasis caveat would be moot.

results/E9/manifest.json

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+{
+  "experiment": "E9",
+  "master_seed": 20260705,
+  "git_commit": "62c68d6c8c4090e62cf9ee17ac7b7d1eff7a6955",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0"
+  },
+  "rows": 720,
+  "results_sha256": "73a737b333ee972ff1f878e18bf91b0aac58cb595c00c7b7fec3c18865971c4f"
+}

results/E9/resolved_config.yaml

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+experiment: E9
+seed: 20260705
+n_replicates: 24
+source_config:
+  experiment: E9
+  kind: recomb_landscape
+  seed: 20260705
+  n_replicates: 24
+  society:
+    L: 12
+    n_parents: 6
+    pop: 200
+  sweep:
+  - param: K
+    values:
+    - 0
+    - 2
+    - 4
+    - 6
+    - 8
+  - param: rate
+    values:
+    - 0.0
+    - 0.05
+    - 0.1
+    - 0.2
+    - 0.35
+    - 0.5
+  output:
+    dir: results/E9