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>

figures/plot_E10.py

@@ -0,0 +1,65 @@
+"""E10 figure — directed sex beats biological sex (the distinctly-AI superpower).
+
+On rugged (epistatic) landscapes, blind "biological" sex — random mates, no offspring selection —
+suffers outbreeding depression: offspring are worse than the parents. But an AI can do what biology
+cannot: choose complementary mates, evaluate *many* recombinant offspring, and keep only the fittest,
+over several rounds, with no two-parent limit. This **directed sex** avoids the catastrophe and
+matches or exceeds the best parent even when skills are entangled.
+
+Two panels: (A) deployed capability vs landscape ruggedness — best single parent, random (blind) sex,
+directed sex, and the global optimum; (B) each strategy's edge over the best parent, making the
+random-sex collapse and the directed-sex rescue explicit. Reads only the committed bundle.
+
+Usage:  python figures/plot_E10.py [results/E10]
+"""
+
+from __future__ import annotations
+
+import sys
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+
+sys.path.insert(0, str(Path(__file__).parent))
+from _figlib import load_bundle, mean_ci, savefig  # noqa: E402
+
+
+def main(results_dir: str = "results/E10") -> None:
+    df, _ = load_bundle(results_dir)
+
+    fig, axes = plt.subplots(1, 2, figsize=(13, 5))
+
+    # Panel A: the three strategies + global optimum vs ruggedness.
+    ax = axes[0]
+    for col, c, lab in [("global_opt", "green", "global optimum"),
+                        ("directed_sex", "#d62728", "directed sex (AI: choose + select)"),
+                        ("best_parent", "#7f7f7f", "best single parent"),
+                        ("random_sex", "#1f77b4", "random sex (blind, biology)")]:
+        k, m, ci = mean_ci(df, "K", col)
+        ls = ":" if col == "global_opt" else "-o"
+        ax.plot(k, m, ls, color=c, label=lab) if col == "global_opt" else \
+            ax.errorbar(k, m, yerr=ci, fmt=ls, color=c, capsize=3, label=lab)
+    ax.set(xlabel="landscape ruggedness $K$ (epistasis)", ylabel="deployed capability (fitness)",
+           title="Random sex craters with ruggedness;\ndirected sex tracks/exceeds the best parent")
+    ax.legend(frameon=False, fontsize=8)
+
+    # Panel B: edge over best parent (random collapse vs directed rescue).
+    ax = axes[1]
+    bp = df.groupby("K")["best_parent"].mean()
+    for col, c, lab in [("directed_sex", "#d62728", "directed sex"),
+                        ("random_sex", "#1f77b4", "random sex")]:
+        s = df.groupby("K")[col].mean() - bp
+        ax.plot(s.index, s.values, "-o", color=c, label=lab)
+    ax.axhline(0, ls=":", color="gray", lw=1, label="best parent")
+    ax.set(xlabel="landscape ruggedness $K$", ylabel="capability − best parent",
+           title="Directed sex stays ≥ parents; blind sex\nfalls far below (outbreeding depression)")
+    ax.legend(frameon=False, fontsize=9)
+
+    fig.suptitle("E10 — directed sex beats biological sex: mate choice + offspring selection + "
+                 "unbounded parents rescue recombination where blind sex fails", y=1.02, fontsize=11)
+    fig.tight_layout()
+    savefig(fig, results_dir, "E10")
+
+
+if __name__ == "__main__":
+    main(*sys.argv[1:])

figures/plot_E9.py

@@ -0,0 +1,66 @@
+"""E9 figure — landscape robustness: when recombination helps, and the outbreeding-depression risk.
+
+The credibility test for the sexual metaphor. E8 used an additive landscape where recombination
+trivially helps; here parents are local optima ("trained models") of a Kauffman NK landscape whose
+ruggedness (epistasis) is tunable. Blindly recombining entangled models breaks co-adapted allele
+blocks and offspring fall *below* the parents — outbreeding depression — worse the more rugged the
+landscape and the higher the recombination rate. With selection (best offspring), a nonzero optimal
+recombination rate re-emerges. Design rule: merge freely when skills are complementary; merge
+sparingly (and always select) when they are entangled.
+
+Two panels: (A) the risk — mean offspring fitness minus best-parent vs recombination rate, one curve
+per ruggedness K (all ≤0, steeper as K grows); (B) with offspring selection — best-of-brood fitness
+vs rate per K, showing an intermediate optimum on rugged landscapes. Reads only the bundle.
+
+Usage:  python figures/plot_E9.py [results/E9]
+"""
+
+from __future__ import annotations
+
+import sys
+from pathlib import Path
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+sys.path.insert(0, str(Path(__file__).parent))
+from _figlib import load_bundle, savefig  # noqa: E402
+
+
+def main(results_dir: str = "results/E9") -> None:
+    df, _ = load_bundle(results_dir)
+    Ks = sorted(df["K"].unique())
+    rates = sorted(df["rate"].unique())
+    colors = plt.cm.viridis(np.linspace(0, 0.85, len(Ks)))
+    bp = df.groupby("K")["best_parent"].mean()
+
+    fig, axes = plt.subplots(1, 2, figsize=(13, 5))
+
+    # Panel A: the risk — mean offspring minus best parent vs rate, per K.
+    ax = axes[0]
+    for K, c in zip(Ks, colors):
+        s = df[df["K"] == K].groupby("rate")["mean_offspring"].mean() - bp[K]
+        ax.plot(s.index, s.values, "-o", color=c, ms=4, label=f"K={K}")
+    ax.axhline(0, ls=":", color="gray", lw=1)
+    ax.set(xlabel="recombination rate", ylabel="mean offspring − best parent",
+           title="The risk: outbreeding depression\n(worse with ruggedness K and recombination rate)")
+    ax.legend(frameon=False, fontsize=8, title="ruggedness")
+
+    # Panel B: with selection — best offspring vs rate, per K (intermediate optimum on rugged).
+    ax = axes[1]
+    for K, c in zip(Ks, colors):
+        s = df[df["K"] == K].groupby("rate")["best_offspring"].mean()
+        ax.plot(s.index, s.values, "-o", color=c, ms=4, label=f"K={K}")
+        ax.axhline(bp[K], ls=":", color=c, lw=0.8, alpha=0.6)
+    ax.set(xlabel="recombination rate", ylabel="best-of-brood fitness (with selection)",
+           title="With offspring selection, an optimal\nrecombination rate re-emerges (dotted = parents)")
+    ax.legend(frameon=False, fontsize=8, title="ruggedness")
+
+    fig.suptitle("E9 — landscape robustness: recombination helps when skills are complementary, but "
+                 "blindly merging entangled models causes outbreeding depression", y=1.02, fontsize=11)
+    fig.tight_layout()
+    savefig(fig, results_dir, "E9")
+
+
+if __name__ == "__main__":
+    main(*sys.argv[1:])