society: multi-locus recombination frame — the vertical claim (E7/E8)

Enter the Lamarckian society with a robust theoretical frame. The single-
locus, fixed-p* model can only express recovery toward a ceiling; the
society's load-bearing claim is vertical -- capability that EXCEEDS any
component. Generalize knowledge to a distribution over genotypes (L
biallelic loci, K=2^L, additive fitness = # correct loci), reusing all the
K-mode machinery. The one new operator is recombination: free recombination
sends p -> product of per-locus marginals (linkage equilibrium).

E8 (star, kind: society) -- the vertical claim / Fisher-Muller: decorrelated
PARENTS (specialists, expert on their loci, agnostic elsewhere) are
recombined; sexual merge assembles a genotype fitter than any parent,
climbing to the optimum (12/12, a genotype no parent had) as parent count
grows and rho->0, while the best single parent (~8.7) and the mean-mixture
"model soup" (~11.6) plateau below. Reuses make_retention_matrix (locus
mastery replaces tail-item retention).

E7 (kind: genotype_lineage) -- the advantage of sex: a single population
adapts toward the optimum; the sexual lineage adapts faster than asexual
(clonal interference) by keeping loci in linkage equilibrium (LD->0 vs LD
spike). Honest scope: a speed advantage, not a permanent Muller's-ratchet
gap (subtle to force); E8 carries the headline.

Metaphor shift (per GG): the society is sexual reproduction with UNBOUNDED
parents, not teacher->pupil. Teacher->pupil caps at the ceiling; n-parent
recombination is combinatorial and generative, and unlike biology there is
no two-parent limit. Collapse = asexual degradation; the cure = sex. This
unifies E4 (merge != average) + E6 (irreversibility) under evolution-of-sex
theory and reaches ground Riis's single-locus n-grams cannot.

New: knowledge/{genotype,genotype_lineage,society}.py, configs/layer1/{E7,
E8}.yaml, figures/plot_{E7,E8}.py, READMEs, tests/test_genotype.py (+7).
experiment.py dispatch (kind in {genotype_lineage, society}); make layer1
wired. 112 tests green.

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

results/E7/README.md

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+# E7 — the advantage of sex: recombination adapts faster than clonal reproduction
+
+**Claim tested.** The dynamic mechanism behind E8: *why* can a recombining society reach capability a
+lone lineage cannot? Because recombination reassorts beneficial variants that arise in different
+sub-lineages, while an asexual (clonal) lineage suffers **clonal interference** — the variants compete
+and cannot combine.
+
+**Setup.** A single population (distribution over `2^L` genotypes, `L=12`) adapts from **all-wrong**
+toward the multi-locus optimum under the composed step: selection (fitness-proportional) + drift
+(resample `n=150`) + mutation (per-locus flips, `μ=0.02`) + recombination. Two arms — **asexual**
+(`recomb_rate=0`) vs **sexual** (`recomb_rate=1`). 20 replicates.
+
+### Symbols
+- **asexual/clonal** = offspring are whole-genotype copies (Layer-1's regime) · **sexual** = loci reassorted across the population each generation.
+- **fitness** = number of correct loci (optimum = `L`) · **linkage disequilibrium |D|** = how far the loci are from statistical independence (correct alleles scattered across different genotypes).
+
+### The two panels
+1. **Advantage of sex.** Mean fitness over generations: the **sexual lineage (red) climbs faster**
+   than the asexual one (grey) through the adaptation phase (gen ~10–35). *Honest scope:* both plateau
+   near the optimum by gen ~40 in this tractable regime — this is a **speed** advantage, not a
+   permanent gap (the single-population Muller's ratchet is subtle to force; E8 carries the headline).
+2. **Mechanism.** Linkage disequilibrium over generations: the asexual lineage spikes to `|D|≈0.04`
+   during adaptation (beneficial alleles held apart, scattered across genotypes), while the sexual
+   lineage stays at `|D|≈0` — it *assembles* them. The LD gap is exactly why sexual adapts faster.
+
+### Takeaway
+Recombination's advantage is real and classical: it combines good ideas that arose independently,
+which clonal reproduction cannot. This is the population-level reason a single evolving model lineage
+degrades or stalls where a recombining **society** climbs — and it grounds the E8 vertical result in
+the evolution-of-sex theory. **Falsifier (not triggered):** if the sexual lineage adapted no faster
+than the asexual one (and kept the same LD), recombination would do no work.

results/E7/manifest.json

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+{
+  "experiment": "E7",
+  "master_seed": 20260705,
+  "git_commit": "871bc39ec6628f82aed75d007fdf675880eebc97",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0"
+  },
+  "rows": 4840,
+  "results_sha256": "4836cd7045ad5419554e7edc65e4e12b23877a551f38969d65e09a4f77715faa"
+}

results/E7/resolved_config.yaml

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+experiment: E7
+seed: 20260705
+n_replicates: 20
+source_config:
+  experiment: E7
+  kind: genotype_lineage
+  seed: 20260705
+  n_replicates: 20
+  genotype:
+    L: 12
+    n: 150
+    mu: 0.02
+    base: 1.3
+    recomb_rate: 0.0
+    init: wrong
+  generations: 120
+  sweep:
+  - param: genotype.recomb_rate
+    values:
+    - 0.0
+    - 1.0
+  output:
+    dir: results/E7