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

results/E8/README.md

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+# E8 — the vertical claim: n-parent recombination exceeds any parent (Fisher–Muller)
+
+**Claim tested.** The society's headline, and the thing no fixed-`p*` model could express: can an
+offspring recombined from **many decorrelated parents** be *fitter than any parent* — capability that
+**exceeds** every component, not merely recovers a ceiling?
+
+**Setup.** A capability is a **genotype** of `L=12` biallelic loci; fitness = number of correct
+loci; the optimum (all-correct, fitness 12) is a genotype **no parent possesses**. Each *parent* is a
+specialist: confident-correct (`hi=0.9`) on the loci it has mastered, agnostic (`lo=0.45`) on the
+rest. Which loci each masters comes from the exact shared-switch construction, so **parent count
+`K_T`** and **decorrelation `ρ`** are clean, independently-swept knobs. Deployed capability = fitness
+of the **mode** (most-probable) genotype — what you would ship. 40 replicates.
+
+### Symbols
+- **parent** = a specialist model; **offspring** = the recombined model; **`K_T`** = number of parents (unbounded — biological sex is stuck at 2; model merging is not).
+- **`ρ`** = correlation of which loci parents master (0 = complementary, 1 = identical clones).
+- **best parent** = fittest single specialist · **average** = mean-mixture "model soup" (combine, don't recombine) · **sexual** = union-preserving recombination (assemble the best allele of each locus).
+
+### The two panels
+1. **Recombination exceeds any parent (ρ=0).** Deployed capability vs `K_T`: **sexual (red) climbs
+   to the optimum (12)** as parents accumulate — a genotype none of them had — while the **best single
+   parent (grey) plateaus at ~8.7** and the **model soup (blue) reaches ~11.6** but is beaten by
+   sexual at every `K_T` (and badly at small `K_T`: at 2 parents, sexual 9.0 vs soup 7.2 vs best 6.9).
+2. **Decorrelation is the fuel.** Sexual capability vs `K_T` for `ρ ∈ {0, 0.5, 1}`: decorrelated
+   parents (`ρ=0`) climb to the optimum; identical clones (`ρ=1`) buy nothing (flat at ~6). The
+   benefit is *combinatorial reach across complementary parents*, not merely "more models".
+
+### Takeaway
+This is the Fisher–Muller effect for AI: recombination assembles beneficial variants that live in
+*different* parents into an offspring fitter than any of them. It is the rigorous, un-preempted core
+of the Lamarckian society — collapse is asexual degradation; the cure is **sex, with no parent
+limit.** It reframes model merging from "averaging weights" to "meiotic reassortment", and it is the
+mechanism by which general capability can *climb while each specialty is re-earned and exceeded.* The
+dynamic version (why a lone lineage cannot do this) is E7. **Falsifier (not triggered):** if sexual
+never exceeded the best parent, or averaging matched it, the vertical claim would fail.

results/E8/manifest.json

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+{
+  "experiment": "E8",
+  "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": 720,
+  "results_sha256": "fec5c4fcaa86999291dd77b015cd650ad8c28cb62f67eab54ca5be04bc18a711"
+}

results/E8/resolved_config.yaml

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+experiment: E8
+seed: 20260705
+n_replicates: 40
+source_config:
+  experiment: E8
+  kind: society
+  seed: 20260705
+  n_replicates: 40
+  society:
+    L: 12
+    q: 0.5
+    hi: 0.9
+    lo: 0.45
+  sweep:
+  - param: K_T
+    values:
+    - 1
+    - 2
+    - 3
+    - 5
+    - 8
+    - 12
+  - param: rho
+    values:
+    - 0.0
+    - 0.5
+    - 1.0
+  output:
+    dir: results/E8