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>

tasks/todo.md

@@ -264,8 +264,30 @@ C3 vertical claim deferred.*
   Lamarckian society + vertical/cumulative C3 claim (not yet run). Reposition: from "collapse is drift"
   to a population-genetic CONTROL THEORY for sustaining open-ended knowledge.
 
-## Remaining (all optional)
+**2026-07-05 — multi-locus society frame (E7/E8): raised the ceiling to enter the society.**
 
+- Prompted by "enter the society with a robust theoretical frame." The single-locus fixed-`p*` model
+  can't express "exceeding" a ceiling. Generalized knowledge to a distribution over **genotypes**
+  (`knowledge/genotype.py`: `L` biallelic loci, `K=2^L`, additive fitness, recombination = product of
+  per-locus marginals). Reuses all K-mode machinery + `make_retention_matrix` (locus mastery).
+- **E8 (star, `kind: society`, `knowledge/society.py`) — the vertical claim:** decorrelated parents
+  recombined; **sexual merge reaches the optimum (12/12, a genotype no parent had)** as parent count
+  grows / `ρ→0`, while best-parent (~8.7) and mean-mixture soup (~11.6) plateau. `configs/layer1/E8.yaml`,
+  `plot_E8.py`, README. The Fisher–Muller effect for AI.
+- **E7 (`kind: genotype_lineage`, `knowledge/genotype_lineage.py`) — advantage of sex:** sexual lineage
+  adapts faster than asexual (LD→0 vs LD spike). Honest: a speed advantage, not a permanent ratchet gap.
+- **Metaphor shift (GG):** sexual reproduction with **unbounded parents**, not teacher→pupil (which caps
+  at the ceiling). Collapse = asexual degradation; cure = sex, no parent limit. Unifies E4+E6 under
+  evolution-of-sex theory; beyond Riis's single-locus n-grams. `tests/test_genotype.py` (+7).
+  Experiment dispatch (`kind` in {genotype_lineage, society}) + `make layer1` wired.
+
+## Remaining (all optional / next)
+
+- [ ] **The dynamic society:** an evolving *population of parents* (specialists) that ground +
+  recombine + select over generations — capability climbing while specialties are re-earned (the full
+  C3, dynamic). E7/E8 give the static + single-population pieces; the multi-parent *lineage* is next.
+- [ ] **NK/epistasis landscape** (sign epistasis can make recombination harmful — the honest limit of
+  "sex always helps"); **multi-allelic loci**. Deepens the frame.
 - [ ] **Learning-kernel refinement:** truth-like smoothing prior (`prior="truth"`) + measurement floor
   for a quantitative RNN match; **multi-locus / linkage** modes (class×style) as the rigorous home for
   recombination. Both enrich predictive power and separate us further from Riis's single-locus n-grams.