Restructure: descriptive tier and experiment names, paper/manuscript
- paper/pnas -> paper/manuscript (venue-neutral)
- configs/layer1 -> configs/inheritance, src/knowledge -> src/inheritance
(imported as `inheritance`), make layer1 -> make inheritance; layer2 alias dropped
- inheritance and trained-network bundles named after the manuscript figure
they feed (fig2_grounding_sweep, figS3_rebaselining, ...), or descriptively
where they feed none; configs keep their `experiment:` value so parquet
hashes are unchanged, only output.dir moves
- figure scripts, SI figure sources, notebooks, REPRODUCING.md, README and the
SI Methods/tables updated; make clean no longer deletes tracked manifests;
reproduce.sh hashes the s{seed}/ layouts too
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm
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results/figS9_specialist_superparent/README.md
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# E8 — the vertical claim: n-parent recombination exceeds any parent (Fisher–Muller)
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**Claim tested.** The society's headline, and the thing no fixed-`p*` model could express: can an
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offspring recombined from **many decorrelated parents** be *fitter than any parent* — capability that
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**exceeds** every component, not merely recovers a ceiling?
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**Setup.** A capability is a **genotype** of `L=12` biallelic loci; fitness = number of correct
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loci; the optimum (all-correct, fitness 12) is a genotype **no parent possesses**. Each *parent* is a
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specialist: confident-correct (`hi=0.9`) on the loci it has mastered, agnostic (`lo=0.45`) on the
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rest. Which loci each masters comes from the exact shared-switch construction, so **parent count
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`K_T`** and **decorrelation `ρ`** are clean, independently-swept knobs. Deployed capability = fitness
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of the **mode** (most-probable) genotype — what you would ship. 40 replicates.
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### Symbols
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- **parent** = a specialist model; **offspring** = the recombined model; **`K_T`** = number of parents (unbounded — biological sex is stuck at 2; model merging is not).
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- **`ρ`** = correlation of which loci parents master (0 = complementary, 1 = identical clones).
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- **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).
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### The two panels
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1. **Recombination exceeds any parent (ρ=0).** Deployed capability vs `K_T`: **sexual (red) climbs
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to the optimum (12)** as parents accumulate — a genotype none of them had — while the **best single
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parent (grey) plateaus at ~8.7** and the **model soup (blue) reaches ~11.6** but is beaten by
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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).
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2. **Decorrelation is the fuel.** Sexual capability vs `K_T` for `ρ ∈ {0, 0.5, 1}`: decorrelated
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parents (`ρ=0`) climb to the optimum; identical clones (`ρ=1`) buy nothing (flat at ~6). The
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benefit is *combinatorial reach across complementary parents*, not merely "more models".
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### Takeaway
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This is the Fisher–Muller effect for AI: recombination assembles beneficial variants that live in
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*different* parents into an offspring fitter than any of them. It is the rigorous, un-preempted core
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of the Lamarckian society — collapse is asexual degradation; the cure is **sex, with no parent
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limit.** It reframes model merging from "averaging weights" to "meiotic reassortment", and it is the
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mechanism by which general capability can *climb while each specialty is re-earned and exceeded.* The
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dynamic version (why a lone lineage cannot do this) is E7. **Falsifier (not triggered):** if sexual
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never exceeded the best parent, or averaging matched it, the vertical claim would fail.
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