papers: consolidate the real-LLM recombination arc (merge/moe/directed + headroom law)

Folds the four LLM runs into both papers now that the arc is fully characterised.

results-summary.md: new section 5 "The claims tested in real LLM weights" — the
Fisher-Muller generalist (7B merge 0.87 > best specialist 0.77), union-vs-fusion
(routing beats averaging where there is headroom), directed sex (breed + select),
and the unifying HEADROOM law that resolves the earlier saturation confound.
Updates design rule 2 ("merge, don't average — where there is headroom"), adds a
plain-language point 8, refreshes the validation counts (131 tests, real-LLM tier).

the-lamarckian-society-v5.md: softens the three "not a language model yet" claims
to acknowledge the prototype; adds the real-LLM confirmation after the
Fisher-Muller and directed-sex claims (with the headroom caveat as a sharpening,
not a weakening); adds an LLM bullet to section 13; reframes the closing gap to
"the operators, checked; the living society, next."

Tone held to the accessibility/honesty bar: prototype scope flagged (signs not
magnitudes), caveats presented as sharpening the claims, nothing over-celebrated.

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

paper/results-summary.md

@@ -13,8 +13,9 @@ sexual society**: reality-checking (grounding) plus **recombination across many
 parents** (sexual reproduction, not teacher→pupil copying) plus **quality-diversity** selection.
 The payoff is not merely arrested collapse but a population whose **offspring exceed their
 parents** and whose general capability **climbs** while specialties are re-earned — and removing
-any one operator breaks it. **122 tests pass**; three of the core predictions are exact closed
-forms, so the headline curves sit on analytic targets rather than eyeballing.
+any one operator breaks it, and a first **real-LLM prototype** (up to 7B on HPC) confirms the
+recombination claims in trained weights. **131 tests pass**; three of the core predictions are exact
+closed forms, so the headline curves sit on analytic targets rather than eyeballing.
 
 ---
 
@@ -145,7 +146,47 @@ Fisher–Muller effect):
   a rugged landscape you need diversity to explore basins, sex to recombine them, and grounding to
   select on reality.
 
-### 5. Positioning — what is prior art, what is ours
+### 5. The claims tested in real LLM weights (Layer 2 prototype)
+
+The analytic operators above make three claims that are testable in *real language-model weights*:
+"merge, don't average" (E4), the Fisher–Muller generalist-from-specialists (E8), and directed sex
+(E10). We tested them with a small, reproducible pipeline — LoRA **specialists** fine-tuned on three
+*disjoint*, procedurally-generated task families (`lists`, `strings`, `arith`) with an **exact-match
+verifier** as reality's "no" — recombined by various operators and scored on held-out tasks. Runs are
+at two scales: **Qwen2.5-0.5B** locally and **Qwen2.5-7B** on Imperial College's CX3 HPC (one L40S).
+This is a prototype (three families, one seed), so read it as **signs, not magnitudes**; the analytic
+layer carries the quantities.
+
+- **Recombining specialists yields a generalist that exceeds every parent (E8).** At 7B, a weight-space
+  **merge of the three specialists reaches 0.87 overall vs 0.77 for the best single specialist**, and
+  beats every specialist on every family — the Fisher–Muller signature, in real weights. At 0.5B the
+  same sign is present but marginal, because a weak base *dilutes* (see below).
+- **Union beats averaging — when there is headroom (E4).** Two ways to recombine: **fusion** (average
+  the LoRA deltas — a "model soup") versus **union** (keep each specialist intact and *route* each
+  input to the right one — a Mixture-of-Experts). On tasks with headroom, **routing beats fusion**
+  because averaging dilutes a specialist's contribution: at 0.5B routing 0.74 > soup 0.64; on *hard*
+  7B tasks routing 0.50 > soup 0.40, with fusion diluting the fragile string-cipher specialist so badly
+  (0.67→0.30) that the soup even loses to the best single specialist. This is E8's `max > mean` in real
+  weights.
+- **Directed sex helps — when there is headroom (E10).** Breeding a population of recombinant offspring
+  (specialists merged at many weightings), scoring each on a held-out split with the verifier, and
+  keeping the fittest **beats the single a-priori soup** where the soup is suboptimal: 0.69 > 0.64 at
+  0.5B, and 0.49 > 0.39 on hard 7B tasks — recovering most of routing's benefit from one deployable
+  model. This is offspring selection (which biology cannot preview) realised in weight space.
+- **The one law that unifies them: headroom, not scale.** Our first 7B runs on *easy* tasks showed the
+  opposite — fusion beating union, and directed selection tied with the soup. That was a **saturation
+  artefact**: the easy families saturated 7B at 1.00, leaving no room to lose to dilution, so the naive
+  soup was already optimal. On *hard* (unsaturated) 7B tasks the original ordering returns. **The
+  operative variable is headroom**: union-preserving merging and offspring selection pay off whenever
+  there is room to lose to dilution — a weak base *or* hard tasks — and only the degenerate corner of
+  easy tasks on a strong base makes naive averaging look sufficient. This both confirms E4/E8/E10 in
+  real weights and delimits exactly when the refinements matter.
+
+Honest scope: three lexically-distinct families (so the router is trivially accurate — an ambiguous-
+skill benchmark is the interesting next stress test), one seed, small LoRA. The full *grounded*
+society on LLMs (collapse under dry self-training, the dynamic society) is the HPC-scale next step.
+
+### 6. Positioning — what is prior art, what is ours
 
 An independent 2026 paper (Riis, *Drift and selection in LLM text ecosystems*) rigorously formalises
 **collapse = Wright–Fisher drift** (martingale of minority mass, rare-first extinction, de Bruijn
@@ -166,8 +207,11 @@ engineered cure and its integration.
 
 1. **Never inherit dry, and ground where it matters** — a little reality (`g*≈5%`) protects most
    diversity, but it protects only what it overlaps, and it can't hold the deep tail.
-2. **Merge, don't average** — union-preserving model-merging realises the multi-teacher benefit;
-   averaging cancels it.
+2. **Merge, don't average — where there is headroom** — union-preserving model-merging (routing /
+   max-merge) realises the multi-teacher benefit; averaging dilutes it. Confirmed in real LLM weights,
+   with a sharp caveat: dilution only bites when the task leaves room for it — on easy tasks a strong
+   base's naive soup already composes to the ceiling, so averaging looks fine. The refinement matters
+   exactly in proportion to how far the naive soup is from optimal.
 3. **Sex, with no parent limit** — recombining decorrelated specialists yields offspring that exceed
    any parent; more, complementary parents climb higher.
 4. **Match recombination to entanglement** — merge freely for complementary skills; sparingly for
@@ -230,6 +274,13 @@ that lets a society climb instead of collapse.
    consensus (the exact analogue of training on the internet's AI-generated crowd); remove **sex** and
    it gets stuck; remove **diversity** and it converges too fast to a worse answer. Each failure is
    distinct; only the full society wins.
+8. **It shows up in real language models — with one clean caveat.** We merged LoRA-specialised
+   Qwen models (0.5B locally, 7B on a university GPU cluster): the recombined model beats every
+   specialist (Fisher–Muller, for real), and *routing* / *offspring-selection* beat naive averaging —
+   but only when the tasks are hard enough to leave room. On easy tasks a strong model's plain average
+   is already at ceiling, so the fancier operators don't help. The lesson is precise: **these
+   recombination tricks matter exactly in proportion to how far the naive average is from the best you
+   could do** — which is a genuinely useful thing to know before you spend compute on them.
 
 ### Why it is novel and why it matters
 
@@ -240,9 +291,10 @@ that lets a society climb instead of collapse.
 - **The sexual-reproduction frame is, we believe, genuinely new for AI** — model merging reframed as
   meiotic recombination, with a rigorous account of when it helps (complementary skills), when it
   hurts (entangled skills), and how to make it reliably win (directed sex, unbounded parents).
-- **It is validated, not vibes.** Three core predictions are exact closed forms; the neural and
-  image results confirm the *signs* in real trained weights; 122 automated tests pass; the whole
-  study is laptop-reproducible from a seed.
+- **It is validated, not vibes.** Three core predictions are exact closed forms; the neural, image,
+  and **real-LLM** results confirm the *signs* in real trained weights (up to 7B on HPC); 131
+  automated tests pass; the whole study is laptop-reproducible from a seed (the LLM tier statistically
+  reproducible on one GPU).
 - **It gives concrete design rules** for anyone building self-improving or model-merging systems:
   ground where it matters, merge-don't-average, match recombination to skill-entanglement, select
   offspring, keep diversity, and gate irreversible consolidation on health.