third review round: mathematical corrections + operator separation + headline calibration

The five priority fixes, in the PNAS draft and propagated to the
long-form document and results documentation:

1. The averaging proposition now proves what it claims: a FIRST-ORDER
   cancellation of the multi-parent retention gain under output-mean
   inheritance in the rare-item regime (n·p/K << 1), with the convexity
   boundary stated (averaging's variance reduction can reduce extinction
   outside that regime — the reviewer's argument) and the union
   operator's renormalisation + oracle requirement explicit. "Adding
   parents cannot help" deleted everywhere.
2. Grounding: g*~=0.05 restated as an operational threshold (equilibrium
   smooth in g — no phase transition); m·p floor restated as
   1−exp(−m·p) per-batch observation probability with
   retention/occupancy/reintroduction distinguished; the deep-tail rule
   de-categoricalised (stratified sampling; recombination recovers only
   what parents retain).
3. Grounded INHERITANCE (data channel) separated from grounded
   EVALUATION (fitness channel) in the society section; retitled to
   "complementary contributions"; general joint necessity disclaimed.
   Table 1 + v6 ledger updated.
4. Alignment contradiction removed everywhere ("cannot be an alignment
   failure" -> the reviewer's formulation); abstract says "remaining
   after permutation-and-rescaling alignment"; group = search space,
   control recovery != global optimality; "specialisation is merge-safe"
   -> "do not treat divergence/specialisation alone as evidence of
   incompatibility".
5. Significance headline matched to the bounded evidence; seed-
   dependence sensitivity added (per-seed rho stable +0.37..+0.53 for
   functional measures, ~0 for geometry, gradient alignment
   seed-UNSTABLE −0.11..−0.55 — reported as its own caveat; LOSO ranges
   in stats script).

Presentation: review-process meta-language stripped; "exact" reserved
for closed forms ("analytic model" labels); headroom rule qualitative;
directed-sex phrasing per review; ratchet = consequence-level
correspondence; compact results table (Table 2) added. Response letter:
paper/response-to-review-3.md. Both PDFs rebuilt; 151 tests green.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BkRLcc18rwT2Lysu6PbG7v

paper/the-evolution-of-sex-for-ai.md

@@ -81,9 +81,11 @@ question the framework is built to test.
 
 From the geneticist's apparatus we extract falsifiable, load-bearing claims (each stated with its
 operator and scope in the text): (i) **"merge, don't average"** — a conservation result: refitting a
-child to the *mean of its parents' output distributions* conserves rare-capability mass at the
-single-parent level, so adding parents cannot help, while union-preserving operators realise the gain
-— exact in the minimal model, with its weight-space image verified as the headroom rule below; (ii)
+child to the *mean of its parents' output distributions* conserves expected rare-capability mass at
+the single-parent level, cancelling the multi-parent gain *to first order in the rare-item regime*
+(outside it, variance reduction from averaging can help — the result is a first-order cancellation,
+not a universal impossibility), while union-preserving operators realise the gain in all regimes —
+derived in the minimal model, with its weight-space image the headroom rule below; (ii)
 **offspring can exceed every parent** (Fisher–Muller), the real argument for sex in model societies;
 (iii) on **rugged, epistatic** task landscapes, blind recombination causes **outbreeding depression**,
 yielding a design rule — *merge freely when skills are additive, sparingly and with selection when
@@ -100,8 +102,8 @@ pre-registered and found: absent conflicting training signals, divergently-speci
 shared ancestry developed *no* isolation at any divergence tested, the merge instead *rescuing* the
 forgetting specialists. Isolation must be provoked by conflict; specialisation alone did not speciate.
 AI also has an advantage biology lacks: **directed sex** — unbounded parents, chosen mates,
-and offspring screened before they are kept — which converts recombination from a gamble into a
-reliable engine and has no biological analogue.
+and offspring screened before they are kept — engineered recombination with a flexibility of parent
+choice and pre-deployment screening that natural mating systems do not approach.
 
 We support the argument with **minimal, reproducible models** — a closed-form-exact account of drift
 and grounding, the same effects in small trained networks and an MNIST image generator, a real-weight
@@ -322,9 +324,11 @@ the fancier operator.
 Four different operators travel under these words, and the conservation result belongs to exactly one
 of them. What is *derived* is this: when a pupil's knowledge is refit to the **mean of the parents'
 output distributions**, the expected mass on any rare item is conserved at the single-parent level —
-in the rare-item regime the 1/K dilution of averaging exactly cancels the union gain of having K
-parents — so adding parents cannot help; whereas an operator that keeps, per item, its **strongest
-source** realises the union. That statement is exact in the minimal model, and it presupposes an
+in the rare-item regime (`n·p/K ≪ 1`) the 1/K dilution of averaging cancels the union gain of having
+K parents to first order — outside that regime, survival is convex in mixed mass and averaging's
+variance reduction can help, so this is a first-order cancellation, not a universal impossibility;
+whereas an operator that keeps, per item, its **strongest source** (and renormalises, which itself
+redistributes mass) realises the union in all regimes. That statement is exact in the minimal model, and it presupposes an
 oracle (or verifier) able to say which source is strongest. The two operators the LLM prototype
 tests — **weight averaging** (a nonlinear network's weight-mean does not compute the mean of its
 parents' outputs) and **routing among intact specialists** (which keeps K models' storage and an input
@@ -436,8 +440,9 @@ on the same task* have a real naive barrier that alignment removes almost entire
 and the aligned merge performs at parent level) — same species, different basis, the canonical Re-Basin
 result, which also proves the aligner works. Two nets that learned *conflicting* label maps have a
 large barrier of which the full symmetry group removes **essentially nothing** (0.502 → 0.497) —
-genuine reproductive isolation, not a missed symmetry, and it cannot be dismissed as a failure to align
-because the very same aligner erased the same-task barrier. It also carries a floor no future alignment
+a conflict-associated barrier the tested alignment leaves largely unchanged — supporting a
+functional-conflict interpretation without proving optimal alignment (control recovery validates a
+special case; the removable share is a lower bound, the residual an upper bound). It also carries a floor no future alignment
 method can breach: models loyal to label maps that conflict on a fraction *μ* of inputs cannot both be
 served by *any* single merged model, which must err at rate ≥ *μ*/2 against at least one parent
 (SI proposition). Sweeping the fraction of conflicting classes traces the **isolation cliff in real
@@ -754,8 +759,9 @@ shape.)
   offspring, beats the naive average — but *only when the task leaves headroom*. On easy tasks a strong
   model's plain average is already at the ceiling and the refinements add nothing; on hard tasks the
   average dilutes a specialist below even the best single parent, and the union-preserving operators win
-  clearly. The practical rule is exact: these tricks pay off in proportion to how far the naive average
-  is from the best attainable. This is a prototype (three task families, one seed), so we read it as
+  clearly. The practical rule, stated qualitatively: these tricks pay off where the naive average falls
+  short of attainable performance, and add nothing where it does not (a quantitative form is untested).
+  This is a prototype (three task families, one seed), so we read it as
   signs, not magnitudes; the *whole grounded society* on a language model remains the open step.
 - *The whole society, and why every part is needed.* In a population evolving on a "reality" landscape,
   the full system — grounding + sexual recombination + preserved diversity — climbs to the top while
@@ -786,7 +792,7 @@ falsifier, not yet established):
 | Confidence weighting improves rank prediction over raw disagreement | **Not supported** (pre-registered internal prediction) | — | Paired Δ\|ρ\| ≈ −0.02, CI [−0.13, +0.06] | Weighting does double the conflict-vs-compat level contrast |
 | The predictor improves budget-matched operator choice | **Open** | — | Soup-vs-route gap readout noise-dominated at 0.5B | The practical payoff; untested |
 | Emergent speciation without conflict | **Not observed** (pre-registered) | Shared ancestry, compatible tasks, tested divergences | E13b: residual 0.000; merge rescues specialists | Bounds the hypothesis; longer horizons/distribution shift/capacity pressure untested |
-| Grounding + sex + diversity jointly necessary | Exact-model result; hypothesis at LLM scale | Conformity stands in for self-consumption | E11 four-arm ablation, each arm failing distinctly | The full grounded LLM society is unbuilt |
+| Grounding + sex + diversity complementary (each ablation fails distinctly) | Analytic-model result; hypothesis at LLM scale | Conformity stands in for self-consumption; general joint necessity not established | E11 four-arm ablation | The full grounded LLM society is unbuilt; alternative schemes untested |
 
 **What is borrowed, and what is ours.** We are deliberate about the ledger, because the surrounding
 literature is crowded and a reader deserves to know exactly where the line falls. **Conceded as prior
@@ -811,8 +817,9 @@ from a thing you must run a search to discover into a thing the landscape's rugg
 the operator-choice design rule that follows (average / union-route / directed-select); **grounding as
 migration–drift balance**, giving a critical real-data fraction and a phase boundary a closed
 self-consuming loop cannot have; **directed sex** as the distinctly-AI advantage (unbounded parents,
-offspring preview, mate choice); and the **integrated society** whose four operators are shown *jointly
-necessary*. The value-add over the machine-learning-native merge theory is that ours predicts *which
+offspring preview, mate choice); and the **integrated society** whose operators make
+*complementary, distinctly-failing contributions* in the tested model (general joint necessity is not
+established). The value-add over the machine-learning-native merge theory is that ours predicts *which
 operator to use and when it will backfire*, not merely how fast quality decays. And it opens — and
 begins to occupy — a question nobody has framed: **model speciation**, the population-genetics of
 *reproductive isolation* (Bateson–Dobzhansky–Muller incompatibilities) as the account of *when two