New Fig. 1 (experimental-programme schematic); Table 2 to SI; figures in citation order; Fig. 2B legible labels

Replaces the results table with a pipeline figure: five questions x three
architecture tiers (exact Wright-Fisher simulator, trained networks, language
models), filled cells naming the experiments, dashed cells the honest gaps.
Table 1 (the dictionary) stays; Table 2 moves to SI Appendix Table S2. The
renumber surfaced a pre-existing citation-order violation (the LLM figure was
cited in the recombination section before Figs. 3-6), so figures are renumbered
to strict first-citation order (LLM tier is now Fig. 3). Fig. 2B: the montage's
baked-in raster labels are cropped away and replaced with vector row numbers
under a rotated "generation" header.

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

paper/pnas/main.md

@@ -1,6 +1,6 @@
 # The evolution of sex for artificial intelligence: a population-genetic framework for multigenerational model populations
 
-**Giorgio F. Gilestro** — Department of Life Sciences, Imperial College London. giorgio@gilest.ro
+**Giorgio F. Gilestro** — Department of Life Sciences, Imperial College London. giorgiogilest.ro
 
 ---
 
@@ -92,8 +92,11 @@ convention and by trial-and-error search. They are also, recognisably, machine l
 problem at a new scale: *continual learning*, the struggle to acquire new abilities without losing old
 ones (26, 27), transposed from a single network to a population whose members inherit from one
 another. Population genetics, I will argue, prices these decisions. Table 1 summarises the
-correspondences on which the argument runs; the sections that follow develop them from closed-form
-theory to experiments in trained networks and language models.
+correspondences on which the argument runs, and Fig. 1 maps the experimental programme built on
+them: the same abstractions tested at three tiers of model architecture — an exact simulator,
+trained neural networks, and language models — with the sections that follow climbing that ladder.
+
+*(FIG:fig1)*
 
 ## The minimal model, and where its exactness ends
 
@@ -120,7 +123,7 @@ refit) reproduces both. Throughout, a real learner is therefore treated as Wrigh
 estimator bias*, and the drift signs (rare-first loss; the grounding response)
 survived that bias in every architecture I tested, including a convolutional VAE retrained on its own
 generated digits, where the dry lineage collapses to a single blurred digit class while 10% grounding
-holds all thirty modes (Fig. 1). Retraining on a single parent is *asexual reproduction*, and sustained loss under it carries the defining consequence
+holds all thirty modes (Fig. 2). Retraining on a single parent is *asexual reproduction*, and sustained loss under it carries the defining consequence
 of *Muller's ratchet* (28), the mechanism by which lineages that never recombine decay irreversibly —
 the reason non-recombining genomes such as the Y chromosome have shed most of their ancestral genes.
 Once every copy of a rare capability is gone from all parents and sources, no recombination can
@@ -171,11 +174,11 @@ or stratified sampling changes that cost, and recombination can recover rare cap
 still retained across complementary parents* (next section). In trained networks the *sign* of the grounding response transfers everywhere I
 looked, with two deviations, both traced to the estimator bias above: sharp thresholds soften,
 and support-counting metrics decouple from truth (forward-KL is the operative collapse metric for a
-smoothing learner). On real images (Fig. 1B), dry self-training collapses a convolutional VAE to one
+smoothing learner). On real images (Fig. 2B), dry self-training collapses a convolutional VAE to one
 mode while ~10% grounding holds all thirty (the trained model needs roughly twice the exact-operator
 fraction, the measured price of the estimator bias).
 
-*(FIG:fig1)*
+*(FIG:fig2)*
 
 ### Recombination: a conservation law, its operators, and offspring that exceed every parent
 
@@ -206,7 +209,7 @@ union-preserving operators beat the weight-average where that average falls shor
 performance, and add nothing where it does not (easy-versus-hard contrasts at two scales; a
 quantitative form of the relationship is untested). On easy tasks a capable base's average is already at ceiling and refinements
 add nothing; on hard tasks the average dilutes a fragile specialist below even the best single parent
-and routing wins by a wide margin (Fig. 6A–B).
+and routing wins by a wide margin (Fig. 3A–B).
 
 The generative payoff is the *Fisher–Muller effect* (35, 36), the classical account of why sex speeds
 adaptation: in an asexual population, beneficial variants arising in different individuals can only
@@ -215,16 +218,16 @@ producing a *genotype* (an individual's combination of variants, one at each *lo
 fitter than any parent.
 In the multi-locus model, sexual merging of decorrelated specialists climbs to the global optimum, a
 genotype no parent held, while the best single parent and the blended average both plateau below
-(Fig. 2). In real language models the signature replicates under seed replication: merges of three
+(Fig. 4). In real language models the signature replicates under seed replication: merges of three
 LoRA (37) specialists beat every parent overall (decisively at 7B: 0.87 vs 0.77), and on the sharper
-worst-family metric the merged models are the only ones competent everywhere, in every seed (Fig. 6A).
+worst-family metric the merged models are the only ones competent everywhere, in every seed (Fig. 3A).
 
 Sex has risks and, for AI, an unfair advantage, both quantified on Kauffman's NK fitness landscapes
 (38), the standard model of *epistasis*, biology's term for interaction between genes: the fitness
 contribution of a variant depends on which variants occupy the other loci, much as a component's
 value in an ML system depends on the components around it. Each of the landscape's `N` sites
 interacts with `K` others (the model's eponymous parameters), and raising that interaction count
-tunes the landscape from smooth and additive to rugged and many-peaked (Fig. 3). When skills are entangled, blind recombination produces offspring *below* their parents,
+tunes the landscape from smooth and additive to rugged and many-peaked (Fig. 5). When skills are entangled, blind recombination produces offspring *below* their parents,
 worsening with ruggedness, and the optimal recombination rate shrinks as entanglement grows. Biology
 knows this failure as *outbreeding depression*, the reason conservation practice warns against
 crossing locally adapted populations: in the textbook case, an ibex herd in the Tatra Mountains
@@ -234,21 +237,23 @@ parents, choose complementary mates, and *screen many candidate offspring agains
 keeping one*. This directed sex converts the outbreeding catastrophe into a reliable gain in the
 model (tracking or exceeding the best parent at every ruggedness) and replicates as a sign in language
 models: bred-and-screened merges beat the a-priori blend in every seed on headroom tasks, including
-one seed where the blend failed catastrophically and selection was immune (Fig. 6A). Finally,
+one seed where the blend failed catastrophically and selection was immune (Fig. 3A). Finally,
 population *structure* is itself a knob: sweeping the mate-pool breadth from monogamous (repeated
 local pairings) to promiscuous (*panmixia*: any model may merge with any other) against ruggedness,
 wide mixing maximises the population mean while
 monotonically destroying diversity, and the best *champion* shifts from wide breadth on smooth
-landscapes to intermediate breadth on rugged ones (Fig. 3C), the mating-system phenomenon known to
+landscapes to intermediate breadth on rugged ones (Fig. 5C), the mating-system phenomenon known to
 structured-population search, mapped onto merging populations.
 
-*(FIG:fig2)*
-
 *(FIG:fig3)*
 
+*(FIG:fig4)*
+
+*(FIG:fig5)*
+
 ### The society: grounding, recombination, and diversity make complementary contributions
 
-Composing the operators (Fig. 4) requires one definitional distinction first. In the inheritance
+Composing the operators (Fig. 6) requires one definitional distinction first. In the inheritance
 model, grounding is *grounded inheritance*: external samples added to the reproduction process (the
 data channel). In the society model, grounding is *grounded evaluation*: selection weights true
 fitness against conformity to the population's own consensus, `g`·true-fitness + (1−g)·conformity,
@@ -264,7 +269,7 @@ make complementary contributions *under the tested conditions*; general joint ne
 established (alternative mutation, restart, archive, or selection schemes could alter the picture). At
 language-model scale this composed loop remains unbuilt; it is the paper's largest stated gap.
 
-*(FIG:fig4)*
+*(FIG:fig6)*
 
 ### The limit of sex: model speciation
 
@@ -273,7 +278,7 @@ separate species (*reproductive isolation*) through Bateson–Dobzhansky–Mulle
 changes harmless on their own genetic background but deleterious in combination — the mechanism behind
 the mule's sterility and the inviability of many between-species crosses, in which two genomes that
 each work perfectly cannot run in the same cell. A merged model is exactly the
-exposed hybrid. I built the analytic model (Fig. 5A): hybrid fitness tracks the parents while
+exposed hybrid. I built the analytic model (Fig. 7A): hybrid fitness tracks the parents while
 compatible, then peels off and crashes below the ancestor; the isolation cliff arrives earlier the
 denser the incompatibilities; and the incompatibility *count* snowballs quadratically with divergence
 (42). Note that a super-linear count does not by itself entail a sharp performance cliff without
@@ -284,7 +289,7 @@ In trained networks, the claim must survive a known alternative: merge barriers
 trained networks are famously *coordinate artefacts*, removable by re-aligning hidden units (43);
 richer symmetry groups remove more (44), with known failures beyond the shared-data regime (45). I therefore aligned under the composition of
 permutation matching and exact per-unit rescaling (the unit symmetry group of plain ReLU MLPs, as the
-search space) and decomposed the barrier (Fig. 5 C and D): two networks trained from different
+search space) and decomposed the barrier (Fig. 7 C and D): two networks trained from different
 initialisations on the *same* task have a barrier that this alignment removes essentially entirely
 (residual ≈ 0.001, the aligned merge performing at parent level): coordinate, not functional; two
 networks trained on *conflicting* label maps have a barrier the same alignment leaves largely
@@ -302,7 +307,7 @@ emergent (each lineage's changes harmless alone), so I let children diverge with
 signal anywhere*, using complementary class specialists and divergent input conventions, to 6.4× the base
 training. No isolation emerged (residual 0.000 throughout); instead the merge *rescued* the two
 catastrophically-forgetting specialists (parents ≈ 0.50, merge ≈ 0.955, a sustained Fisher–Muller
-rescue). The same double result appears at the language-model tier (Fig. 5 E and F): conflicting conventions
+rescue). The same double result appears at the language-model tier (Fig. 7 E and F): conflicting conventions
 produce *function-specific* hybrid breakdown (the merge scores below both parents on the conflicted
 function, while a budget-controlled design shows the disjoint skills merge unharmed), and over-training
 disjoint specialists 1→12 epochs (cf. the merging literature's expert-duration effect; 46) produces
@@ -311,11 +316,11 @@ tested, isolation had to be provoked by functional conflict; specialisation alon
 — a bound on the analogy that sharpens the design rule: what breaks merging is conflicting conventions
 on shared circuitry, not divergence per se.
 
-*(FIG:fig5)*
+*(FIG:fig7)*
 
 ### A controlled predictive test: functional conflict, measured pre-merge, predicts merge damage
 
-The framework's prediction-level claim was put to a designed test (Fig. 6C). Thirty-nine parent pairs
+The framework's prediction-level claim was put to a designed test (Fig. 3C). Thirty-nine parent pairs
 (13 conditions × 3 seeds; rows are not independent — parents share task-data seeds across conditions,
 so inference is condition-clustered, and because shared seeds also couple rows *across* conditions I
 report per-seed and leave-one-seed-out sensitivity alongside) span three axes decorrelated by construction: *conflict*
@@ -349,21 +354,7 @@ the specifically population-genetic mechanism. Whether the prediction improves a
 operator choice, and whether it generalises to unfamiliar conflict structures and real task pairs,
 are the experiment's open front.
 
-*(FIG:fig6)*
-
-**Table 2.** Headline quantitative results with sample sizes, uncertainty, and outcome definitions
-(full per-experiment tables and falsifier status in SI Appendix and per-experiment documentation).
-
-| Result | Setting / n | Outcome definition | Headline |
-|---|---|---|---|
-| Closed-form validation | Analytic tier; standing tests | Simulated vs closed-form H-decay, immigration equilibrium, multi-teacher union | Agreement < 0.5% |
-| Grounding retention | Minimal model; 18+ replicates per point | Fraction of equilibrium diversity retained at grounding g (operational threshold) | g ≈ 0.05 retained ≥95% (tested setting); smooth in g |
-| MNIST collapse & rescue | Conv-VAE, 4 replicates; frozen oracle (98.5% mode acc.) | Mode support / forward-KL over generations | Dry: 30→1 modes; 10% grounding: 30/30 held |
-| Fisher–Muller in LLMs | 5 seeds (0.5B), fixed tests; single 7B run | Merged vs best-specialist accuracy (overall; worst family) | Ties 0.647±0.027 vs 0.592±0.009; 7B 0.87 vs 0.77 |
-| Union vs blend (headroom) | 3 seeds (0.5B hard); single 7B-hard run | Paired per-seed ordering, routing vs weight-average | Routing > blend in 3/3 seeds; one catastrophic blend failure avoided |
-| Speciation decomposition | MLPs, 3 replicates | LMC error barrier residual after permutation+rescaling alignment | Same-task 0.001; conflict 0.497 (naive 0.502) |
-| Emergent isolation | MLPs 4 reps to 6.4× base training; LLM 1→12 epochs | Residual barrier; merged vs parent accuracy | 0.000 everywhere; merge rescues parents (≈0.955 vs ≈0.50) |
-| Predictive test | 13 conditions × 3 seeds (0.5B) | Merge penalty vs oracle parent potential (pre-registered; ±: clustered 95% CI) | Functional ρ +0.45/+0.46, CI excl. 0; LOCO ρ ≈ 0.4; geometry n.s.; paired differences n.s. |
+Headline quantitative results, with sample sizes, uncertainty, and outcome definitions, are collected in SI Appendix, Table S2.
 
 ## Discussion