typography: remove bold-for-emphasis from the main text (PNAS convention)

All 48 in-text bold spans converted: term first-introductions to italics
(model merging, genetic drift, continual learning, Fisher-Muller effect,
outbreeding depression, directed sex, grounded inheritance/evaluation,
and kin), pure-emphasis spans to plain text (the organising-claim
sentence, the emergent-null statements, the supported-conclusion
sentence). Bold retained only where PNAS uses it: run-in paragraph
headings (Design rules. / Analytic tier. / etc.), table labels, and
reference volume numbers. Repeat mentions of first-use-italicised terms
de-italicised (italics at first use only). 18-pp rebuild clean.

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

paper/pnas/main.md

@@ -47,7 +47,7 @@ millions of models (Hugging Face alone grew past three million by 2026), and the
 independent creations: the overwhelming majority are fine-tunes, distillations, or merges of a small
 number of foundation models, forming large family trees whose lineage structure, inherited traits,
 and mutation dynamics are already being mapped with explicitly phylogenetic methods (1–3).
-This population also reproduces. Weight-space **model merging**, the direct combination of trained
+This population also reproduces. Weight-space *model merging*, the direct combination of trained
 parents into a new model, is mainstream community practice with standard tooling and thousands of
 hybrid checkpoints, including leaderboard-topping ones (4–7), and the engineering literature
 describes it in evolutionary vocabulary: "crossover," "mutation," "mate choice," populations of
@@ -62,14 +62,14 @@ exhausted by frontier training within this decade (16). Meanwhile persistent mul
 emerging agent economies put many interacting models into sustained contact (17–20). A population
 whose members inherit from one another, recombine, and retransmit under these conditions is an
 evolving population in the technical sense. The claim of this paper is that the vocabulary should be
-given its mathematics: **multigenerational model populations are systems whose inheritance,
+given its mathematics: multigenerational model populations are systems whose inheritance,
 diversity, and compatibility must be managed, not merely collections of models to optimise, and the
 branch of biology that studies exactly this problem, the population genetics of the evolution of sex,
-transfers as a quantitative framework.**
+transfers as a quantitative framework.
 
 The frame's entry point is the diagnosis. Training each generation of a model on the previous
 generation's output degrades it (*model collapse*): rare capabilities vanish first and the lineage
-drifts toward its own most common behaviour (21). That this is the mathematics of **genetic drift** in
+drifts toward its own most common behaviour (21). That this is the mathematics of *genetic drift* in
 a finite population is a conclusion we reached independently in building the present framework, and
 one that has been derived in parallel from several other directions (22–24), including a closed-form
 first-extinction law placing collapse onset at the Wright–Fisher first-extinction time (23), and that
@@ -82,22 +82,22 @@ recombination, selection, population structure) to its limit (reproductive isola
 framework from closed forms to trained networks to language models.
 
 In machine learning's own terms, the problem this frame addresses is the field's oldest,
-**continual learning**, reappearing one level up. Within a single network, sequential learning
+*continual learning*, reappearing one level up. Within a single network, sequential learning
 overwrites prior knowledge (catastrophic forgetting; 26, 27), and the discipline's remedies are, one
-by one, the population operators of this paper in single-model form: **rehearsal and replay** of past
+by one, the population operators of this paper in single-model form: *rehearsal and replay* of past
 data is grounding's within-lineage counterpart, and the field's empirically settled replay fractions,
 on the order of 1% for instruction tuning (28) and 5% to 25% by distribution-shift strength in
 continual pretraining (29), sit where the minimal model's operational grounding threshold lies, a
 correspondence for which the framework supplies the missing theory (equilibrium diversity, and a
-per-capability survival law). **Pseudo-rehearsal**, the replay of the network's own generated
+per-capability survival law). *Pseudo-rehearsal*, the replay of the network's own generated
 samples, proposed as a cure in 1995 (30) and revived as generative replay (31), is this paper's
 ungrounded null: immigration from a drifting source, benign for one hop and compounding into
 collapse over generations; verifier-filtering (32, 33) converts it back into grounding.
-**Parameter isolation** (34, and frozen-base adapters, which forget far less; 35) is the engineered
-decorrelation our specialists use; **complementary-learning-systems consolidation** (36–38) is our
-periodic adapter-into-base merge; the recent turn to **merging as a continual-learning mechanism**
+*Parameter isolation* (34, and frozen-base adapters, which forget far less; 35) is the engineered
+decorrelation our specialists use; *complementary-learning-systems consolidation* (36–38) is our
+periodic adapter-into-base merge; the recent turn to *merging as a continual-learning mechanism*
 (39–42) applies recombination within one lineage over time, where we apply it across lineages; and
-the observation that **rare examples and long-tail knowledge are forgotten first** (43–45) is
+the observation that rare examples and long-tail knowledge are forgotten first (43–45) is
 tail-allele extinction observed one model at a time. One distinction is kept explicit throughout:
 catastrophic forgetting is largely deterministic interference from shifted training, whereas collapse
 is stochastic sampling drift; the two phenomena share their victims, the rare, and their remedies, but not their mechanism. To our knowledge, no prior work carries population-genetic formalism into continual
@@ -105,36 +105,36 @@ learning itself; that bridge (replay as immigration with a survival law, merging
 compatibility criterion, consolidation as the slow store of a two-speed memory) is where this
 framework may matter most.
 
-We are explicit about what kind of contribution each claim is, distinguishing **interpretation** (an existing result understood in population-genetic terms),
-**explanation** (the transferred mechanism accounts for observations existing accounts leave open),
-and **prediction** (the framework forecasts an unmeasured outcome). The paper is strongest on the
+We are explicit about what kind of contribution each claim is, distinguishing *interpretation* (an existing result understood in population-genetic terms),
+*explanation* (the transferred mechanism accounts for observations existing accounts leave open),
+and *prediction* (the framework forecasts an unmeasured outcome). The paper is strongest on the
 first; makes concrete progress on the second (separating merge failures that are coordinate artefacts
 from those that are functional); and reports a first, bounded step on the third: a controlled
 predictive test in which pre-merge functional-disagreement measures, chosen by the framework,
 predicted merge damage on a constructed task grid while the tested weight-geometry baselines showed
 no detectable association.
 
-The correspondences we develop, summarised in Table 1: single-teacher retraining is **asexual
-reproduction**, and the irreversible arm of its decay shares the defining consequence of **Muller's
-ratchet** (46): once every copy of a rare capability is gone from all parents and sources, no
+The correspondences we develop, summarised in Table 1: single-teacher retraining is *asexual
+reproduction*, and the irreversible arm of its decay shares the defining consequence of *Muller's
+ratchet* (46): once every copy of a rare capability is gone from all parents and sources, no
 recombination can rebuild it, which is why remedies must act before fixation-by-loss (a consequence-
 level correspondence: the minimal model lacks the ratchet's recurrent deleterious-mutation mechanism,
 so irreversible loss alone does not identify that specific mechanism). Injecting verified real data is
-**immigration** from a non-drifting source (32, 47, 48). Model merging is **recombination**, and its
-central payoff, a merged model exceeding every parent, is the **Fisher–Muller effect** (49, 50).
-Merging entangled skills courts **outbreeding depression**; screening many candidate merges is
+*immigration* from a non-drifting source (32, 47, 48). Model merging is *recombination*, and its
+central payoff, a merged model exceeding every parent, is the *Fisher–Muller effect* (49, 50).
+Merging entangled skills courts *outbreeding depression*; screening many candidate merges is
 engineered recombination with unusually flexible parent choice and pre-deployment screening (we use
-the shorthand **directed sex**); restricting who merges with whom is **population structure**. Merging's hard limit, models too diverged in function to combine, is **reproductive
-isolation**, for which the Bateson–Dobzhansky–Muller theory of incompatibilities (51, 52) supplies the
+the shorthand *directed sex*); restricting who merges with whom is *population structure*. Merging's hard limit, models too diverged in function to combine, is *reproductive
+isolation*, for which the Bateson–Dobzhansky–Muller theory of incompatibilities (51, 52) supplies the
 structure. The nearest precursor to this programme reads sex as an algorithm for mixability in the
 theory of computation (53), pre-dating model merging; the model-merging literature itself has strong
 empirical operators (4, 54, 55) and emerging merge-success predictors (56, 57), to which our delta is
 mechanism: *when and why* failure is coordinate versus functional, and what moves the boundary.
 
 We support the framework at three tiers of evidence, in ascending realism and descending exactness: a
-**minimal analytic model** validated against closed forms to a fraction of a percent; **small trained
-networks** (MLPs, recurrent networks, an MNIST image generator) where the operators are measured in
-real weights; and **language models** (LoRA-specialised Qwen models, 0.5B locally and 7B on a compute
+*minimal analytic model* validated against closed forms to a fraction of a percent; *small trained
+networks* (MLPs, recurrent networks, an MNIST image generator) where the operators are measured in
+real weights; and *language models* (LoRA-specialised Qwen models, 0.5B locally and 7B on a compute
 cluster) where the claims are tested as signs under seed replication. Negative results are reported with the same prominence as confirmations; they include the failure of
 an internal pre-registered prediction, a null on emergent speciation that bounds the analogy, and the
 sensitivity analyses on the predictive test.
@@ -145,7 +145,7 @@ Knowledge is modelled as a distribution `p_t` over `K` discrete items (capabilit
 behaviour), with a fixed true distribution `p*` whose rare tail carries the knowledge most at risk.
 One generation is: *draw `n` samples from the parent's distribution, optionally mix in `m` verified
 real samples ("grounding", `g = m/(n+m)`), and refit the child*. In this minimal inheritance model the
-resampling step **is** the Wright–Fisher process: the same equations, which we exploit as an
+resampling step *is* the Wright–Fisher process: the same equations, which we exploit as an
 engineering gate: our simulator reproduces the classical closed forms (heterozygosity decay
 `E[H_t] = H_0(1 − 1/n)^t`; the exact immigration–drift equilibrium; the closed-form multi-teacher
 union) to within 0.5%, and these are standing tests in the codebase, not one-off checks.
@@ -154,7 +154,7 @@ The boundary of the exactness matters, and we measured it rather than assumed it
 approximation, optimisation noise, and inductive bias, and when trained networks are fit against the
 exact drift null they deviate in *opposite, architecture-specific* directions: a smoothing recurrent
 network resists collapse (keeping spurious variants alive), while a sharpening image generator
-accelerates it. A one-parameter **learning kernel** (a smoothing knob and a sharpening knob on the
+accelerates it. A one-parameter *learning kernel* (a smoothing knob and a sharpening knob on the
 refit) reproduces both. Throughout, a real learner is therefore treated as Wright–Fisher *plus a signed, measurable
 estimator bias*, and the drift signs (rare-first loss; the grounding response)
 survived that bias in every architecture we tested, including a convolutional VAE retrained on its own
@@ -222,16 +222,16 @@ cancellation is a first-order result about rare items, not a universal impossibi
 contrasting union operator (keep each item's strongest source, then renormalise, which itself
 redistributes mass and presupposes a verifier or oracle to identify the strongest source) increases
 expected retention with K in all regimes in the minimal model. The practically important
-operators, **weight averaging** (a nonlinear network's weight-mean does not compute its parents'
-output-mean) and **routing among intact specialists** (58) (different storage and inference budgets from a
-single child), are its empirical cousins, and the measured bridge is a **headroom rule**, stated qualitatively: in language models,
+operators, *weight averaging* (a nonlinear network's weight-mean does not compute its parents'
+output-mean) and *routing among intact specialists* (58) (different storage and inference budgets from a
+single child), are its empirical cousins, and the measured bridge is a *headroom rule*, stated qualitatively: in language models,
 union-preserving operators beat the weight-average where that average falls short of attainable
 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).
 
-The generative payoff is the **Fisher–Muller effect**: recombination assembles, in one offspring,
+The generative payoff is the Fisher–Muller effect: recombination assembles, in one offspring,
 complementary variants that arose in different lineages, producing a genotype 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
@@ -241,10 +241,10 @@ worst-family metric the merged models are the only ones competent everywhere, in
 
 Sex has risks and, for AI, an unfair advantage, both quantified on rugged (epistatic) NK landscapes (60)
 (Fig. 3). When skills are entangled, blind recombination produces offspring *below* their parents
-(**outbreeding depression**), worsening with ruggedness, and the optimal recombination rate shrinks as
+(outbreeding depression), worsening with ruggedness, and the optimal recombination rate shrinks as
 entanglement grows. But an engineered population can do what biology cannot: recombine unbounded
 parents, choose complementary mates, and *screen many candidate offspring against a verifier before
-keeping one*. This **directed sex** converts the outbreeding catastrophe into a reliable gain in the
+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,
@@ -261,8 +261,8 @@ structured-population search, mapped onto merging populations.
 ### The society: grounding, recombination, and diversity make complementary contributions
 
 Composing the operators (Fig. 4) 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
+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,
 the analogue of scoring models by the crowd's approval (the fitness channel). These are related design
 ideas, since both couple the lineage to a non-drifting external signal, but they are different operators,
@@ -281,7 +281,7 @@ language-model scale this composed loop remains unbuilt; it is the paper's large
 ### The limit of sex: model speciation
 
 Recombination presupposes compatible parents. In biology, lineages pushed far enough apart become
-separate species (**reproductive isolation**) through Bateson–Dobzhansky–Muller incompatibilities:
+separate species (reproductive isolation) through Bateson–Dobzhansky–Muller incompatibilities:
 changes harmless on their own background but deleterious in combination. A merged model is exactly the
 exposed hybrid. We built the analytic model (Fig. 5A): hybrid fitness tracks the parents while
 compatible, then peels off and crashes below the ancestor; the isolation cliff arrives earlier the
@@ -307,17 +307,17 @@ information-theoretic (no single model can satisfy contradictory conventions; SI
 Proposition S2), with the framework's role being the *structure around it*: which divergences
 generate conflict, and what moves the cliff.
 
-The strongest constraint comes from the pre-registered **emergent test**: true BDM incompatibilities are
+The strongest constraint comes from the pre-registered *emergent test*: true BDM incompatibilities are
 emergent (each lineage's changes harmless alone), so we let children diverge with *no conflicting
 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
+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
-produce **function-specific** hybrid breakdown (the merge scores below both parents on the conflicted
+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; 65) produces
 no isolation at all — the merge improves. Across every tier
-tested, **isolation had to be provoked by functional conflict; specialisation alone did not speciate**
+tested, isolation had to be provoked by functional conflict; specialisation alone did not speciate
 — a bound on the analogy that sharpens the design rule: what breaks merging is conflicting conventions
 on shared circuitry, not divergence per se.
 
@@ -331,8 +331,8 @@ so inference is condition-clustered, and because shared seeds also couple rows *
 report per-seed and leave-one-seed-out sensitivity alongside) span three axes decorrelated by construction: *conflict*
 (contradictory conventions on shared prompts, private budgets fixed), *compatible overlap* (the same
 shared prompts under the same convention — overlap and volume without conflict), and *duration* (weight
-divergence with zero conflict). Before merging, six predictors are computed: **confidence-weighted
-functional conflict** (bilateral confident disagreement on probes drawn blind to where conflict lives —
+divergence with zero conflict). Before merging, six predictors are computed: *confidence-weighted
+functional conflict* (bilateral confident disagreement on probes drawn blind to where conflict lives —
 a proposed proxy for merge-relevant interactions, motivated by the observation that raw disagreement
 counts harmless complementation, one parent merely ignorant, as conflict), raw disagreement, gradient
 alignment at the shared base (56), LoRA-delta cosine and distance, and a cross-task performance
@@ -340,10 +340,10 @@ baseline. The pre-registered outcome is the merge penalty against oracle parent
 hybrid-load analogue), also reported against best- and mean-parent references because the predictor
 ordering is sensitive to that choice.
 
-The supported conclusion, stated conditionally: **across this controlled grid, pre-merge functional
+The supported conclusion, stated conditionally: across this controlled grid, pre-merge functional
 disagreement predicted merge penalties (clustered bootstrap CIs excluding zero; held-out
 leave-one-condition-out ρ ≈ 0.35–0.40), whereas LoRA-delta cosine and L2 showed no statistically
-detectable association; gradient alignment carried intermediate signal.** Head-to-head predictor
+detectable association; gradient alignment carried intermediate signal. Head-to-head predictor
 differences are not individually significant at this sample size; only these baselines were tested;
 and with three seeds, uncertainty about seed generalisation remains substantial — though the seed
 sensitivity favours the functional measures (per-seed ρ stable at +0.37 to +0.53 in each seed alone,
@@ -351,7 +351,7 @@ geometry ≈ 0 in every seed, gradient alignment seed-unstable at −0.11 to −
 bound the claim: the initial two-axis grid's best predictor
 was delta-cosine (ρ = +0.60) — an overlap artefact that the compatible-overlap control was added to
 expose, and did (collapse to +0.03); and the pre-registered internal prediction that confidence
-weighting would beat raw disagreement **failed** (they are statistically indistinguishable as rank
+weighting would beat raw disagreement *failed* (they are statistically indistinguishable as rank
 predictors), so the present evidence favours functional disagreement generally, not the DMI-specific
 refinement. The framework motivated the measurement and the controls; their success does not validate
 the specifically population-genetic mechanism. Whether the prediction improves a budget-matched
@@ -393,19 +393,19 @@ evidence of incompatibility* — in every regime we tested, what broke merging w
 conventions on shared circuitry, which is the thing to detect.
 
 **What this offers continual learning.** Read into the field where these results most directly land:
-(i) a first-principles account of the **replay ratio**: the field's constants (≈1%, 5%, 25%; 28, 29)
+(i) a first-principles account of the *replay ratio*: the field's constants (≈1%, 5%, 25%; 28, 29)
 acquire an equilibrium theory and a sharper prediction, that the required fraction is set by the
 rarest capability one refuses to lose (the `1 − e^{−m·p}` law) rather than by average loss, which is
-testable against published replay sweeps; (ii) a **failure theory for generative replay**:
+testable against published replay sweeps; (ii) a *failure theory for generative replay*:
 self-generated rehearsal is safe for short horizons and compounds into collapse across generations
-unless verifier-filtered back into grounding (30–33); (iii) **pre-merge interference
-prediction with a mechanism**: where the current state of the art fits regressions over candidate
+unless verifier-filtered back into grounding (30–33); (iii) *pre-merge interference
+prediction with a mechanism*: where the current state of the art fits regressions over candidate
 metrics (56), the functional-conflict measure arrives at a convergent signal from principle and comes
 with an operator prescription — when conflict is high, do not average; route or breed-and-screen;
-(iv) a candidate **decision rule for the consolidate-versus-stay-modular question** that currently
+(iv) a candidate *decision rule for the consolidate-versus-stay-modular question* that currently
 splits the field's practice (keep adapters separate vs merge them; 54–58): union-preserving operators
 where headroom exists, fusion where the base composes, consolidation as the slow-store step; and (v)
-**tail monitoring as the leading indicator**: continual-learning evaluation that averages over
+*tail monitoring as the leading indicator*: continual-learning evaluation that averages over
 capabilities hides exactly the losses that drift theory says come first and, past a threshold, become
 irreversible. On that last point we note the standing objection that apparent forgetting can be
 skewed task-inference over latent capability rather than erasure (66); our irreversibility results