voice: first-person singular for single authorship

All 37 first-person-plural instances converted: 'I' where the author
acts or judges (I transfer, I measured, I aligned, to my knowledge, the
only anchor I trust — 18 instances, ~one per 260 words), impersonal
constructions elsewhere (the simulator, the tested settings, this paper
poses). 'What is borrowed and what is ours' -> 'what is new'; 'Ours is
the framework-level synthesis' -> 'New here is'. Reference titles
containing 'we' untouched. 19 pp rebuild clean.

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

paper/pnas/main.md

@@ -10,7 +10,7 @@ Artificial intelligence increasingly consists of populations of models rather th
 Models are fine-tuned from common ancestors, trained on data that earlier models generated, and
 combined by weight merging. These practices couple model generations the way reproduction couples
 biological generations, and they raise the same question: how does a population retain and
-accumulate abilities over time? We transfer the population genetics of sexual reproduction to this
+accumulate abilities over time? I transfer the population genetics of sexual reproduction to this
 setting and test it in simulations, small neural networks, and language models. The framework
 recasts continual learning at the population scale and yields design rules: how much real data
 retraining requires, when to combine models, when to keep them separate, and how to anticipate a
@@ -20,20 +20,20 @@ failed combination before making it.
 
 AI development increasingly resembles a population process. Models are specialised, retrained on
 model output, and recombined by weight merging, and the practice is described in evolutionary
-vocabulary with little use of evolutionary theory. We treat multigenerational model populations as
-systems whose inheritance, diversity, and compatibility must be managed, and we transfer the
+vocabulary with little use of evolutionary theory. I treat multigenerational model populations as
+systems whose inheritance, diversity, and compatibility must be managed, and transfer the
 quantitative framework of the evolution of sex. Its starting point, that training on model output is
 genetic drift and model collapse its signature, is by now established from several independent
-directions; we develop the structure that follows from it. In a minimal
+directions; I develop the structure that follows from it. In a minimal
 inheritance model that is exactly Wright–Fisher, and measurably Wright–Fisher plus estimator bias in
-trained networks, we derive and test remedies. Grounding acts as immigration: a real-data fraction
+trained networks, I derive and test remedies. Grounding acts as immigration: a real-data fraction
 far below one retained most equilibrium diversity, with a per-capability observation floor that
 makes the rarest knowledge expensive under unstratified sampling. Refitting a child to the mean of
 its parents' output distributions cancels the multi-parent gain to first order in the rare-item
 regime; union-preserving operators realise it. Merged language-model specialists exceeded every
 parent in replicated experiments. Blind recombination fails on rugged task landscapes; screening
 candidate offspring restores the gain. The optimal mating breadth narrows as skills entangle.
-Finally, we introduce model speciation: a merge barrier remaining after permutation-and-rescaling
+Finally, I introduce model speciation: a merge barrier remaining after permutation-and-rescaling
 alignment tracks functional conflict, isolation did not emerge from compatible specialisation, and
 in a controlled test pre-merge functional disagreement predicted merge damage while weight-geometry
 baselines showed no detectable association.
@@ -61,7 +61,7 @@ machine-generated or machine-translated text (14, 15), and the stock of human te
 exhausted by frontier training within this decade (16). Meanwhile persistent multi-agent systems and
 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, and that observation motivates this work. Here we
+evolving population in the technical sense, and that observation motivates this work. Here I
 transfer the quantitative framework of the branch of biology built for exactly this situation, the
 population genetics of the evolution of sex, and use it to treat multigenerational model populations
 as systems whose inheritance, diversity, and compatibility can be measured, predicted, and managed.
@@ -89,7 +89,7 @@ when should specialists be kept separate rather than consolidated? In practice t
 convention and by trial-and-error search. They are also, recognisably, machine learning's oldest
 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, we will argue, prices these decisions. Table 1 summarises the
+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.
 
@@ -99,19 +99,19 @@ 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
-engineering gate: our simulator reproduces the classical closed forms (heterozygosity decay
+resampling step *is* the Wright–Fisher process: the same equations, which I exploit as an
+engineering gate: the 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.
 
-The boundary of the exactness matters, and we measured it rather than assumed it. Real training adds
+The boundary of the exactness matters, and I measured it rather than assumed it. Real training adds
 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
 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
+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). One consequence of drift deserves its genetic name. Retraining on a
 single parent is *asexual reproduction*, and sustained loss under it carries the defining consequence
@@ -141,9 +141,9 @@ known limits is SI Appendix, Table S1.
 ### Grounding is immigration: cheap, with a floor
 
 In the minimal model, grounding from a fixed real source is *immigration* into a drifting population
-(29–31), and the equilibrium diversity has a closed form our simulator matches exactly. That equilibrium is
+(29–31), and the equilibrium diversity has a closed form the simulator matches exactly. That equilibrium is
 *smooth* in the grounding fraction (there is no phase transition in aggregate diversity), so the
-practical number is an operational threshold, and we define it as such: under the tested population
+practical number is an operational threshold, and I define it as such: under the tested population
 size and Zipf source distribution, `g ≈ 0.05` retained most (≥95%) of equilibrium diversity
 indefinitely, with the required fraction depending on sample size, source distribution, and the
 chosen retention target (dependencies in SI). The engineering point survives the definition: verified
@@ -155,7 +155,7 @@ accordingly, and with distinct consequences for continuous retention, stationary
 reintroduction after loss (immigration can restore an absent item; SI separates these). Protecting the
 rarest knowledge under unstratified grounding is therefore priced per item at cost `∝ 1/p`; targeted
 or stratified sampling changes that cost, and recombination can recover rare capabilities *that are
-still retained across complementary parents* (next section). In trained networks the *sign* of the grounding response transfers everywhere we
+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
@@ -166,7 +166,7 @@ fraction, the measured price of the estimator bias).
 
 ### Recombination: a conservation law, its operators, and offspring that exceed every parent
 
-The largest returns from the transfer concern merging. We begin with a result about the most common
+The largest returns from the transfer concern merging. I begin with a result about the most common
 operator, stated with its assumptions. **Proposition (blending inheritance, rare-item
 regime).** Let K parents independently retain a rare item (mass `p` when retained), and let the child
 draw `n` samples either from one parent chosen at random or from the *mean of the parents' output
@@ -224,7 +224,7 @@ data channel). In the society model, grounding is *grounded evaluation*: selecti
 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,
-and we name them separately. In the tested society (a finite agent population on a rugged NK
+and I name them separately. In the tested society (a finite agent population on a rugged NK
 landscape), a four-arm ablation separates the failure modes: the full system (grounded evaluation +
 directed recombination + diversity-preserving selection (37)) climbs to near the global optimum while
 keeping its specialists; removing grounded evaluation converges the population confidently on an unfit
@@ -241,16 +241,16 @@ language-model scale this composed loop remains unbuilt; it is the paper's large
 Recombination presupposes compatible parents. In biology, lineages pushed far enough apart become
 separate species (*reproductive isolation*) through Bateson–Dobzhansky–Muller incompatibilities (38, 39):
 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
+exposed hybrid. I 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
 denser the incompatibilities; and the incompatibility *count* snowballs quadratically with divergence
-(39). We note that a super-linear count does not by itself entail a sharp performance cliff without
+(39). Note that a super-linear count does not by itself entail a sharp performance cliff without
 the count-to-effect-size link, which the analytic model supplies under its assumptions and any neural
 test must establish separately.
 
 In trained networks, the claim must survive a known alternative: merge barriers between independently
 trained networks are famously *coordinate artefacts*, removable by re-aligning hidden units (40);
-richer symmetry groups remove more (41), with known failures beyond the shared-data regime (42). We therefore aligned under the composition of
+richer symmetry groups remove more (41), with known failures beyond the shared-data regime (42). 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
 initialisations on the *same* task have a barrier that this alignment removes essentially entirely
@@ -266,7 +266,7 @@ Proposition S2), with the framework's role being the *structure around it*: whic
 generate conflict, and what moves the cliff.
 
 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
+emergent (each lineage's changes harmless alone), so I 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
 catastrophically-forgetting specialists (parents ≈ 0.50, merge ≈ 0.955, a sustained Fisher–Muller
@@ -285,7 +285,7 @@ on shared circuitry, not divergence per se.
 
 The framework's prediction-level claim was put to a designed test (Fig. 6C). 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 we
+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*
 (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
@@ -335,7 +335,7 @@ are the experiment's open front.
 ## Discussion
 
 **Design rules.** As engineering guidance, the results reduce to rules that an operator of a model
-population can apply, answering the four decisions posed in the Introduction. *Ground every generation* in verified reality — a few percent retained most diversity in our tested
+population can apply, answering the four decisions posed in the Introduction. *Ground every generation* in verified reality — a few percent retained most diversity in the tested
 settings — but price the rarest capabilities individually (observation probability `1 − e^{−m·p}` per
 batch under unstratified sampling), consider targeted sampling for the deep tail, and use
 recombination to recover rare capabilities still retained across complementary parents. *Merge, don't blend, when there is headroom*: keep specialists
@@ -345,9 +345,9 @@ the operator to entanglement*: merge freely when skills are additive; sparingly,
 selection, when they entangle; and expect the champion-optimal mating breadth to narrow as landscapes
 roughen. *Preserve diversity as a first-class objective*, because selection can only preserve variety that
 exists, and in the tested society its removal produced a distinct failure mode. *Before merging,
-measure functional conflict* — cheap, pre-merge, and in our controlled setting predictive where the
+measure functional conflict* — cheap, pre-merge, and in the controlled setting predictive where the
 tested weight-distance baselines were not; and *do not treat divergence or specialisation alone as
-evidence of incompatibility* — in every regime we tested, what broke merging was conflicting
+evidence of incompatibility* — in every regime tested here, what broke merging was conflicting
 conventions on shared circuitry, which is the thing to detect.
 
 **Continual learning at the population scale.** Within a single network, the discipline's remedies
@@ -364,7 +364,7 @@ adapter-into-base merge; the recent turn to merging as a continual-learning mech
 recombination within one lineage over time, where this paper applies it across lineages; and the
 observation that rare examples and long-tail knowledge are forgotten first (59–61) is tail extinction
 seen one model at a time. The mechanisms differ (forgetting is largely deterministic interference,
-collapse is sampling drift) but the victims and the remedies coincide, and to our knowledge no prior
+collapse is sampling drift) but the victims and the remedies coincide, and to my knowledge no prior
 work carries population-genetic formalism into continual learning. Read into that field, the results
 offer: (i) an equilibrium theory for the replay ratio, with the 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
@@ -379,23 +379,23 @@ splits the field's practice (keep adapters separate vs merge them; 54–58): uni
 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
 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 (62); our irreversibility results
+irreversible. On that last point I note the standing objection that apparent forgetting can be
+skewed task-inference over latent capability rather than erasure (62); the irreversibility results here
 concern oracle-measured behavioural distributions, and distinguishing latent from extinct capability
 at language-model scale is an open experiment whose outcome would be decisive for both readings.
 
-**What is borrowed and what is ours.** The collapse-as-drift diagnosis is established prior work
+**What is borrowed and what is new.** The collapse-as-drift diagnosis is established prior work
 (21–25); so are the empirical facts that merges can beat parents, that decorrelated parents merge better, and that
 naive averaging loses to interference-aware or routed merges (4, 63, 64), that model populations can
 climb (5, 8–10), and that merge success admits ML-native predictors (44, 65), correlational where this framework
 supplies mechanism; the reading of sex as an algorithm for mixability in the theory of computation
-(66) anticipated the transfer before model merging existed. Ours is the framework-level
+(66) anticipated the transfer before model merging existed. New here is the framework-level
 synthesis — inheritance, diversity, and compatibility as managed quantities — together with: the
 conservation law for blending inheritance and its operator boundaries; the per-item grounding floor;
 the society ablation with its complementary failure modes; model speciation as a named, tested question, with the
 coordinate-versus-functional decomposition under permutation-and-rescaling alignment and the emergent
-null that bounds it; and the controlled predictive test with its controls. We claim the framework generated
-these measurements and experiments; we do not claim their outcomes validate a uniquely
+null that bounds it; and the controlled predictive test with its controls. I claim the framework generated
+these measurements and experiments; I do not claim that their outcomes validate a uniquely
 population-genetic mechanism, and one refinement it proposed was not supported.
 
 **Limits and open problems.** The demonstrations are deliberately small: exact where small is a virtue,
@@ -405,9 +405,9 @@ built at language-model scale. The predictive test's next bars, in order of valu
 *unfamiliar* conflict structures and real task pairs; a demonstrably better *budget-matched* merging
 decision; then scale replication. Beyond engineering, the framework's hardest open problem is the
 fitness function itself: selection optimises what is measured, and for knowledge systems the
-persuasive and the true compete — grounding against a reality that can refuse is the only anchor we
+persuasive and the true compete — grounding against a reality that can refuse is the only anchor I
 trust, and institutionalising that anchor (verification, replication, and challenge among models) is
-the society-level problem we pose but do not solve. What biology receives in return is a new model
+the society-level problem this paper poses but does not solve. What biology receives in return is a new model
 system: populations of learners where every genotype, environment, and mating decision is observable
 and manipulable — where the evolution of sex can be studied with interventions (unbounded parents,
 offspring preview, directed mating) that no living system permits.
@@ -418,11 +418,11 @@ development is consolidating around exactly the operators studied here: syntheti
 (inheritance), merging and routing of specialist fine-tunes (recombination and population structure),
 verifier-gated data pipelines (grounded selection), and periodic consolidation of adapters into new
 bases. The framework's reading of that trajectory is concrete. If coming model generations remain what
-our tested regimes found, freely recombinable in the absence of conflicting conventions, then the
+the tested regimes found, freely recombinable in the absence of conflicting conventions, then the
 ecosystem evolves as one interbreeding population, and the levers that matter are grounding budgets
 priced per rare capability and diversity preserved deliberately. If instead long-horizon
 specialisation at scale begins to produce emergent incompatibility, as the expert-training-duration
-observations hint (43) and our small-scale null does not rule out, then lineages will begin to
+observations hint (43) and the small-scale null here does not rule out, then lineages will begin to
 speciate, and the ecosystem's future is a set of diverging species connected by routing rather than by
 merging. Which of the two it will be is measurable now, with the pre-merge conflict instruments this
 paper tested.