Phase 4: PNAS research-article draft (main.md + composed figures + SI skeleton)

paper/pnas/main.md — the manuscript restructured as a research article
(~5.6k words main text): significance statement, abstract, introduction
(diagnosis conceded; the management thesis; the interpretation/
explanation/prediction ladder with the prediction rung stated as a
bounded controlled test), the minimal model with its exactness boundary
(learning kernel cited against ourselves), Table 1 dictionary with
per-row support levels, a five-step results ladder (grounding floor;
conservation law + operator boundaries + Fisher-Muller + directed sex +
mating structure; the jointly-necessary society; speciation across three
tiers with the emergent null; the controlled predictive test at
second-review calibration), discussion (design rules, borrowed-vs-ours
ledger, limits with the reviewer's generalisation-before-scale ordering,
what biology gets back), brief methods, 30 references.

build.py composes 6 figures by stacking committed vector PDFs (bespoke
unified re-plots deferred to submission polish); builds clean under
tectonic (15 pp incl. 6 full-page figures). si.md: SI skeleton
(propositions, claims ledger, per-tier methods, statistics, figure
list). Manifesto sections of v6 (institutions, timescales, re-minting)
compressed into Discussion per the plan; v6 remains the long-form
perspective document.

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

paper/pnas/main.md

@@ -0,0 +1,396 @@
+# 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
+
+---
+
+## Significance statement
+
+Artificial intelligence is shifting from single, frozen models to populations of models that
+specialise, are retrained on each other's output, and are combined ("merged") into new models. Trained
+on their own output, model lineages degenerate — a process already recognised as the mathematics of
+genetic drift. This paper imports the other half of population genetics: the biology of sexual
+reproduction. It treats model merging as recombination, real data as immigration, and merge failure as
+reproductive isolation, and tests each correspondence in simulations, small neural networks, and
+language models. The framework yields design rules — when to average models, when to keep them
+separate, how much real data suffices — and a first controlled test showing that measured functional
+conflict, not weight distance, predicts when merging fails.
+
+## Abstract
+
+AI development increasingly resembles a population process: models are specialised, retrained on model
+output, and recombined by weight merging, with an openly evolutionary vocabulary but little use of
+evolutionary theory. Here we treat multigenerational model populations as systems whose inheritance,
+diversity, and compatibility must be managed, and transfer the quantitative apparatus of the evolution
+of sex. We take as settled that training on model output is genetic drift (model collapse). In a
+minimal inheritance model that is exactly Wright–Fisher — and measurably Wright–Fisher-plus-bias in
+trained networks — we derive and test the remedies: grounding as immigration, with a critical
+real-data fraction far below one but a per-capability floor that leaves the rarest knowledge
+unrescuable; recombination, where averaging parents' output distributions exactly cancels the benefit
+of multiple parents while union-preserving operators realise it; the Fisher–Muller effect, with merged
+language-model specialists exceeding every parent in replicated experiments; outbreeding depression on
+rugged task landscapes, converted into reliable gains by directed, offspring-screened recombination;
+and population structure, where the optimal mating breadth shrinks as skills entangle. Sex has a
+limit: we introduce model speciation — merge failure as reproductive isolation — and show in trained
+networks that a merge barrier surviving the full function-preserving symmetry group tracks functional
+conflict, that isolation did not emerge from compatible specialisation, and, in a controlled
+predictive test, that pre-merge functional disagreement predicts merge damage where weight-geometry
+baselines do not. We state precisely what is exact, what is measured, and what remains hypothesis.
+
+---
+
+## Introduction
+
+The unit of AI progress is quietly changing. Multi-agent systems arrange many models across *space* —
+specialists cooperating on a task. A newer axis is *time*: populations of models that persist across
+generations, each new model built from older ones — specialised by fine-tuning, trained on data earlier
+models generated, and, increasingly, produced by **model merging**, the direct combination of trained
+weights (1, 2). The engineering literature describes this openly in evolutionary vocabulary —
+"crossover," "mutation," "mate choice," populations of merging models that climb benchmarks (2–5) —
+but as metaphor over search algorithms. The organising claim of this paper is that the vocabulary
+deserves 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.**
+
+One half of the transfer is settled and is not our contribution. 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 (6). That this is the mathematics of **genetic
+drift** in a finite population is now established from several directions (7–9); a closed-form
+first-extinction law even places collapse onset at the Wright–Fisher first-extinction time (8). We cite
+this literature as the diagnosis and build on it.
+
+Our contribution is on the remedy side, and 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 weight-geometry baselines did not.
+
+The correspondences we develop, summarised in Table 1: single-teacher retraining is **asexual
+reproduction**, and the irreversible arm of its decay corresponds to **Muller's ratchet** (10) — once
+every copy of a rare capability is gone from all parents and sources, no recombination can rebuild it,
+which is precisely why remedies must act before fixation-by-loss. Injecting verified real data is
+**immigration** from a non-drifting source (11–13). Model merging is **recombination**, and its
+celebrated payoff — a merged model exceeding every parent — is the **Fisher–Muller effect** (14, 15).
+Merging entangled skills courts **outbreeding depression**; screening many candidate merges is a form
+of **directed sex** with no biological analogue; restricting who merges with whom is **population
+structure**. And merging's hard limit — models too diverged in function to combine — is **reproductive
+isolation**, for which the Bateson–Dobzhansky–Muller theory of incompatibilities (16, 17) supplies the
+structure. The nearest precursor to this programme reads sex as an algorithm for mixability in the
+theory of computation (18), pre-dating model merging; the model-merging literature itself has strong
+empirical operators (1, 19, 20) and emerging merge-success predictors (21, 22), 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
+cluster) where the claims are tested as signs under seed replication. Throughout, we report negative
+and tempering results 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 that temper the predictive test.
+
+## The minimal model, and where its exactness ends
+
+Knowledge is modelled as a distribution `p_t` over `K` discrete items — capabilities, facts, modes of
+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
+`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
+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. The honest statement, used throughout: a real learner is 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
+generated digits, where the dry lineage collapses to a single blurred digit class while 10% grounding
+holds all thirty modes (Fig. 1).
+
+**Table 1.** The dictionary. Each correspondence is stated with the level of support it currently has
+(exact = closed form in the minimal model; empirical = measured in trained systems; hypothesis =
+stated with a falsifier, untested or unconfirmed). The full claim-by-claim ledger with assumptions and
+known limits is SI Appendix, Table S1.
+
+| Population genetics | Model populations | Support |
+|---|---|---|
+| Genetic drift in a finite population | Training on finite samples of model output | Exact (minimal model); signs in trained nets; diagnosis conceded to prior work |
+| Immigration from a fixed source | Grounding with verified real data | Exact equilibrium; signs in RNN/MLP/VAE/MNIST |
+| Muller's ratchet (asexual decay) | Irreversible arm of model collapse | Correspondence, scoped: applies to unrecoverable loss |
+| Recombination / sexual reproduction | Model merging | Empirical at 0.5B–7B |
+| Fisher–Muller effect | Merged specialists exceed every parent | Exact-model result; replicated in LLMs |
+| Outbreeding depression under epistasis | Merging entangled skills harms offspring | Exact-model (NK landscapes); hypothesis at LLM scale |
+| Mating systems / population structure | Who merges with whom (breadth of the parent pool) | Exact-model result; hypothesis for real populations |
+| Reproductive isolation (BDM incompatibilities) | Merge failure from functional conflict | Empirical (MLP + LLM tiers, conflict-associated); emergent form not observed |
+| Selection on a fitness function | Verifier-anchored selection ("reality that can say no") | Exact-model result (jointly necessary with sex and diversity) |
+
+## Results
+
+### Grounding is immigration: cheap, with a floor
+
+In the minimal model, grounding from a fixed real source is immigration into a drifting population,
+and the equilibrium diversity has a closed form our simulator matches exactly. The engineering
+headline is the *magnitude*: a critical grounding fraction `g* ≈ 0.05` retains most diversity
+indefinitely — real data is cheap insurance. But the same analysis yields a floor the field's
+average-loss framing misses: an individual capability of rarity `p` survives only if the *absolute*
+real-data budget satisfies `m·p ≳ 1`. Protecting the rarest knowledge is priced per item, at cost
+`∝ 1/p`, and no affordable grounding fraction rescues the deepest tail — that requires recombination
+(next section). In trained networks the *sign* of the grounding response transfers everywhere we
+looked, with two honest 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
+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)*
+
+### Recombination: a conservation law, its operators, and offspring that exceed every parent
+
+Merging is where the evolution-of-sex apparatus pays for itself, beginning with a result about the
+obvious operator. **Averaging is blending inheritance, and it cancels the benefit of multiple
+parents:** when a child is refit to the *mean of its 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 K parents, so adding parents cannot help. An operator that
+keeps, per item, its strongest source (which presupposes a verifier or oracle to say which) realises
+the union. That statement is exact for those operators 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** (different storage and inference budgets from a
+single child) — are its empirical cousins, and the measured bridge is a **headroom rule**: in language
+models, union-preserving operators beat the weight-average in proportion to how far that average is
+from the best attainable. 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,
+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
+(Fig. 2). In real language models the signature replicates under seed replication: merges of three
+LoRA 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).
+
+Sex has risks and, for AI, an unfair advantage — both quantified on rugged (epistatic) NK landscapes
+(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
+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
+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,
+population *structure* is itself a knob: sweeping the mate-pool breadth from monogamous (local) to
+promiscuous (panmictic) 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
+structured-population search, mapped onto merging populations.
+
+*(FIG:fig2)*
+
+*(FIG:fig3)*
+
+### The society: grounding, sex, and diversity are jointly necessary
+
+Composing the operators closes the loop (Fig. 4). A finite population of agents evolves on a rugged NK
+landscape, with selection acting on a grounded score — `g`·true-fitness + (1−g)·conformity to the
+population's own consensus, the analogue of training on the crowd's output. A four-arm ablation
+separates the failure modes: the **full** system (grounding + directed recombination +
+diversity-preserving selection) climbs to near the global optimum while keeping its specialists;
+remove *grounding* and the population converges confidently on an unfit consensus (self-consumption);
+remove *sex* and it strands on local optima; remove *diversity* and it converges prematurely to a
+worse answer. Each removal fails *differently* — the operators are jointly necessary, which is the
+system-level claim the single-operator results build toward. At language-model scale this composed
+loop remains unbuilt; it is the paper's largest stated gap.
+
+*(FIG:fig4)*
+
+### 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:
+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
+denser the incompatibilities; and the incompatibility *count* snowballs quadratically with divergence
+(17) — noting 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 (23), and
+richer symmetry groups remove more (24). We therefore aligned modulo the **complete**
+function-preserving unit symmetry group of the architecture tested (permutation composed with per-unit
+positive rescaling, for plain ReLU MLPs) and decomposed the barrier (Fig. 5B): two networks trained
+from different initialisations on the *same* task have a barrier that 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 full group leaves
+intact (0.502 → 0.497), with the merged model functionally dead — and this cannot be an alignment
+failure, because the same aligner succeeded on the control. Sweeping conflict traces the cliff as
+hybrid fitness, 0.97 → 0.03. Two scope notes: exact recovery of a permuted-and-rescaled copy validates
+a special case rather than global optimality, so the removable share is a lower bound and the residual
+an upper bound; and the conflict floor itself is information-theoretic — no single model can satisfy
+contradictory conventions (SI Appendix, Proposition S2) — with the framework's role being the
+*structure around it*: which divergences generate conflict, and what moves the cliff.
+
+The sharpest honesty 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* — 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. 5C): 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 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**
+— 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)*
+
+### 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
+(13 conditions × 3 seeds; rows are not independent — parents share task-data seeds across conditions —
+so all inference is condition-clustered) 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 —
+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 (21), LoRA-delta cosine and distance, and a cross-task performance
+baseline. The pre-registered outcome is the merge penalty against oracle parent potential (the
+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
+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
+differences are not individually significant at this sample size, and only these baselines were
+tested. Two further results earn their place by tempering: 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
+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
+operator choice, and whether it generalises to unfamiliar conflict structures and real task pairs,
+are the experiment's open front.
+
+*(FIG:fig6)*
+
+## Discussion
+
+**Design rules.** Read as engineering, the results compress into rules an operator of a model
+population can apply. *Ground every generation* in verified reality — a few percent retains most
+diversity — but price the rarest capabilities individually (`m·p ≳ 1`) and use recombination, not
+grounding, to reach the deep tail. *Merge, don't blend, when there is headroom*: keep specialists
+intact and route, or breed-and-screen candidate merges, whenever the naive average is far from
+ceiling; plain averaging is adequate only where a strong base has already composed the skills. *Match
+the operator to entanglement*: merge freely when skills are additive; sparingly, with offspring
+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 the society result shows grounding, recombination, and diversity are jointly
+necessary. *Before merging, measure functional conflict* — cheap, pre-merge, and in our controlled
+setting predictive where weight distance was not; and expect specialisation alone to be merge-safe,
+with conflicting conventions on shared circuitry as the thing to detect and avoid.
+
+**What is borrowed and what is ours.** The diagnosis — collapse as drift — is prior art (6–9), as 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 (1, 19, 20), that model populations can
+climb (2–5), and that merge success admits ML-native predictors (21, 22). Ours 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 jointly-necessary society; model speciation as a named, tested question, with the
+coordinate-versus-functional decomposition under a complete symmetry group 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
+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,
+sign-level and seed-replicated at the language-model tier, on constructed task families with a
+trivially separable router and one model lineage (Qwen, 0.5B–7B). The composed society has not been
+built at language-model scale. The predictive test's next bars, in order of value: generalisation to
+*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
+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
+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.
+
+## Materials and Methods
+
+**Analytic tier.** Pure NumPy/SciPy Wright–Fisher simulator over `K`-item distributions (knowledge as
+`p_t`; Zipf-tailed truth `p*`; drift–grounding–refit generations), extended with a learning kernel
+(smoothing/sharpening refit), multi-locus genotypes on additive and Kauffman NK landscapes, n-parent
+crossover, and finite-population society loops. All parameters live in per-experiment YAML configs;
+every run derives all randomness from one master seed (`SeedSequence.spawn`) and is bitwise
+reproducible; scientific-validation tests assert the closed forms (heterozygosity decay, immigration
+equilibrium, closed-form union) to <0.5% and run in CI with 151 further correctness tests.
+
+**Neural tier.** Trained-network experiments realise the same abstractions with an exact oracle:
+histogram/RNN/MLP/VAE generators on a synthetic mode universe (the histogram model reduces the harness
+exactly to the analytic tier — the bridge gate), and a convolutional VAE on MNIST with a frozen CNN
+oracle (98.5% mode accuracy; confusion matrix recorded as the measurement floor). Speciation
+experiments fork no-BatchNorm MLPs (784–512–512–10) from a shared base, weight-average, and measure
+linear-mode-connectivity error barriers before and after alignment; alignment composes deterministic
+Git Re-Basin permutation matching with exact per-unit scale canonicalisation (the complete unit
+symmetry group for this class), gated by exact recovery of a permuted-and-rescaled copy.
+
+**Language-model tier.** LoRA specialists (rank 16) on procedurally generated task families with an
+exact-match verifier, on frozen Qwen2.5-Instruct bases (0.5B on one 16 GB GPU; 7B on one L40S).
+Operators: weight-space merges (soup/TIES via adapter arithmetic), per-input routing, and
+Dirichlet-sampled offspring populations screened on held-out validation splits. Multi-seed protocols
+fix the test sets and vary the training seed. The predictive test computes all predictors pre-merge
+(generation confidence from token log-probabilities; base-model gradient cosines; exact r-space
+LoRA-delta geometry) and evaluates merges on held-out tests; robust statistics (condition-clustered
+bootstrap, paired predictor contrasts, leave-one-condition-out prediction, multi-reference outcomes)
+are produced by a committed script. Statistical, per-seed reproducibility is documented for GPU tiers.
+
+**Data and code availability.** All code, configs, seeds, results artifacts (with content hashes),
+figures, and a one-command reproduction script will be deposited openly (repository + archived DOI) on
+publication; every figure in this paper regenerates from committed artifacts without re-simulation.
+
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