\section{Introduction}\label{sec:intro}

Independently trained language models appear to converge toward similar linear representation
geometries \citep{huh2024platonic,kornblith2019similarity,raghu2017svcca}, and affine maps between the
residual streams of related models transfer probes, sparse-autoencoder dictionaries and steering vectors
\citep{chen2025transferring,kim2026one,agarwal2026cross}. Whether such maps can carry a
\emph{capability}---a reusable computation that the recipient could not perform before---is open. The one
controlled attempt we know of reports a null: a linear bridge between two Pythia models aligns hidden states
almost perfectly yet does not improve multi-hop answering when injected \citep{zhang2026negative}.

This paper asks the question under conditions where it can be answered. We (i) \emph{manufacture} a
capability gap by training donor and recipient transformers on the same micro-world except for one invented
operator $\Omega$ that the recipient never sees, (ii) \emph{causally localize} where the donor executes
$\Omega$ by interchange interventions before attempting any transfer, and (iii) compare six transplant
families against a battery of matched controls (sham map, norm-matched random rows, shuffled items, shuffled
layers, unrelated-skill donors) and against conventional learning on the same data. The word \emph{organ} is a
metaphor for a bounded, causally identified subsystem; it carries no biological or phenomenal claim. We then
test the same protocol on three open-weight models (Qwen2.5-1.5B, Qwen2.5-3B, Llama-3.2-3B) with the
capability defined as performing a verifiable task without demonstrations.

\paragraph{What we find.} In the micro-world the answer is positive, specific and bounded.
A donor-in-the-loop \emph{activation graft}---replacing the recipient's post-layer-0 residual row at every
read position by the donor's row through an orthogonal Procrustes map fitted on \emph{task-free} rows---lifts
the recipient from chance to near-perfect accuracy on held-out $\Omega$ programs (confirmatory: $\Delta_T^{\mathrm{adj}}$
reported in \S\ref{sec:results}) while leaving the control stratum intact, for same- and different-initialization
pairs, across a width mismatch, a depth mismatch and a harder stride-2 variant. The graft carries the
\emph{rule}: maps fitted on six of the eleven operand values transfer to the five unseen values. An
eight-dimensional subspace of the 128-dimensional residual stream suffices; a random subspace of the same
size does nothing. Ablating the donor's layer-0 attention output destroys the donor; grafting the same
component from an intact donor of another seed rescues it; a sham map does not. All controls sit at chance,
and the sham map and random rows also destroy the control stratum, so retention is itself diagnostic.

Three findings bound the claim. First, the choice of alignment map is not a detail: maps fitted by regression
toward the recipient on rows where the donor computes $\Omega$ \emph{remove} the $\Omega$-specific component
(Proposition~\ref{prop:annihilation}), which is why ridge and CCA grafts fail where orthogonal and task-free
maps succeed, and why rescaling or more data cannot help them. Second, donor-free variants are weaker and
qualitatively different: a saved affine adapter conveys part of the effect in a fresh process but behaves as a
cache (zero on unseen operands); weight grafts partly transfer $\Omega$ at the cost of the control stratum;
steering vectors transfer nothing. Third, on this task a supervised adapter with the same parameter count, or
distillation on the same items, reaches perfect accuracy: transplantation is a way to move a computation
\emph{without} labels or gradient steps, not a cheaper way to learn. On open-weight models, task vectors are
causally sufficient within a model for antonyms and capitals but not for an invented morphology, and
cross-model transfer of mapped vectors is \emph{reported as measured} in \S\ref{sec:results}; we do not
extrapolate from the micro-world to them.

\paragraph{Contributions.}
(1) An operational theory of transplantable subsystems with explicit estimands, a control battery and a
persistence vocabulary (\S\ref{sec:theory}), including an elementary annihilation result for regression-fitted
alignment maps. (2) A controlled micro-world and an open-weight framework with exact hook semantics,
preregistered hypotheses and a registry of every run (\S\ref{sec:design}). (3) Confirmatory evidence on
localization, sufficiency, necessity, rescue, selectivity, dimensionality, rule-versus-cache and portability
of an activation graft in the micro-world (\S\ref{sec:results}--\S\ref{sec:mechanism}). (4) A map of the
failure boundaries: regression-fitted maps, donor-free adapters, weight grafts and steering vectors, and the
open-weight task-vector transfer (\S\ref{sec:robustness}--\S\ref{sec:discussion}).