# DRCT v17 — Transferable Concept Invention

A one-world macro is not yet a reusable concept.

v17 requires a newly invented abstraction to:
1. recur across independently solved source worlds;
2. reduce total description length after paying its definition cost;
3. be frozen before target worlds are exposed;
4. transfer under new variable bindings and composition;
5. be rejected on negative-control worlds where it is irrelevant.

Each source world is first solved with a generic latent relation table. Recovered
tables are quotiented under explicitly allowed coordinate conventions (argument
swap and invertible affine output relabeling).

Promote C only when

\[
\Delta L
=
L_{\rm raw}
-
\left[L(C)+\sum_i L(\text{binding}_i,\text{wrapper}_i\mid C)\right]
>0.
\]

After promotion, C is frozen. On unseen targets compare prospective predictive
uncertainty and description length against a solver that must learn relations
from scratch.

A compositional target may reuse C multiple times:

\[
Q=\alpha C(X_i,X_j)+\beta C(X_k,X_\ell)+b.
\]

Negative controls are mandatory: a library that forces its familiar concept
onto unrelated worlds has failed abstraction.

The no-library solver in v17 is deliberately strong enough to fit any finite
training set using an unrestricted full-state lookup table. That fallback pays
the full description-length price and generally does not generalize to unseen
states. This prevents transfer success from being an artifact of an incapable
baseline.

This experiment is directly adjacent to DreamCoder/Stitch-style program library
learning and predicate invention. DRCT does not claim reusable abstraction
learning as a new general idea.

The DRCT-specific research program tested here is:

\[
\text{predictive closure residual}
\to
\text{independent world-specific relations}
\to
\text{quotient recurring structure}
\to
\text{MDL promotion}
\to
\text{freeze}
\to
\text{prospective transfer}
\to
\text{negative-control rejection}.
\]

The remaining meta-language wall is substantial: residual concepts are still
finite relation tables, and the equivalence group used to decide when two
relations count as the same concept is supplied rather than learned.