ifc-0037

2.6 From LINCS repair to creative transformation

LINCS begins with declared compositional obligations, probes their failures, localizes an obstruction, proposes a typed repair, and independently admits or rejects the proposal. Infinitesimal creativity inherits that discipline but widens the repair language.

For fixed-theory learning, the repair acts inside \(\mathbb S\):

\[ D\rightsquigarrow D'. \]

For transformational creativity, a persistent obstruction can instead motivate a declaration intervention:

\[ \begin{aligned} \mathbb S& \xrightarrow {\text{diagnose}} (\omega ,\gamma ) \xrightarrow {\text{propose}} \mathbb S^{+},\\ \mathbb S^{+} & \xrightarrow {\text{transport and test}} \{ \text{admit},\text{revise},\text{reject},\text{abstain}\} . \end{aligned} \]

The obstruction may include the internal interchange defect \(\Theta _{\mathrm{int}}\), or its classical cochain observer \(\Omega _{\mathrm{cre}}\), but it does not logically determine the extension. Many incompatible theories can repair the same failure. Frontier models are therefore useful as proposal engines: they can generate analogies, mechanisms, new types, and candidate laws. They do not thereby become their own judges.

. Non-compositionality is a source of diagnostic evidence, not a complete theory of creativity. It can identify where an inherited structure fails without uniquely specifying the concept that should replace or extend it.