2.1.7 Identification under a core doctrine

2.1.7 Identification under a core doctrine

ORACLE is not asked to recover a literal code for \((\mathcal C_\star ,M_\star )\). Its target is an equivalence class in \(\mathfrak H_{\mathrm{core}}\), because equivalences preserving the declared structure have the same core-categorical content. This is finer than bare categorical equivalence when the same category admits inequivalent interpretations of objecthood, agency, or social relation.

The restriction from \(\mathbf{Cat}_{\mathcal U}\) to \(\mathbf{Cat}_{\mathcal U}^{\mathrm{core}}\) can make identification easier: extensions that violate the core doctrine are no longer admissible competing hypotheses. But the gain is not free. Every positive theorem must now state which fragment of the doctrine is known, how it is exposed by presentation, and whether convergence is required for the underlying category, the interpretation, or both. These are the categorical analogues of asking which universal grammar the learner possesses and which language remains to be identified.