ora-0185
16.5 Usefulness by future factorization
A structure is persistent only relative to uses. A learned product is useful when later compatibility problems factor through it; a learned quotient is useful when later observers respect it; a repair pattern is useful when it turns a new obstruction into an admitted filler. This suggests measuring knowledge by a doctrine of future diagrams rather than by the number of parameters retained.
Let \(K\) be a structural knowledge package and \(\mathcal D\) a family of future diagrammatic problems. Its utility profile is the subfamily
A transport of \(K\) is utility preserving on \(\mathcal D\) when it induces an equivalence of these factorization spaces, not merely equality of their cardinalities.
This definition captures the Yoneda-like aspiration of ORACLE: knowledge is characterized by the family of compositional questions it can answer and the witnesses it supplies. A construction with a large utility profile can earn its keep across modalities even when its concrete realization changes.
For the collider learner, a symmetry principle, conservation law, or reusable amplitude factorization has persistent value when it continues to organize predictions across detectors, energies, and reaction channels. Its utility profile is the family of probe diagrams whose responses factor through that structure with certified comparisons. An isolated fitted constant may be useful, but it occupies a lower rung than a generative relation that supports many such factorizations.