19.17 Open mathematical obligations

Several bridge results remain open. First, the quotient obstruction must be defined invariantly when anchor images change rank. Second, the internal Weil profile must be connected rigorously to the mixed core or interchange data of a double involution algebroid. Third, one needs conditions under which a persistent quotient class admits a finite sketch generator rather than only a local analytic direction. Fourth, Kan transport must be shown to remain inside the doctrine-preserving category of visual models. Finally, equivalent presentations of a recovered technique require a suitable Morita-style or model-category notion of sameness.

These obligations are not technical decoration. They separate three claims that an empirical system might otherwise conflate:

The DILATE program succeeds only when it can travel across all three while recording the evidence for each transition.

The final chapter gathers the lessons of these testbeds without treating DIAL as a universal theory of creativity. It separates what the present constructions demonstrate from what remains conjectural, and asks which parts of the framework could transfer to creative domains not studied experimentally here.