20.8 Open obligations

The theoretical construction remains incomplete. A rigorous development must clarify the relationship between classical double Lie algebroids and involution algebroids internal to tangent categories; define quotient obstructions when ranks and presentations vary; establish conditions under which local residuals integrate into finite sketch extensions; and specify when Kan transport is conservative in the chosen doctrine. Equivalent theory presentations require a principled notion of sameness, perhaps Morita-like, so that rediscovering a generator under a new name is not scored as a new theory.

The algorithmic agenda is equally substantial. Systems must acquire sketches and observers rather than receive all of them by hand; estimate uncertainty and abstain under ambiguity; search variable-size proposal languages without rewarding gratuitous complexity; preserve provenance across composed workflows; and separate the cost of diagnosis from the cost of acting in the world. Human and multi-agent settings require explicit protocols for teaching, criticism, disagreement, attribution, and governance.

Finally, benchmarks must test capabilities that existing generative models do not solve by surface fluency. Withheld-generator worlds remain valuable calibrations because their ground truth is known. Domain-grounded simulators, independently annotated images, executable proofs, and prospective scientific experiments supply distinct admission environments with different authorities and blind spots. The long-term test is not whether DIAL can attach a new name to a latent direction, but whether the resulting theory changes what a community can reliably explain, construct, or discover.