10.13 Boundary of the algorithmic claim

DIAL-X is an architectural schema whose exact realization depends on \(X\). The generic algorithm does not prove that every application admits a double involution algebroid, that its numerical residual is invariant, that a local repair integrates, or that its proposal language contains the required creative repair. Nor does tensor symmetry make the two realized orders equal: the interchange law is a declaration whose satisfaction must be observed. Those are application-level obligations.

This boundary is also the answer to the chapter’s motivating question. The creative contribution is not the residual and not the word accommodation. It is the construction and admission of an artifact or theory that was unavailable in the declared reference space. DIAL contributes a disciplined trigger, a typed site of revision, and an audit trail for that event. The proposal engine may be symbolic search, a frontier model, a simulator-guided scientist, or a human collaborator; its creative reach must be tested rather than assumed.

Nor does DIAL-X manufacture observability. If no probe distinguishes two declarations, the correct output is an intervention request or abstention. Finally, a successful repair in one coordinate presentation does not establish intrinsic transport. The DIAL-GIRL state experiments make this caveat concrete: raw parameter addition can be an informative control while still failing to define a presentation-independent learner-state geometry.

The remaining chapters of Part II now have a precise role. CLIC, OPTIC, and RELIC instantiate target cards and domain-specific side operations; AGENTIC then tests whether their certified outputs can be composed without collapsing their evidence types. Part III carries those constructions into controlled testbeds. None tests DIAL in the abstract: each must distinguish local diagnosis from finite realization and compare the resulting package changes, including theory extensions when present, with registered ablations.