14.12 From orchestration sketch to workflow theory

The initial meta-sketch is an empirical scaffold. Repeated experiments may support stronger mathematics. Stable sequential and parallel laws would motivate a symmetric monoidal or PROP-like presentation. Multi-input creative operations with substitution may suggest an operadic account. Stateful processes and explicit interfaces may favor double categories or structured cospans. None should be selected for elegance alone.

The transformational endpoint is a system that can propose a conservative package comparison

with \(J_{COR}:\mathbb S_{COR}\to \mathbb S_{COR}^{+}\) when the presentation changes, transport old component histories, state what the new connection permits, and design an independent test. That is creativity applied recursively to the organization of creativity itself.

. A meta-controller that selects among three fixed API calls demonstrates routing, not transformational creativity. Meta-creativity requires a declared workflow reference space, an extension absent from that space, a localized reason for proposing it, and independent evidence that the extension composes without corrupting previously admitted structure.

Part III stress-tests the shared compositional discipline in five non-equivalent evidence regimes: exact mathematical certificates, model-relative simulators, heterogeneous scientific corpora, structural observers of visual assurance, and open-ended admission of reusable artistic operations. The last two share a visual medium but license different claims. Their order reflects decreasing direct executability, not a ranking of epistemic value. The testbeds instantiate different subsets and orderings of the AGENTIC workflow; they do not all claim a fully learned three-component integration. What unifies them is the requirement to preserve typed proposals, provenance, independent admission, and conservative abstention as evidence moves between components.

The progression is deliberate. Chapter 15 begins where admission can be exact but the worlds are controlled; Chapter 16 adds executable mechanisms and interventions; Chapter 17 removes the privileged executable world and reconstructs testable proposals from heterogeneous documents. Chapters 18 and 19 then make the distinction between repair and theory extension visible: the first enforces a declared visual language, while the second asks whether a reusable operation missing from that language can be constructed and admitted.