6.8 Local novelty, integrability, and persistence

The differential account adds a distinction that is often absent from creativity benchmarks. A proposal may be locally novel and locally beneficial without defining a realizable creative process. An infinitesimal direction can fail to extend to a finite trajectory; an apparently repaired interaction can accumulate path dependence; a new symbolic rule can work on the chart that suggested it and fail under transport to the next context.

We therefore distinguish three evaluative questions:

Local possibility

Does the proposal reduce a typed obstruction or open a previously unavailable direction?

Integrability

Can successive local changes be composed into a finite, coherent path under the declared dynamics?

Persistence

Does the resulting object or theory retain its value on an untouched cover, recurrence, intervention, proof obligation, or later task?

Classical Lie integration gives this distinction its sharpest mathematical form, but computational applications may use registered empirical observers. Examples include multi-step rollout stability, approximate holonomy, cycle-consistency, continuation under context shift, or reuse after a regime returns. These are not interchangeable tests. Each application must explain why its observer is evidence for finite realization.

This criterion also clarifies what the literature’s artifact/process distinction leaves open. A process can generate an attractive artifact while being structurally unstable, and a stable process can produce an artifact that lacks novelty or value. Integrability is consequently neither a complete definition of creativity nor another name for quality. It is the bridge from a local creative opportunity to a sustained construction.

. Do not credit an infinitesimal creative proposal as a realized transition until it survives a finite composition or persistence test. Report local novelty, integrability evidence, and independent value as separate endpoints.