2.5 Four evaluation media, five admission regimes

The creativity mode says what kind of change occurred. A testbed says where the claim can be evaluated. We use four testbed media whose admission mechanisms are deliberately different. The visual medium supports two regimes because assurance relative to a declared scene and invention of a reusable artistic operation warrant different claims.

Mathematical theory construction.

Formal systems offer proof, countermodel, and conservative-extension tests. Historical reconstructions provide recognizable controls, while generated miniature worlds reduce contamination by memorized mathematical prose.

Simulator-grounded theory extension.

An executable simulator supplies interventions and consequences that are not available from text alone. The Prometheus packages—including singing mice, the Indus Valley collapse, and microparticle pollution—offer initial scientific environments in which proposed abstractions can be tested under held-out regimes.

Scientific documents to testable theories.

A closed, source-bearing corpus is converted into local models, disagreements, candidate mechanisms, and an extensible algebraic theory. This stage can admit provenance and corpus-relative derivations, but causal admission requires a simulator, laboratory, clinical study, or independent structured evidence. The GLP-1 challenge is an initial demanding case: the aim is not a fluent review, but a theory that organizes mechanisms and supports discriminating predictions.

Generative visual-language construction.

A text-to-image system supplies a continuous generative process whose outputs are immediately inspectable, while its conditioning vocabulary exposes a representational boundary. ARTISTIC first asks whether a supplied or estimated scene declaration can diagnose and repair violations while preserving unaffected content. DILATE asks the stronger question: whether persistent failure warrants a reusable visual operation unavailable in the frozen language, and whether that operation survives transport and independent admission. A successful repair is therefore infrastructure for artistic theory extension, not evidence of that extension by itself.

This matrix is the organizing canvas of the book. It prevents two common collapses: identifying creativity with unconstrained generation, and identifying a creativity mode with a particular domain. Each experiment is tagged by a pair such as Mathematics–E, Simulation–T, or Visual–T.