8.8 Exploration across the testbeds

Mathematical theory construction.

Search traverses expressions, diagrams, lemmas, models, and countermodels. Legality is comparatively strong because proof or computation can often be checked. Interestingness and choice of definitions remain open-ended.

Simulator-grounded discovery.

Search includes both hypothesis selection and experiment selection. The simulator supplies controlled interventions, but conclusions remain relative to its mechanisms and numerical regime. An exploit of the simulator is not a scientific discovery about the target world.

Scientific corpus to theory.

Search traverses claims, entities, mechanisms, and sources. The space is only partly observed, provenance is heterogeneous, and absence of a statement is not evidence of impossibility. Exploration must therefore preserve uncertainty and source boundaries.

Generative visual languages.

Search traverses prompts, seeds, layouts, scene-preserving edits, and rendering controls already available in the declared visual language. A visually unusual image may be a valuable reachable consequence without changing that language. When no registered path can satisfy a persistent semantic obligation, the trace should localize the failure and hand it to transformation rather than quietly adding a token or control.

Experiment: Active exploratory creativity. Epistemic status: proposed benchmark design, not a completed result.
Input: a versioned theory, an initial state, a finite probe budget, and hidden targets or held-out consequences.
Policy: choose sequential probes using uncertainty, proposal discrimination, novelty, and cost.
Output: a reachable construction, its path, probe history, observer scores, and any localized obstruction.
Admission: validity, registered novelty and value, held-out consequence, transfer, and calibrated abstention.
Search comparison: sample and compute efficiency against random and passive policies, reported separately from creative admission.
Transformational control: include instances whose target is not expressible in the supplied language; a sound explorer should diagnose or abstain rather than fabricate an in-language answer.