4 Skill Optimization for Creative Exploration

Markdown Programs and Lie Algebroid Geometry

Chapter 3 supplied probe shapes for local variation. It did not yet say how an artificial agent should represent and select the operations that move a theory through those variations. This chapter adds that operational layer. In the proposed realization, a creative workflow is written as a typed Markdown program; its executable interpretation is a skill; and a Lie algebroid describes how locally available skills act on the current theory state.

¹1. The proposal adapts LASKO—skill optimization over Lie algebroids—from artifact editing to conceptual exploration [ Mahadevan , 2026d ] . ↩

The phrase “Markdown-parameterized search space” must be read carefully. Raw token strings do not form a smooth manifold merely because they describe an experiment. Markdown supplies a human-readable control language. The geometry belongs to the semantic theory states and to the anchored bundle of skills compiled from that language.

. Markdown declares typed control artifacts. A semantic compiler turns a local skill artifact into an available section, while a distinct policy compiler turns a workflow artifact into choices among typed actions. The anchor map reveals the change that executing a selected skill can produce in the maintained theory. The scripts parameterize exploration without being identified with their differential geometry.

The first sections deliberately study one Lie algebroid \(A\to M\). This is the operational unit inherited from LASKO, not yet the full double DIAL object. In DIAL-SkillOpt the construction is applied sidewise to \(A_{\mathrm{asm}}\) and \(B_{\mathrm{acc}}\); their double repair geometry supplies the mixed interchange and core information that no single algebroid carries.