ifc-0065

4.6 Two coupled optimization problems

The framework separates two levels that are easily conflated.

Object-level exploration.

For a fixed script language, compiler, and Lie algebroid, the agent selects and composes sections to move through \(M\). Continuous coefficients, when the skill fiber supports them, can be optimized by geometric or natural-gradient methods. Discrete skill choices can be screened by rollouts and bracket proxies.

Meta-level skill optimization.

The system revises the Markdown program

\[ m\longrightarrow m^+ \]

using observed failures, traces, and evaluation outcomes. Within a benchmark version, validation outcomes drive edits; released admission outcomes may become training evidence only in a new, explicitly versioned cycle. This is a controlled program transformation, not an infinitesimal vector in raw token space unless an additional continuous relaxation and its semantics have been declared. A revision can change the selected section, its domain of availability, or the permissions under which it acts.

The creative optimization landscape is consequently not a scalar function over prompts. It is the structured package

\[ \mathfrak L_{\mathrm{cre}} =\bigl(M,A,\rho ,[\cdot ,\cdot ]_A, \mathsf{Md}_{\mathrm{adm}},\operatorname {compile}^{\mathrm{sec}}_E, \Lambda ,\mathcal R,\mathcal A\bigr), \]

where \(\Lambda \) contains observers, \(\mathcal R\) records typed residuals, and \(\mathcal A\) is the family of admission procedures. Scalar scores may rank candidates inside this package, but they do not define its types, legal moves, or certificates.