ifc-0066

4.7.1 Typed state and actions

At decision time, let the discovery state be

\[ z_t= \bigl(\mathfrak R_t,x_t,H_t,b_t\bigr), \]

where \(\mathfrak R_t\) is the versioned representational package containing the current sketch, DIAL geometry, observers, and compilers; \(x_t\) is its current semantic state; \(H_t\) is the provenance-bearing history; and \(b_t\) is the remaining experiment and computation budget. Compiling a discovery-controller document in environment \(E\) uses the policy interface

\[ \operatorname {compile}^{\mathrm{pol}}_E: \operatorname {Ob}(\mathsf{Md}_{\mathrm{pol}}) \rightharpoonup \Pi _{\mathrm{adm}} \]

and yields a partial policy

\[ \pi _m(\, cdot\mid z_t) =\operatorname {compile}^{\mathrm{pol}}_E(m)(z_t) \]

over the typed action family

\[ \begin{aligned} \mathcal U(z_t)=\{ & \operatorname {Assimilate}(s), \operatorname {Probe}(r), \operatorname {Compare}(s,r),\\ & \operatorname {Propose}(\Upsilon ;J,\bar J,\phi _A,\chi ), \operatorname {RequestEvidence}(e), \operatorname {Abstain}\} . \end{aligned} \]

Here \(s\) and \(r\) are locally available sections of the assimilatory and proto-accommodative side bundles. The proposal action first declares the package comparison \(\Upsilon \). When the presentation changes, it also contains a finite sketch map \(J:\mathbb S\to \mathbb S^+\), its semantic transport \(\bar J\), skill transport \(\phi _A\), and differential comparison data \(\chi \); otherwise those fields are omitted or replaced by the transport data appropriate to the changed package components. Ill-typed or unauthorized actions are absent rather than merely assigned a large penalty.

Within a fixed theory fiber, the anchors realize the selected sections as vector fields. A curve object integrates them, when possible, to partial flows \(\Phi _{\mathrm{asm}}\) and \(\Phi _{\mathrm{acc}}\). For a small probe scale \(\epsilon \) and observer \(O\), an empirical mixed witness is

\[ \widehat\Delta _{\epsilon }(s,r;x) =O\! \left(\Phi _{\mathrm{acc}}^{\epsilon } \Phi _{\mathrm{asm}}^{\epsilon }(x)\right) -O\! \left(\Phi _{\mathrm{asm}}^{\epsilon } \Phi _{\mathrm{acc}}^{\epsilon }(x)\right). \]

The normalized small-loop behavior estimates an observer-relative bracket or interchange effect. DIAL-SkillOpt learns when such a comparison is worth its cost and how to respond to a persistent, uncertainty-qualified defect. It is not trained to regard every nonzero finite-sample loop as accommodation.